5U-R-RL

Derivation of differential equations and kinetic matrices describing evolution of spin concentrations

 

 

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NOTE: This document is based on IDAP/Mathematical_models/Equilibrium_thermodynamic_models/U-multi-path-models/nU/5U-R-RL

 

NOTE 2: The model with one isomerization, 1U-R-RL, is not identical to U-R-RL because the latter contains a transition connecting R* and RL* directly, which is absent from nU-R-RL family models! It, however , is identical to U-1R-RL from U-nR-RL family (with different order of the species).

 

Strategy:

I will develop kinetic matrices for  five cases to have from one to five isomers of R. I will explicitly use all rate constants of similar transitions to be able to simplify in the next steps by setting them to one value. The thermodynamic model includes 5-isomers and was designed to be reducible by appropriate settings of the equilibrium constants.

 

Order of species to allow for easy expansion of matrices:

R*, RL*, R', RL',  R'', RL'',  R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

 

Accurate extraction of K matrix:

Workflow for accurate extraction of the K matrix

- prepare empty matrix

- copy-paste one equation at a time to MATLAB script

- in MATLAB: arrange terms with increasing coefficients, place commas after  groups with the same coefficient , insert zeros for the absent coefficients

- cut-and-paste entire line into the MuPad.

- execute cell after every equation to see how matrix is filled

- delete coefficients (keep negative signs!!!)

- check rules along the column and the row

 

 

 

 

Contents

 

Definitions of transitions and strategy

 

 

Reaction, partial conversion, and net rates

 

 

Expression in terms of spin (monomer) concentrations

 

 

 

Control derivation of 1U-R-RL mechanism with conventional order of species

 

 

 

Expession of K matrix for 1U-R-RL mechanism with current order of species

 

  K matrix for 1U-R-RL model with new species order

 

 

Expession of K matrix for 2U-R-RL mechanism

   K matrix for 2U-R-RL

 

 

 

 

Expession of K matrix for 3U-R-RL mechanism

   K matrix for 3U-R-RL

 

 

 

Expession of K matrix for 4U-R-RL mechanism

   K matrix for 4U-R-RL

 

 

 

Expession of K matrix for 5U-R-RL mechanism

   K matrix for 5U-R-RL

 

 

 

Conclusions

 

 

 

 

Back to Contents

 

clean up workspace

reset()

 

 

 

 


  Definition of transitions and strategy

 

 

Write properly balanced reactions equations for all transitions in the mechanism:

 

Binding reaction, transitions A:   

R'+L<=>RL'

Constants: k_1_A_p_1 (forward), k_2_A_p_1 (reverse).     

 

R''+L<=>RL''

Constants: k_1_A_p_2 (forward), k_2_A_p_2 (reverse).

 

R'''+L<=>RL'''

Constants: k_1_A_p_3 (forward), k_2_A_p_3 (reverse).

 

R''''+L<=>RL''''

Constants: k_1_A_p_4 (forward), k_2_A_p_4 (reverse).

 

R'''''+L<=>RL'''''

Constants: k_1_A_p_5 (forward), k_2_A_p_5 (reverse).

 

 

 

 

Isomerization of R' to R* species: transitions B1

 

R* <=> R'

Constants: k_1_B_1_p_1 (forward), k_2_B_1_p_1 (reverse).    

 

R* <=> R''

Constants: k_1_B_1_p_2 (forward), k_2_B_1_p_2 (reverse).

 

R* <=> R'''

Constants: k_1_B_1_p_3 (forward), k_2_B_1_p_3 (reverse).

 

R* <=> R''''

Constants: k_1_B_1_p_4 (forward), k_2_B_1_p_4 (reverse).

 

R* <=> R'''''

Constants: k_1_B_1_p_5 (forward), k_2_B_1_p_5 (reverse).

 

 

 

 

Isomerization of RL-primed to RL* species: transition B2

 

RL' <=> R*L

Constants: k_1_B_2_p_1 (forward), k_2_B_2_p_1 (reverse).

 

RL'' <=> R*L

Constants: k_1_B_2_p_2 (forward), k_2_B_2_p_2 (reverse).

 

RL'''<=> R*L

Constants: k_1_B_2_p_3 (forward), k_2_B_2_p_3 (reverse).

 

RL'''' <=> R*L

Constants: k_1_B_2_p_4 (forward), k_2_B_2_p_4 (reverse).

 

RL''''' <=> R*L

Constants: k_1_B_2_p_5 (forward), k_2_B_2_p_5 (reverse).

 

 

 

 

Interconversion of R-primed isomers: transitions C1

 

-- R' --

R' <=> R''

Constants: k_1_C_1_p_1_2 (forward), k_2_C_1_p_1_2 (reverse).   

 

R' <=> R'''

Constants: k_1_C_1_p_1_3 (forward), k_2_C_1_p_1_3 (reverse).    

 

R' <=> R''''

Constants: k_1_C_1_p_1_4 (forward), k_2_C_1_p_1_4 (reverse).  

 

R' <=> R'''''

Constants: k_1_C_1_p_1_5 (forward), k_2_C_1_p_1_5 (reverse).

 

 

-- R'' --

R'' <=> R'''

Constants: k_1_C_1_p_2_3 (forward), k_2_C_1_p_2_3 (reverse).

 

R'' <=> R''''

Constants: k_1_C_1_p_2_4 (forward), k_2_C_1_p_2_4 (reverse).

 

R'' <=> R'''''

Constants: k_1_C_1_p_2_5 (forward), k_2_C_1_p_2_5 (reverse).

 

 

 

-- R''' --

R''' <=> R''''

Constants: k_1_C_1_p_3_4 (forward), k_2_C_1_p_3_4 (reverse).

 

R''' <=> R'''''

Constants: k_1_C_1_p_3_5 (forward), k_2_C_1_p_3_5 (reverse).

 

-- R'''' --

R'''' <=> R'''''

Constants: k_1_C_1_p_4_5 (forward), k_2_C_1_p_4_5 (reverse).

 

 

 

 

Interconversion of RL-primed isomers: transitions C2

 

-- RL' --

RL' <=> RL''

Constants: k_1_C_2_p_1_2 (forward), k_2_C_2_p_1_2 (reverse).

 

RL' <=> RL'''

Constants: k_1_C_2_p_1_3 (forward), k_2_C_2_p_1_3 (reverse).

 

RL' <=> RL''''

Constants: k_1_C_2_p_1_4 (forward), k_2_C_2_p_1_4 (reverse).

 

RL' <=> RL'''''

Constants: k_1_C_2_p_1_5 (forward), k_2_C_2_p_1_5 (reverse).

 

 

-- RL'' --

RL'' <=> RL'''

Constants: k_1_C_2_p_2_3 (forward), k_2_C_2_p_2_3 (reverse).

 

RL'' <=> RL''''

Constants: k_1_C_2_p_2_4 (forward), k_2_C_2_p_2_4 (reverse).

 

RL'' <=> RL'''''

Constants: k_1_C_2_p_2_5 (forward), k_2_C_2_p_2_5 (reverse).

 

 

 

-- RL''' --

RL''' <=> RL''''

Constants: k_1_C_2_p_3_4 (forward), k_2_C_2_p_3_4 (reverse).

 

RL''' <=> RL'''''

Constants: k_1_C_2_p_3_5 (forward), k_2_C_2_p_3_5 (reverse).

 

-- RL'''' --

RL'''' <=> RL'''''

Constants: k_1_C_2_p_4_5 (forward), k_2_C_2_p_4_5 (reverse).

 

 

 

 

 

Back to Contents

 

 

 

 

 

 

Reaction, partial conversion, and net rates

 

WORKING NOTE: Species completed and not completed yet: R*, RL*, R', RL', R'', RL'', R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

Contents

 

R' derivation

                    -   Summary equations for R'

 

 

R'' derivation

- Summary equations for R''

 

 

R''' derivation

- Summary equations for R'''

 

 

R'''' derivation

- Summary equations for R''''

 

 

R''''' derivation

- Summary equations for R'''''

 

 

RL' derivation

- Summary equations for RL'

 

 

RL'' derivation

- Summary of equations for RL''

 

 

RL''' derivation

- Summary of equations for RL'''

 

 

RL'''' derivation

- Summary of equations for RL''''

 

 

RL''''' derivation

- Summary of equations for RL'''''

 

 

R* derivation

- Summary of equations for R*

 

 

RL* derivation

- Summary of equations for RL*

 

 

 

 

Write reaction rates

Here, we distinguish reaction rate (elementary reaction acts per unit time; denote as "Rate_reaction-label") and conversion rates (number of moles of specific species consumed/produced per unit time, dc/dt). Conversion rates, dc/dt, for species are related to reaction rates, Rate, through molecularity coefficients.

 

We also distinguish here partial conversion rates from net (overall) conversion rates. The net conversion rate is the actual rate of change in measured concentration of the species due to all transitions this species is involved with (denote at Rate_reaction-label_N). Partial conversion rate is the conversion rate of the species along a specific branch of the reaction mechanism (denote 'dC-component-dt-reaction-label'). Summation of the partial conversion rates of the species gives the net conversion rate.

 

NOTE: In this mechanism, all transition involve only one molecules of species of each kind, therefore all  partial conversion rates are equal to reaction rates. This is reflected by setting 'molecularity' to 1 for all transitions. The molecularity sign also indicates whether the species is created or destroyed in this transition.

 

Strategy:

We need equations for the net conversion rates for each species. For this purpose, we write partial conversion rates originating from every individual (forward or reverse) process. To obtain the partial conversion rate for a process, we use the reaction rate equation times molecularity of the process in terms of this particular species.

 

In the following subsections, I am developing equations to account for net rate of change of every particular species.

Strategy

1. Each species is analyzed in a separate "Equations group".

2. Inside the group, I analyze transitions involving this species one-by-one in individual "subgroups"

3. In each subgroup, equations have uniform numbering system. Yet, beware of cut-and-paste errors!

4. Inside each subgroup, first three equations are to account for FORWARD process. The second three are for REVERSE. It is

   reliable to write the first three from scratch and then copy-paste with necessary modifications to make last three.

5. When I finish the subgroup (it means I worked through a specific transition), I mark it as "done" in the list of transitions

   in Definitions of transitions and strategy

 

 

 

Species: R'

Equations group: Rp1 

 

 

R'+L<=>RL'

Constants: k_1_A_p_1 (forward), k_2_A_p_1 (reverse).

 

Equations subgroup: Ap1

 

a forward reaction rate

eq_Rp1_Ap1_1a:= Rate_1_A_p_1 = k_1_A_p_1*R_p_1*L

Rate_1_A_p_1 = L*R_p_1*k_1_A_p_1

a partial conversion rate of R' in this transition

molecularity:=-1:
eq_Rp1_Ap1_1b:= dcRp1dt_1_A_p_1 = molecularity*Rate_1_A_p_1

dcRp1dt_1_A_p_1 = -Rate_1_A_p_1

The final form

eq_Rp1_Ap1_1c:= eq_Rp1_Ap1_1b | eq_Rp1_Ap1_1a

dcRp1dt_1_A_p_1 = -L*R_p_1*k_1_A_p_1

 

a reverse reaction rate for the transition

eq_Rp1_Ap1_2a:= Rate_2_A_p_1 = k_2_A_p_1*RL_p_1

Rate_2_A_p_1 = RL_p_1*k_2_A_p_1

a partial conversion rate of R in this transition

molecularity:=1:
eq_Rp1_Ap1_2b:= dcRp1dt_2_A_p_1 = molecularity*Rate_2_A_p_1

dcRp1dt_2_A_p_1 = Rate_2_A_p_1

The final form

eq_Rp1_Ap1_2c:= eq_Rp1_Ap1_2b | eq_Rp1_Ap1_2a

dcRp1dt_2_A_p_1 = RL_p_1*k_2_A_p_1

 

 

 

 

 

R* <=> R'

Constants: k_1_B_1_p_1 (forward), k_2_B_1_p_1 (reverse).

 

Equations subgroup: B1p1

 

a forward reaction rate  for the transition

eq_Rp1_B1p1_1a:= Rate_1_B_1_p_1 = k_1_B_1_p_1*R_s

Rate_1_B_1_p_1 = R_s*k_1_B_1_p_1

a partial conversion rate of R' in this transition

molecularity:=1:
eq_Rp1_B1p1_1b:= dcRp1dt_1_B_1_p_1 = molecularity*Rate_1_B_1_p_1

dcRp1dt_1_B_1_p_1 = Rate_1_B_1_p_1

The final form

eq_Rp1_B1p1_1c:= eq_Rp1_B1p1_1b | eq_Rp1_B1p1_1a

dcRp1dt_1_B_1_p_1 = R_s*k_1_B_1_p_1

 

 

a reverse reaction rate for the transition

eq_Rp1_B1p1_2a:= Rate_2_B_1_p_1 = k_2_B_1_p_1*R_p_1

Rate_2_B_1_p_1 = R_p_1*k_2_B_1_p_1

a partial conversion rate of R' in this transition

molecularity:=-1:
eq_Rp1_B1p1_2b:= dcRp1dt_2_B_1_p_1 = molecularity*Rate_2_B_1_p_1

dcRp1dt_2_B_1_p_1 = -Rate_2_B_1_p_1

The final form

eq_Rp1_B1p1_2c:= eq_Rp1_B1p1_2b | eq_Rp1_B1p1_2a

dcRp1dt_2_B_1_p_1 = -R_p_1*k_2_B_1_p_1

 

 

 

 

R' <=> R''

Constants: k_1_C_1_p_1_2 (forward), k_2_C_1_p_1_2 (reverse).

 

Equations subgroup: C1p12

 

a forward reaction rate  for the transition

eq_Rp1_C1p12_1a:= Rate_1_C_1_p_1_2 =  k_1_C_1_p_1_2*R_p_1

Rate_1_C_1_p_1_2 = R_p_1*k_1_C_1_p_1_2

a partial conversion rate of R' in this transition

molecularity:=-1:
eq_Rp1_C1p12_1b:= dcRp1dt_1_C_1_p_1_2 = molecularity*Rate_1_C_1_p_1_2

dcRp1dt_1_C_1_p_1_2 = -Rate_1_C_1_p_1_2

The final form

eq_Rp1_C1p12_1c:= eq_Rp1_C1p12_1b | eq_Rp1_C1p12_1a

dcRp1dt_1_C_1_p_1_2 = -R_p_1*k_1_C_1_p_1_2

 

a reverse reaction rate for the transition

eq_Rp1_C1p12_2a:= Rate_2_C_1_p_1_2 =  k_2_C_1_p_1_2*R_p_2

Rate_2_C_1_p_1_2 = R_p_2*k_2_C_1_p_1_2

a partial conversion rate of R' in this transition

molecularity:=1:
eq_Rp1_C1p12_2b:= dcRp1dt_2_C_1_p_1_2 = molecularity*Rate_2_C_1_p_1_2

dcRp1dt_2_C_1_p_1_2 = Rate_2_C_1_p_1_2

The final form

eq_Rp1_C1p12_2c:= eq_Rp1_C1p12_2b | eq_Rp1_C1p12_2a

dcRp1dt_2_C_1_p_1_2 = R_p_2*k_2_C_1_p_1_2

 

 


 

R' <=> R'''

Constants: k_1_C_1_p_1_3 (forward), k_2_C_1_p_1_3 (reverse).

 

Equations subgroup: C1p13

 

a forward reaction rate  for the transition

eq_Rp1_C1p13_1a:= Rate_1_C_1_p_1_3 =  k_1_C_1_p_1_3*R_p_1

Rate_1_C_1_p_1_3 = R_p_1*k_1_C_1_p_1_3

a partial conversion rate of R' in this transition

molecularity:=-1:
eq_Rp1_C1p13_1b:= dcRp1dt_1_C_1_p_1_3 = molecularity*Rate_1_C_1_p_1_3

dcRp1dt_1_C_1_p_1_3 = -Rate_1_C_1_p_1_3

The final form

eq_Rp1_C1p13_1c:= eq_Rp1_C1p13_1b | eq_Rp1_C1p13_1a

dcRp1dt_1_C_1_p_1_3 = -R_p_1*k_1_C_1_p_1_3

 

a reverse reaction rate for the transition

eq_Rp1_C1p13_2a:= Rate_2_C_1_p_1_3 =  k_2_C_1_p_1_3*R_p_3

Rate_2_C_1_p_1_3 = R_p_3*k_2_C_1_p_1_3

a partial conversion rate of R' in this transition

molecularity:=1:
eq_Rp1_C1p13_2b:= dcRp1dt_2_C_1_p_1_3 = molecularity*Rate_2_C_1_p_1_3

dcRp1dt_2_C_1_p_1_3 = Rate_2_C_1_p_1_3

The final form

eq_Rp1_C1p13_2c:= eq_Rp1_C1p13_2b | eq_Rp1_C1p13_2a

dcRp1dt_2_C_1_p_1_3 = R_p_3*k_2_C_1_p_1_3

 

 

 

R' <=> R''''

Constants: k_1_C_1_p_1_4 (forward), k_2_C_1_p_1_4 (reverse).

 

Equations subgroup: C1p14

 

a forward reaction rate  for the transition

eq_Rp1_C1p14_1a:= Rate_1_C_1_p_1_4 =  k_1_C_1_p_1_4*R_p_1

Rate_1_C_1_p_1_4 = R_p_1*k_1_C_1_p_1_4

a partial conversion rate of R' in this transition

molecularity:=-1:
eq_Rp1_C1p14_1b:= dcRp1dt_1_C_1_p_1_4 = molecularity*Rate_1_C_1_p_1_4

dcRp1dt_1_C_1_p_1_4 = -Rate_1_C_1_p_1_4

The final form

eq_Rp1_C1p14_1c:= eq_Rp1_C1p14_1b | eq_Rp1_C1p14_1a

dcRp1dt_1_C_1_p_1_4 = -R_p_1*k_1_C_1_p_1_4

 

a reverse reaction rate for the transition

eq_Rp1_C1p14_2a:= Rate_2_C_1_p_1_4 =  k_2_C_1_p_1_4*R_p_4

Rate_2_C_1_p_1_4 = R_p_4*k_2_C_1_p_1_4

a partial conversion rate of R' in this transition

molecularity:=1:
eq_Rp1_C1p14_2b:= dcRp1dt_2_C_1_p_1_4 = molecularity*Rate_2_C_1_p_1_4

dcRp1dt_2_C_1_p_1_4 = Rate_2_C_1_p_1_4

The final form

eq_Rp1_C1p14_2c:= eq_Rp1_C1p14_2b | eq_Rp1_C1p14_2a

dcRp1dt_2_C_1_p_1_4 = R_p_4*k_2_C_1_p_1_4

 

 

 

 

R' <=> R'''''

Constants: k_1_C_1_p_1_5 (forward), k_2_C_1_p_1_5 (reverse).

 

Equations subgroup: C1p15

 

a forward reaction rate  for the transition

eq_Rp1_C1p15_1a:= Rate_1_C_1_p_1_5 =  k_1_C_1_p_1_5*R_p_1

Rate_1_C_1_p_1_5 = R_p_1*k_1_C_1_p_1_5

a partial conversion rate of R' in this transition

molecularity:=-1:
eq_Rp1_C1p15_1b:= dcRp1dt_1_C_1_p_1_5 = molecularity*Rate_1_C_1_p_1_5

dcRp1dt_1_C_1_p_1_5 = -Rate_1_C_1_p_1_5

The final form

eq_Rp1_C1p15_1c:= eq_Rp1_C1p15_1b | eq_Rp1_C1p15_1a

dcRp1dt_1_C_1_p_1_5 = -R_p_1*k_1_C_1_p_1_5

 

 

a reverse reaction rate for the transition

eq_Rp1_C1p15_2a:= Rate_2_C_1_p_1_5 =  k_2_C_1_p_1_5*R_p_5

Rate_2_C_1_p_1_5 = R_p_5*k_2_C_1_p_1_5

a partial conversion rate of R' in this transition

molecularity:=1:
eq_Rp1_C1p15_2b:= dcRp1dt_2_C_1_p_1_5 = molecularity*Rate_2_C_1_p_1_5

dcRp1dt_2_C_1_p_1_5 = Rate_2_C_1_p_1_5

The final form

eq_Rp1_C1p15_2c:= eq_Rp1_C1p15_2b | eq_Rp1_C1p15_2a

dcRp1dt_2_C_1_p_1_5 = R_p_5*k_2_C_1_p_1_5

 

 

 

Summary of partial conversion rates for the species

eq_Rp1_Ap1_1c;eq_Rp1_Ap1_2c;

dcRp1dt_1_A_p_1 = -L*R_p_1*k_1_A_p_1
dcRp1dt_2_A_p_1 = RL_p_1*k_2_A_p_1

eq_Rp1_B1p1_1c;eq_Rp1_B1p1_2c

dcRp1dt_1_B_1_p_1 = R_s*k_1_B_1_p_1
dcRp1dt_2_B_1_p_1 = -R_p_1*k_2_B_1_p_1

eq_Rp1_C1p12_1c;eq_Rp1_C1p12_2c;
eq_Rp1_C1p13_1c;eq_Rp1_C1p13_2c;
eq_Rp1_C1p14_1c;eq_Rp1_C1p14_2c;
eq_Rp1_C1p15_1c;eq_Rp1_C1p15_2c;

dcRp1dt_1_C_1_p_1_2 = -R_p_1*k_1_C_1_p_1_2
dcRp1dt_2_C_1_p_1_2 = R_p_2*k_2_C_1_p_1_2
dcRp1dt_1_C_1_p_1_3 = -R_p_1*k_1_C_1_p_1_3
dcRp1dt_2_C_1_p_1_3 = R_p_3*k_2_C_1_p_1_3
dcRp1dt_1_C_1_p_1_4 = -R_p_1*k_1_C_1_p_1_4
dcRp1dt_2_C_1_p_1_4 = R_p_4*k_2_C_1_p_1_4
dcRp1dt_1_C_1_p_1_5 = -R_p_1*k_1_C_1_p_1_5
dcRp1dt_2_C_1_p_1_5 = R_p_5*k_2_C_1_p_1_5

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1

     Substitute (use all equations)

eq_Rp1_N__1U_R_RL:= % | eq_Rp1_Ap1_1c | eq_Rp1_Ap1_2c \
| eq_Rp1_B1p1_1c | eq_Rp1_B1p1_2c \
| eq_Rp1_C1p12_1c | eq_Rp1_C1p12_2c \
| eq_Rp1_C1p13_1c | eq_Rp1_C1p13_2c \
| eq_Rp1_C1p14_1c | eq_Rp1_C1p14_2c \
| eq_Rp1_C1p15_1c | eq_Rp1_C1p15_2c;

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - L*R_p_1*k_1_A_p_1


 

 

2U-R-RL

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 +\
dcRp1dt_1_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_2;

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 + dcRp1dt_1_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_2

     Substitute (use all equations)

eq_Rp1_N__2U_R_RL:= % | eq_Rp1_Ap1_1c | eq_Rp1_Ap1_2c \
| eq_Rp1_B1p1_1c | eq_Rp1_B1p1_2c \
| eq_Rp1_C1p12_1c | eq_Rp1_C1p12_2c \
| eq_Rp1_C1p13_1c | eq_Rp1_C1p13_2c \
| eq_Rp1_C1p14_1c | eq_Rp1_C1p14_2c \
| eq_Rp1_C1p15_1c | eq_Rp1_C1p15_2c;

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 + R_p_2*k_2_C_1_p_1_2 - L*R_p_1*k_1_A_p_1

 

 

3U-R-RL

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 +\
dcRp1dt_1_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_2 + \
dcRp1dt_1_C_1_p_1_3 + dcRp1dt_2_C_1_p_1_3;

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 + dcRp1dt_1_C_1_p_1_2 + dcRp1dt_1_C_1_p_1_3 + dcRp1dt_2_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_3

     Substitute (use all equations)

eq_Rp1_N__3U_R_RL:= % | eq_Rp1_Ap1_1c | eq_Rp1_Ap1_2c \
| eq_Rp1_B1p1_1c | eq_Rp1_B1p1_2c \
| eq_Rp1_C1p12_1c | eq_Rp1_C1p12_2c \
| eq_Rp1_C1p13_1c | eq_Rp1_C1p13_2c \
| eq_Rp1_C1p14_1c | eq_Rp1_C1p14_2c \
| eq_Rp1_C1p15_1c | eq_Rp1_C1p15_2c;

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 - L*R_p_1*k_1_A_p_1

 

 

4U-R-RL

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 +\
dcRp1dt_1_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_2 + \
dcRp1dt_1_C_1_p_1_3 + dcRp1dt_2_C_1_p_1_3 + \
dcRp1dt_1_C_1_p_1_4 + dcRp1dt_2_C_1_p_1_4;

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 + dcRp1dt_1_C_1_p_1_2 + dcRp1dt_1_C_1_p_1_3 + dcRp1dt_1_C_1_p_1_4 + dcRp1dt_2_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_3 + dcRp1dt_2_C_1_p_1_4

     Substitute (use all equations)

eq_Rp1_N__4U_R_RL:= % | eq_Rp1_Ap1_1c | eq_Rp1_Ap1_2c \
| eq_Rp1_B1p1_1c | eq_Rp1_B1p1_2c \
| eq_Rp1_C1p12_1c | eq_Rp1_C1p12_2c \
| eq_Rp1_C1p13_1c | eq_Rp1_C1p13_2c \
| eq_Rp1_C1p14_1c | eq_Rp1_C1p14_2c \
| eq_Rp1_C1p15_1c | eq_Rp1_C1p15_2c;

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 - L*R_p_1*k_1_A_p_1

 

 

5U-R-RL

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 +\
dcRp1dt_1_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_2 + \
dcRp1dt_1_C_1_p_1_3 + dcRp1dt_2_C_1_p_1_3 + \
dcRp1dt_1_C_1_p_1_4 + dcRp1dt_2_C_1_p_1_4 + \
dcRp1dt_1_C_1_p_1_5 + dcRp1dt_2_C_1_p_1_5;

dcRp1dt_N = dcRp1dt_1_A_p_1 + dcRp1dt_2_A_p_1 + dcRp1dt_1_B_1_p_1 + dcRp1dt_2_B_1_p_1 + dcRp1dt_1_C_1_p_1_2 + dcRp1dt_1_C_1_p_1_3 + dcRp1dt_1_C_1_p_1_4 + dcRp1dt_1_C_1_p_1_5 + dcRp1dt_2_C_1_p_1_2 + dcRp1dt_2_C_1_p_1_3 + dcRp1dt_2_C_1_p_1_4 + dcRp1dt_2_C_1_p_1_5

     Substitute (use all equations)

eq_Rp1_N__5U_R_RL:= % | eq_Rp1_Ap1_1c | eq_Rp1_Ap1_2c \
| eq_Rp1_B1p1_1c | eq_Rp1_B1p1_2c \
| eq_Rp1_C1p12_1c | eq_Rp1_C1p12_2c \
| eq_Rp1_C1p13_1c | eq_Rp1_C1p13_2c \
| eq_Rp1_C1p14_1c | eq_Rp1_C1p14_2c \
| eq_Rp1_C1p15_1c | eq_Rp1_C1p15_2c;

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 - R_p_1*k_1_C_1_p_1_5 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 + R_p_5*k_2_C_1_p_1_5 - L*R_p_1*k_1_A_p_1


 

Summary equations for R'

eq_Rp1_N__1U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - L*R_p_1*k_1_A_p_1

eq_Rp1_N__2U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 + R_p_2*k_2_C_1_p_1_2 - L*R_p_1*k_1_A_p_1

eq_Rp1_N__3U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 - L*R_p_1*k_1_A_p_1

eq_Rp1_N__4U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 - L*R_p_1*k_1_A_p_1

eq_Rp1_N__5U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 - R_p_1*k_1_C_1_p_1_5 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 + R_p_5*k_2_C_1_p_1_5 - L*R_p_1*k_1_A_p_1

 

 

 

 

Back to  Equations for each species

 

 

 

 

Species: R''

Equations group: Rp2 

 

R''+L<=>RL''

Constants: k_1_A_p_2 (forward), k_2_A_p_2 (reverse).

 

Equations subgroup: Ap2

 

a forward reaction rate

eq_Rp2_Ap2_1a:= Rate_1_A_p_2 = k_1_A_p_2*R_p_2*L

Rate_1_A_p_2 = L*R_p_2*k_1_A_p_2

a partial conversion rate of R'' in this transition

molecularity:=-1:
eq_Rp2_Ap2_1b:= dcRp2dt_1_A_p_2 = molecularity*Rate_1_A_p_2

dcRp2dt_1_A_p_2 = -Rate_1_A_p_2

The final form

eq_Rp2_Ap2_1c:= eq_Rp2_Ap2_1b | eq_Rp2_Ap2_1a

dcRp2dt_1_A_p_2 = -L*R_p_2*k_1_A_p_2

 

a reverse reaction rate for the transition

eq_Rp2_Ap2_2a:= Rate_2_A_p_2 = k_2_A_p_2*RL_p_2

Rate_2_A_p_2 = RL_p_2*k_2_A_p_2

a partial conversion rate of R'' in this transition

molecularity:=1:
eq_Rp2_Ap2_2b:= dcRp2dt_2_A_p_2 = molecularity*Rate_2_A_p_2

dcRp2dt_2_A_p_2 = Rate_2_A_p_2

The final form

eq_Rp2_Ap2_2c:= eq_Rp2_Ap2_2b | eq_Rp2_Ap2_2a

dcRp2dt_2_A_p_2 = RL_p_2*k_2_A_p_2

 

 

R* <=> R''

Constants: k_1_B_1_p_2 (forward), k_2_B_1_p_2 (reverse).

 

Equations subgroup: B1p2

 

a forward reaction rate  for the transition

eq_Rp2_B1p2_1a:= Rate_1_B_1_p_2 = k_1_B_1_p_2*R_s

Rate_1_B_1_p_2 = R_s*k_1_B_1_p_2

a partial conversion rate of R'' in this transition

molecularity:=1:
eq_Rp2_B1p2_1b:= dcRp2dt_1_B_1_p_2 = molecularity*Rate_1_B_1_p_2

dcRp2dt_1_B_1_p_2 = Rate_1_B_1_p_2

The final form

eq_Rp2_B1p2_1c:= eq_Rp2_B1p2_1b | eq_Rp2_B1p2_1a

dcRp2dt_1_B_1_p_2 = R_s*k_1_B_1_p_2

 

a reverse reaction rate for the transition

eq_Rp2_B1p2_2a:= Rate_2_B_1_p_2 = k_2_B_1_p_2*R_p_2

Rate_2_B_1_p_2 = R_p_2*k_2_B_1_p_2

a partial conversion rate of R'' in this transition

molecularity:=-1:
eq_Rp2_B1p2_2b:= dcRp2dt_2_B_1_p_2 = molecularity*Rate_2_B_1_p_2

dcRp2dt_2_B_1_p_2 = -Rate_2_B_1_p_2

The final form

eq_Rp2_B1p2_2c:= eq_Rp2_B1p2_2b | eq_Rp2_B1p2_2a

dcRp2dt_2_B_1_p_2 = -R_p_2*k_2_B_1_p_2

 

 

 

R' <=> R''

Constants: k_1_C_1_p_1_2 (forward), k_2_C_1_p_1_2 (reverse).

 

NOTE: Kinetic equations for this transitions were already defined!

 

Equations subgroup: C1p12

a forward reaction rate  for the transition

eq_Rp2_C1p12_1a:= eq_Rp1_C1p12_1a

Rate_1_C_1_p_1_2 = R_p_1*k_1_C_1_p_1_2

a partial conversion rate of R'' in this transition

molecularity:=1:
eq_Rp2_C1p12_1b:= dcRp2dt_1_C_1_p_1_2 = molecularity*Rate_1_C_1_p_1_2

dcRp2dt_1_C_1_p_1_2 = Rate_1_C_1_p_1_2

The final form

eq_Rp2_C1p12_1c:= eq_Rp2_C1p12_1b | eq_Rp2_C1p12_1a

dcRp2dt_1_C_1_p_1_2 = R_p_1*k_1_C_1_p_1_2

 

a reverse reaction rate for the transition

eq_Rp2_C1p12_2a:= eq_Rp1_C1p12_2a

Rate_2_C_1_p_1_2 = R_p_2*k_2_C_1_p_1_2

a partial conversion rate of R'' in this transition

molecularity:=-1:
eq_Rp2_C1p12_2b:= dcRp2dt_2_C_1_p_1_2 = molecularity*Rate_2_C_1_p_1_2

dcRp2dt_2_C_1_p_1_2 = -Rate_2_C_1_p_1_2

The final form

eq_Rp2_C1p12_2c:= eq_Rp2_C1p12_2b | eq_Rp2_C1p12_2a

dcRp2dt_2_C_1_p_1_2 = -R_p_2*k_2_C_1_p_1_2

 

 

R'' <=> R'''

Constants: k_1_C_1_p_2_3 (forward), k_2_C_1_p_2_3 (reverse).

 

Equations subgroup: C1p23

 

a forward reaction rate  for the transition

eq_Rp2_C1p23_1a:= Rate_1_C_1_p_2_3 =  k_1_C_1_p_2_3*R_p_2

Rate_1_C_1_p_2_3 = R_p_2*k_1_C_1_p_2_3

a partial conversion rate of R'' in this transition

molecularity:=-1:
eq_Rp2_C1p23_1b:= dcRp2dt_1_C_1_p_2_3 = molecularity*Rate_1_C_1_p_2_3

dcRp2dt_1_C_1_p_2_3 = -Rate_1_C_1_p_2_3

The final form

eq_Rp2_C1p23_1c:= eq_Rp2_C1p23_1b | eq_Rp2_C1p23_1a

dcRp2dt_1_C_1_p_2_3 = -R_p_2*k_1_C_1_p_2_3

 

a reverse reaction rate for the transition

eq_Rp2_C1p23_2a:= Rate_2_C_1_p_2_3 =  k_2_C_1_p_2_3*R_p_3

Rate_2_C_1_p_2_3 = R_p_3*k_2_C_1_p_2_3

a partial conversion rate of R'' in this transition

molecularity:=1:
eq_Rp2_C1p23_2b:= dcRp2dt_2_C_1_p_2_3 = molecularity*Rate_2_C_1_p_2_3

dcRp2dt_2_C_1_p_2_3 = Rate_2_C_1_p_2_3

The final form

eq_Rp2_C1p23_2c:= eq_Rp2_C1p23_2b | eq_Rp2_C1p23_2a

dcRp2dt_2_C_1_p_2_3 = R_p_3*k_2_C_1_p_2_3

 

 

 

R'' <=> R''''

Constants: k_1_C_1_p_2_4 (forward), k_2_C_1_p_2_4 (reverse).

 

Equations subgroup: C1p24

a forward reaction rate  for the transition

eq_Rp2_C1p24_1a:= Rate_1_C_1_p_2_4 =  k_1_C_1_p_2_4*R_p_2

Rate_1_C_1_p_2_4 = R_p_2*k_1_C_1_p_2_4

a partial conversion rate of R'' in this transition

molecularity:=-1:
eq_Rp2_C1p24_1b:= dcRp2dt_1_C_1_p_2_4 = molecularity*Rate_1_C_1_p_2_4

dcRp2dt_1_C_1_p_2_4 = -Rate_1_C_1_p_2_4

The final form

eq_Rp2_C1p24_1c:= eq_Rp2_C1p24_1b | eq_Rp2_C1p24_1a

dcRp2dt_1_C_1_p_2_4 = -R_p_2*k_1_C_1_p_2_4

 

a reverse reaction rate for the transition

eq_Rp2_C1p24_2a:= Rate_2_C_1_p_2_4 =  k_2_C_1_p_2_4*R_p_4

Rate_2_C_1_p_2_4 = R_p_4*k_2_C_1_p_2_4

a partial conversion rate of R'' in this transition

molecularity:=1:
eq_Rp2_C1p24_2b:= dcRp2dt_2_C_1_p_2_4 = molecularity*Rate_2_C_1_p_2_4

dcRp2dt_2_C_1_p_2_4 = Rate_2_C_1_p_2_4

The final form

eq_Rp2_C1p24_2c:= eq_Rp2_C1p24_2b | eq_Rp2_C1p24_2a

dcRp2dt_2_C_1_p_2_4 = R_p_4*k_2_C_1_p_2_4

 

 

 

R'' <=> R'''''

Constants: k_1_C_1_p_2_5 (forward), k_2_C_1_p_2_5 (reverse).

 

Equations subgroup: C1p25

 

a forward reaction rate  for the transition

eq_Rp2_C1p25_1a:= Rate_1_C_1_p_2_5 =  k_1_C_1_p_2_5*R_p_2

Rate_1_C_1_p_2_5 = R_p_2*k_1_C_1_p_2_5

a partial conversion rate of R'' in this transition

molecularity:=-1:
eq_Rp2_C1p25_1b:= dcRp2dt_1_C_1_p_2_5 = molecularity*Rate_1_C_1_p_2_5

dcRp2dt_1_C_1_p_2_5 = -Rate_1_C_1_p_2_5

the final form

eq_Rp2_C1p25_1c:= eq_Rp2_C1p25_1b | eq_Rp2_C1p25_1a

dcRp2dt_1_C_1_p_2_5 = -R_p_2*k_1_C_1_p_2_5

 

a reverse reaction rate for the transition

eq_Rp2_C1p25_2a:= Rate_2_C_1_p_2_5 =  k_2_C_1_p_2_5*R_p_5

Rate_2_C_1_p_2_5 = R_p_5*k_2_C_1_p_2_5

a partial conversion rate of R'' in this transition

molecularity:=1:
eq_Rp2_C1p25_2b:= dcRp2dt_2_C_1_p_2_5 = molecularity*Rate_2_C_1_p_2_5

dcRp2dt_2_C_1_p_2_5 = Rate_2_C_1_p_2_5

The final form

eq_Rp2_C1p25_2c:= eq_Rp2_C1p25_2b | eq_Rp2_C1p25_2a

dcRp2dt_2_C_1_p_2_5 = R_p_5*k_2_C_1_p_2_5

 

 

Summary of partial conversion rates for the species

eq_Rp2_Ap2_1c;eq_Rp2_Ap2_2c;

dcRp2dt_1_A_p_2 = -L*R_p_2*k_1_A_p_2
dcRp2dt_2_A_p_2 = RL_p_2*k_2_A_p_2

eq_Rp2_B1p2_1c;eq_Rp2_B1p2_2c

dcRp2dt_1_B_1_p_2 = R_s*k_1_B_1_p_2
dcRp2dt_2_B_1_p_2 = -R_p_2*k_2_B_1_p_2

eq_Rp2_C1p12_1c;eq_Rp2_C1p12_2c;
eq_Rp2_C1p23_1c;eq_Rp2_C1p23_2c;
eq_Rp2_C1p24_1c;eq_Rp2_C1p24_2c;
eq_Rp2_C1p25_1c;eq_Rp2_C1p25_2c;

dcRp2dt_1_C_1_p_1_2 = R_p_1*k_1_C_1_p_1_2
dcRp2dt_2_C_1_p_1_2 = -R_p_2*k_2_C_1_p_1_2
dcRp2dt_1_C_1_p_2_3 = -R_p_2*k_1_C_1_p_2_3
dcRp2dt_2_C_1_p_2_3 = R_p_3*k_2_C_1_p_2_3
dcRp2dt_1_C_1_p_2_4 = -R_p_2*k_1_C_1_p_2_4
dcRp2dt_2_C_1_p_2_4 = R_p_4*k_2_C_1_p_2_4
dcRp2dt_1_C_1_p_2_5 = -R_p_2*k_1_C_1_p_2_5
dcRp2dt_2_C_1_p_2_5 = R_p_5*k_2_C_1_p_2_5

 

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL  - not needed (does not have R'' species)

 

2U-R-RL

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 +\
dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2  +\
dcRp2dt_1_C_1_p_1_2 + dcRp2dt_2_C_1_p_1_2  ;

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 + dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2 + dcRp2dt_1_C_1_p_1_2 + dcRp2dt_2_C_1_p_1_2

    Substitute (use all equations)

eq_Rp2_N__2U_R_RL:= % |\
eq_Rp2_Ap2_1c | eq_Rp2_Ap2_2c |\
eq_Rp2_B1p2_1c | eq_Rp2_B1p2_2c |\
eq_Rp2_C1p12_1c | eq_Rp2_C1p12_2c |\
eq_Rp2_C1p23_1c | eq_Rp2_C1p23_2c |\
eq_Rp2_C1p24_1c | eq_Rp2_C1p24_2c |\
eq_Rp2_C1p25_1c | eq_Rp2_C1p25_2c;

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_2_C_1_p_1_2 - L*R_p_2*k_1_A_p_2

 

 

 

3U-R-RL

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 +\
dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2  +\
dcRp2dt_1_C_1_p_1_2 + dcRp2dt_2_C_1_p_1_2 +\
dcRp2dt_1_C_1_p_2_3 + dcRp2dt_2_C_1_p_2_3  ;

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 + dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2 + dcRp2dt_1_C_1_p_1_2 + dcRp2dt_1_C_1_p_2_3 + dcRp2dt_2_C_1_p_1_2 + dcRp2dt_2_C_1_p_2_3

Substitute (use all equations)

eq_Rp2_N__3U_R_RL:= % |\
eq_Rp2_Ap2_1c | eq_Rp2_Ap2_2c |\
eq_Rp2_B1p2_1c | eq_Rp2_B1p2_2c |\
eq_Rp2_C1p12_1c | eq_Rp2_C1p12_2c |\
eq_Rp2_C1p23_1c | eq_Rp2_C1p23_2c |\
eq_Rp2_C1p24_1c | eq_Rp2_C1p24_2c |\
eq_Rp2_C1p25_1c | eq_Rp2_C1p25_2c;

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 - L*R_p_2*k_1_A_p_2

 

 

 

4U-R-RL

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 +\
dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2  +\
dcRp2dt_1_C_1_p_1_2 + dcRp2dt_2_C_1_p_1_2 +\
dcRp2dt_1_C_1_p_2_3 + dcRp2dt_2_C_1_p_2_3  +\
dcRp2dt_1_C_1_p_2_4 + dcRp2dt_2_C_1_p_2_4  ;

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 + dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2 + dcRp2dt_1_C_1_p_1_2 + dcRp2dt_1_C_1_p_2_3 + dcRp2dt_1_C_1_p_2_4 + dcRp2dt_2_C_1_p_1_2 + dcRp2dt_2_C_1_p_2_3 + dcRp2dt_2_C_1_p_2_4

Substitute (use all equations)

eq_Rp2_N__4U_R_RL:= % |\
eq_Rp2_Ap2_1c | eq_Rp2_Ap2_2c |\
eq_Rp2_B1p2_1c | eq_Rp2_B1p2_2c |\
eq_Rp2_C1p12_1c | eq_Rp2_C1p12_2c |\
eq_Rp2_C1p23_1c | eq_Rp2_C1p23_2c |\
eq_Rp2_C1p24_1c | eq_Rp2_C1p24_2c |\
eq_Rp2_C1p25_1c | eq_Rp2_C1p25_2c;

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 - L*R_p_2*k_1_A_p_2

 

 

 

 

5U-R-RL

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 +\
dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2  +\
dcRp2dt_1_C_1_p_1_2 + dcRp2dt_2_C_1_p_1_2 +\
dcRp2dt_1_C_1_p_2_3 + dcRp2dt_2_C_1_p_2_3  +\
dcRp2dt_1_C_1_p_2_4 + dcRp2dt_2_C_1_p_2_4  +\
dcRp2dt_1_C_1_p_2_5 + dcRp2dt_2_C_1_p_2_5  ;

dcRp2dt_N = dcRp2dt_1_A_p_2 + dcRp2dt_2_A_p_2 + dcRp2dt_1_B_1_p_2 + dcRp2dt_2_B_1_p_2 + dcRp2dt_1_C_1_p_1_2 + dcRp2dt_1_C_1_p_2_3 + dcRp2dt_1_C_1_p_2_4 + dcRp2dt_1_C_1_p_2_5 + dcRp2dt_2_C_1_p_1_2 + dcRp2dt_2_C_1_p_2_3 + dcRp2dt_2_C_1_p_2_4 + dcRp2dt_2_C_1_p_2_5

Substitute (use all equations)

eq_Rp2_N__5U_R_RL:= % |\
eq_Rp2_Ap2_1c | eq_Rp2_Ap2_2c |\
eq_Rp2_B1p2_1c | eq_Rp2_B1p2_2c |\
eq_Rp2_C1p12_1c | eq_Rp2_C1p12_2c |\
eq_Rp2_C1p23_1c | eq_Rp2_C1p23_2c |\
eq_Rp2_C1p24_1c | eq_Rp2_C1p24_2c |\
eq_Rp2_C1p25_1c | eq_Rp2_C1p25_2c;

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_1_C_1_p_2_5 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 + R_p_5*k_2_C_1_p_2_5 - L*R_p_2*k_1_A_p_2

 

 

Summary equations for R''

eq_Rp2_N__2U_R_RL

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_2_C_1_p_1_2 - L*R_p_2*k_1_A_p_2

eq_Rp2_N__3U_R_RL

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 - L*R_p_2*k_1_A_p_2

eq_Rp2_N__4U_R_RL

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 - L*R_p_2*k_1_A_p_2

eq_Rp2_N__5U_R_RL

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_1_C_1_p_2_5 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 + R_p_5*k_2_C_1_p_2_5 - L*R_p_2*k_1_A_p_2

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

 

 

 

Species: R'''

Equations group: Rp3 

 

R'''+L<=>RL'''

Constants: k_1_A_p_3 (forward), k_2_A_p_3 (reverse).

 

Equations subgroup: Ap3

 

a forward reaction rate

eq_Rp3_Ap3_1a:= Rate_1_A_p_3 = k_1_A_p_3*R_p_3*L

Rate_1_A_p_3 = L*R_p_3*k_1_A_p_3

a partial conversion rate of R''' in this transition

molecularity:=-1:
eq_Rp3_Ap3_1b:= dcRp3dt_1_A_p_3 = molecularity*Rate_1_A_p_3

dcRp3dt_1_A_p_3 = -Rate_1_A_p_3

the final form

eq_Rp3_Ap3_1c:= eq_Rp3_Ap3_1b | eq_Rp3_Ap3_1a

dcRp3dt_1_A_p_3 = -L*R_p_3*k_1_A_p_3

 

a reverse reaction rate for the transition

eq_Rp3_Ap3_2a:= Rate_2_A_p_3 = k_2_A_p_3*RL_p_3

Rate_2_A_p_3 = RL_p_3*k_2_A_p_3

a partial conversion rate of R''' in this transition

molecularity:=1:
eq_Rp3_Ap3_2b:= dcRp3dt_2_A_p_3 = molecularity*Rate_2_A_p_3

dcRp3dt_2_A_p_3 = Rate_2_A_p_3

the final form

eq_Rp3_Ap3_2c:= eq_Rp3_Ap3_2b | eq_Rp3_Ap3_2a

dcRp3dt_2_A_p_3 = RL_p_3*k_2_A_p_3

 

 

 

R* <=> R'''

Constants: k_1_B_1_p_3 (forward), k_2_B_1_p_3 (reverse).

 

Equations subgroup: B1p3

 

a forward reaction rate  for the transition

eq_Rp3_B1p3_1a:= Rate_1_B_1_p_3 = k_1_B_1_p_3*R_s

Rate_1_B_1_p_3 = R_s*k_1_B_1_p_3

    a partial conversion rate of R''' in this transition

molecularity:=1:
eq_Rp3_B1p3_1b:= dcRp3dt_1_B_1_p_3 = molecularity*Rate_1_B_1_p_3

dcRp3dt_1_B_1_p_3 = Rate_1_B_1_p_3

the final form

eq_Rp3_B1p3_1c:= eq_Rp3_B1p3_1b | eq_Rp3_B1p3_1a

dcRp3dt_1_B_1_p_3 = R_s*k_1_B_1_p_3

 

 

a reverse reaction rate for the transition

eq_Rp3_B1p3_2a:= Rate_2_B_1_p_3 = k_2_B_1_p_3*R_p_3

Rate_2_B_1_p_3 = R_p_3*k_2_B_1_p_3

     a partial conversion rate of R''' in this transition

molecularity:=-1:
eq_Rp3_B1p3_2b:= dcRp3dt_2_B_1_p_3 = molecularity*Rate_2_B_1_p_3

dcRp3dt_2_B_1_p_3 = -Rate_2_B_1_p_3

The final form

eq_Rp3_B1p3_2c:= eq_Rp3_B1p3_2b | eq_Rp3_B1p3_2a

dcRp3dt_2_B_1_p_3 = -R_p_3*k_2_B_1_p_3

 

 

 

 

 

R' <=> R'''

Constants: k_1_C_1_p_1_3 (forward), k_2_C_1_p_1_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p13

 

     a forward reaction rate  for the transition

eq_Rp3_C1p13_1a:= eq_Rp1_C1p13_1a

Rate_1_C_1_p_1_3 = R_p_1*k_1_C_1_p_1_3

    a partial conversion rate of R''' in this transition

molecularity:=1:
eq_Rp3_C1p13_1b:= dcRp3dt_1_C_1_p_1_3 = molecularity*Rate_1_C_1_p_1_3

dcRp3dt_1_C_1_p_1_3 = Rate_1_C_1_p_1_3

    the final form

eq_Rp3_C1p13_1c:= eq_Rp3_C1p13_1b | eq_Rp3_C1p13_1a

dcRp3dt_1_C_1_p_1_3 = R_p_1*k_1_C_1_p_1_3

 

 

a reverse reaction rate for the transition

eq_Rp3_C1p13_2a:= eq_Rp1_C1p13_2a

Rate_2_C_1_p_1_3 = R_p_3*k_2_C_1_p_1_3

a partial conversion rate of R''' in this transition

molecularity:=-1:
eq_Rp3_C1p13_2b:= dcRp3dt_2_C_1_p_1_3 = molecularity*Rate_2_C_1_p_1_3

dcRp3dt_2_C_1_p_1_3 = -Rate_2_C_1_p_1_3

the final form

eq_Rp3_C1p13_2c:= eq_Rp3_C1p13_2b | eq_Rp3_C1p13_2a

dcRp3dt_2_C_1_p_1_3 = -R_p_3*k_2_C_1_p_1_3

 

 

 

R'' <=> R'''

Constants: k_1_C_1_p_2_3 (forward), k_2_C_1_p_2_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p23

 

    a forward reaction rate  for the transition

eq_Rp3_C1p23_1a:= eq_Rp2_C1p23_1a

Rate_1_C_1_p_2_3 = R_p_2*k_1_C_1_p_2_3

    a partial conversion rate of R''' in this transition

molecularity:=1:
eq_Rp3_C1p23_1b:= dcRp3dt_1_C_1_p_2_3 = molecularity*Rate_1_C_1_p_2_3

dcRp3dt_1_C_1_p_2_3 = Rate_1_C_1_p_2_3

    the final form

eq_Rp3_C1p23_1c:= eq_Rp3_C1p23_1b | eq_Rp3_C1p23_1a

dcRp3dt_1_C_1_p_2_3 = R_p_2*k_1_C_1_p_2_3

 

 

a reverse reaction rate for the transition

eq_Rp3_C1p23_2a:= eq_Rp2_C1p23_2a

Rate_2_C_1_p_2_3 = R_p_3*k_2_C_1_p_2_3

a partial conversion rate of R''' in this transition

molecularity:=-1:
eq_Rp3_C1p23_2b:= dcRp3dt_2_C_1_p_2_3 = molecularity*Rate_2_C_1_p_2_3

dcRp3dt_2_C_1_p_2_3 = -Rate_2_C_1_p_2_3

the final form

eq_Rp3_C1p23_2c:= eq_Rp3_C1p23_2b | eq_Rp3_C1p23_2a

dcRp3dt_2_C_1_p_2_3 = -R_p_3*k_2_C_1_p_2_3

 

 

 

R''' <=> R''''

Constants: k_1_C_1_p_3_4 (forward), k_2_C_1_p_3_4 (reverse).

 

Equations subgroup: C1p34

 

a forward reaction rate  for the transition

eq_Rp3_C1p34_1a:= Rate_1_C_1_p_3_4 =  k_1_C_1_p_3_4*R_p_3

Rate_1_C_1_p_3_4 = R_p_3*k_1_C_1_p_3_4

a partial conversion rate of R''' in this transition

molecularity:=-1:
eq_Rp3_C1p34_1b:= dcRp3dt_1_C_1_p_3_4 = molecularity*Rate_1_C_1_p_3_4

dcRp3dt_1_C_1_p_3_4 = -Rate_1_C_1_p_3_4

the final form

eq_Rp3_C1p34_1c:= eq_Rp3_C1p34_1b | eq_Rp3_C1p34_1a

dcRp3dt_1_C_1_p_3_4 = -R_p_3*k_1_C_1_p_3_4

 

a reverse reaction rate for the transition

eq_Rp3_C1p34_2a:= Rate_2_C_1_p_3_4 =  k_2_C_1_p_3_4*R_p_4

Rate_2_C_1_p_3_4 = R_p_4*k_2_C_1_p_3_4

a partial conversion rate of R''' in this transition

molecularity:=1:
eq_Rp3_C1p34_2b:= dcRp3dt_2_C_1_p_3_4 = molecularity*Rate_2_C_1_p_3_4

dcRp3dt_2_C_1_p_3_4 = Rate_2_C_1_p_3_4

the final form

eq_Rp3_C1p34_2c:= eq_Rp3_C1p34_2b | eq_Rp3_C1p34_2a

dcRp3dt_2_C_1_p_3_4 = R_p_4*k_2_C_1_p_3_4

 

 

 

 

R''' <=> R'''''

Constants: k_1_C_1_p_3_5 (forward), k_2_C_1_p_3_5 (reverse).

 

Equations subgroup: C1p35

 

a forward reaction rate  for the transition

eq_Rp3_C1p35_1a:= Rate_1_C_1_p_3_5 =  k_1_C_1_p_3_5*R_p_3

Rate_1_C_1_p_3_5 = R_p_3*k_1_C_1_p_3_5

a partial conversion rate of R''' in this transition

molecularity:=-1:
eq_Rp3_C1p35_1b:= dcRp3dt_1_C_1_p_3_5 = molecularity*Rate_1_C_1_p_3_5

dcRp3dt_1_C_1_p_3_5 = -Rate_1_C_1_p_3_5

the final form

eq_Rp3_C1p35_1c:= eq_Rp3_C1p35_1b | eq_Rp3_C1p35_1a

dcRp3dt_1_C_1_p_3_5 = -R_p_3*k_1_C_1_p_3_5

 

a reverse reaction rate for the transition

eq_Rp3_C1p35_2a:= Rate_2_C_1_p_3_5 =  k_2_C_1_p_3_5*R_p_5

Rate_2_C_1_p_3_5 = R_p_5*k_2_C_1_p_3_5

a partial conversion rate of R''' in this transition

molecularity:=1:
eq_Rp3_C1p35_2b:= dcRp3dt_2_C_1_p_3_5 = molecularity*Rate_2_C_1_p_3_5

dcRp3dt_2_C_1_p_3_5 = Rate_2_C_1_p_3_5

the final form

eq_Rp3_C1p35_2c:= eq_Rp3_C1p35_2b | eq_Rp3_C1p35_2a

dcRp3dt_2_C_1_p_3_5 = R_p_5*k_2_C_1_p_3_5

 

 

 

 

Summary of partial conversion rates for the species

eq_Rp3_Ap3_1c;eq_Rp3_Ap3_2c;

dcRp3dt_1_A_p_3 = -L*R_p_3*k_1_A_p_3
dcRp3dt_2_A_p_3 = RL_p_3*k_2_A_p_3

eq_Rp3_B1p3_1c;eq_Rp3_B1p3_2c

dcRp3dt_1_B_1_p_3 = R_s*k_1_B_1_p_3
dcRp3dt_2_B_1_p_3 = -R_p_3*k_2_B_1_p_3

eq_Rp3_C1p13_1c;eq_Rp3_C1p13_2c;
eq_Rp3_C1p23_1c;eq_Rp3_C1p23_2c;
eq_Rp3_C1p34_1c;eq_Rp3_C1p34_2c;
eq_Rp3_C1p35_1c;eq_Rp3_C1p35_2c;

dcRp3dt_1_C_1_p_1_3 = R_p_1*k_1_C_1_p_1_3
dcRp3dt_2_C_1_p_1_3 = -R_p_3*k_2_C_1_p_1_3
dcRp3dt_1_C_1_p_2_3 = R_p_2*k_1_C_1_p_2_3
dcRp3dt_2_C_1_p_2_3 = -R_p_3*k_2_C_1_p_2_3
dcRp3dt_1_C_1_p_3_4 = -R_p_3*k_1_C_1_p_3_4
dcRp3dt_2_C_1_p_3_4 = R_p_4*k_2_C_1_p_3_4
dcRp3dt_1_C_1_p_3_5 = -R_p_3*k_1_C_1_p_3_5
dcRp3dt_2_C_1_p_3_5 = R_p_5*k_2_C_1_p_3_5

 

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL, 2U-R-RL  - not needed (does not have R''' species)

 

 

 

3U-R-RL

dcRp3dt_N = dcRp3dt_1_A_p_3 + dcRp3dt_2_A_p_3 +\
dcRp3dt_1_B_1_p_3 + dcRp3dt_2_B_1_p_3  +\
dcRp3dt_1_C_1_p_1_3 + dcRp3dt_2_C_1_p_1_3 +\
dcRp3dt_1_C_1_p_2_3 + dcRp3dt_2_C_1_p_2_3  ;

dcRp3dt_N = dcRp3dt_1_A_p_3 + dcRp3dt_2_A_p_3 + dcRp3dt_1_B_1_p_3 + dcRp3dt_2_B_1_p_3 + dcRp3dt_1_C_1_p_1_3 + dcRp3dt_1_C_1_p_2_3 + dcRp3dt_2_C_1_p_1_3 + dcRp3dt_2_C_1_p_2_3

Substitute (use all equations)

eq_Rp3_N__3U_R_RL:= % |\
eq_Rp3_Ap3_1c | eq_Rp3_Ap3_2c |\
eq_Rp3_B1p3_1c | eq_Rp3_B1p3_2c |\
eq_Rp3_C1p13_1c | eq_Rp3_C1p13_2c |\
eq_Rp3_C1p23_1c | eq_Rp3_C1p23_2c |\
eq_Rp3_C1p34_1c | eq_Rp3_C1p34_2c |\
eq_Rp3_C1p35_1c | eq_Rp3_C1p35_2c;

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 - L*R_p_3*k_1_A_p_3

 

 

 

4U-R-RL

dcRp3dt_N = dcRp3dt_1_A_p_3 + dcRp3dt_2_A_p_3 +\
dcRp3dt_1_B_1_p_3 + dcRp3dt_2_B_1_p_3  +\
dcRp3dt_1_C_1_p_1_3 + dcRp3dt_2_C_1_p_1_3 +\
dcRp3dt_1_C_1_p_2_3 + dcRp3dt_2_C_1_p_2_3  +\
dcRp3dt_1_C_1_p_3_4 + dcRp3dt_2_C_1_p_3_4  ;

dcRp3dt_N = dcRp3dt_1_A_p_3 + dcRp3dt_2_A_p_3 + dcRp3dt_1_B_1_p_3 + dcRp3dt_2_B_1_p_3 + dcRp3dt_1_C_1_p_1_3 + dcRp3dt_1_C_1_p_2_3 + dcRp3dt_1_C_1_p_3_4 + dcRp3dt_2_C_1_p_1_3 + dcRp3dt_2_C_1_p_2_3 + dcRp3dt_2_C_1_p_3_4

Substitute (use all equations)

eq_Rp3_N__4U_R_RL:= % |\
eq_Rp3_Ap3_1c | eq_Rp3_Ap3_2c |\
eq_Rp3_B1p3_1c | eq_Rp3_B1p3_2c |\
eq_Rp3_C1p13_1c | eq_Rp3_C1p13_2c |\
eq_Rp3_C1p23_1c | eq_Rp3_C1p23_2c |\
eq_Rp3_C1p34_1c | eq_Rp3_C1p34_2c |\
eq_Rp3_C1p35_1c | eq_Rp3_C1p35_2c;

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 - L*R_p_3*k_1_A_p_3

 

 

 

 

5U-R-RL

dcRp3dt_N = dcRp3dt_1_A_p_3 + dcRp3dt_2_A_p_3 +\
dcRp3dt_1_B_1_p_3 + dcRp3dt_2_B_1_p_3  +\
dcRp3dt_1_C_1_p_1_3 + dcRp3dt_2_C_1_p_1_3 +\
dcRp3dt_1_C_1_p_2_3 + dcRp3dt_2_C_1_p_2_3  +\
dcRp3dt_1_C_1_p_3_4 + dcRp3dt_2_C_1_p_3_4  +\
dcRp3dt_1_C_1_p_3_5 + dcRp3dt_2_C_1_p_3_5  ;

dcRp3dt_N = dcRp3dt_1_A_p_3 + dcRp3dt_2_A_p_3 + dcRp3dt_1_B_1_p_3 + dcRp3dt_2_B_1_p_3 + dcRp3dt_1_C_1_p_1_3 + dcRp3dt_1_C_1_p_2_3 + dcRp3dt_1_C_1_p_3_4 + dcRp3dt_1_C_1_p_3_5 + dcRp3dt_2_C_1_p_1_3 + dcRp3dt_2_C_1_p_2_3 + dcRp3dt_2_C_1_p_3_4 + dcRp3dt_2_C_1_p_3_5

Substitute (use all equations)

eq_Rp3_N__5U_R_RL:= % |\
eq_Rp3_Ap3_1c | eq_Rp3_Ap3_2c |\
eq_Rp3_B1p3_1c | eq_Rp3_B1p3_2c |\
eq_Rp3_C1p13_1c | eq_Rp3_C1p13_2c |\
eq_Rp3_C1p23_1c | eq_Rp3_C1p23_2c |\
eq_Rp3_C1p34_1c | eq_Rp3_C1p34_2c |\
eq_Rp3_C1p35_1c | eq_Rp3_C1p35_2c;

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_1_C_1_p_3_5 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_3_5 - L*R_p_3*k_1_A_p_3

 

 

 

 

Summary equations for R'''

eq_Rp3_N__3U_R_RL

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 - L*R_p_3*k_1_A_p_3

eq_Rp3_N__4U_R_RL

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 - L*R_p_3*k_1_A_p_3

eq_Rp3_N__5U_R_RL

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_1_C_1_p_3_5 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_3_5 - L*R_p_3*k_1_A_p_3

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

Species: R''''

Equations group: Rp4 

 

R''''+L<=>RL''''

Constants: k_1_A_p_4 (forward), k_2_A_p_4 (reverse).

 

Equations subgroup: Ap4

 

 

a forward reaction rate

eq_Rp4_Ap4_1a:= Rate_1_A_p_4 = k_1_A_p_4*R_p_4*L

Rate_1_A_p_4 = L*R_p_4*k_1_A_p_4

a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp4_Ap4_1b:= dcRp4dt_1_A_p_4 = molecularity*Rate_1_A_p_4

dcRp4dt_1_A_p_4 = -Rate_1_A_p_4

the final form

eq_Rp4_Ap4_1c:= eq_Rp4_Ap4_1b | eq_Rp4_Ap4_1a

dcRp4dt_1_A_p_4 = -L*R_p_4*k_1_A_p_4

 

 

a reverse reaction rate for the transition

eq_Rp4_Ap4_2a:= Rate_2_A_p_4 = k_2_A_p_4*RL_p_4

Rate_2_A_p_4 = RL_p_4*k_2_A_p_4

a partial conversion rate of R'''' in this transition

molecularity:=1:
eq_Rp4_Ap4_2b:= dcRp4dt_2_A_p_4 = molecularity*Rate_2_A_p_4

dcRp4dt_2_A_p_4 = Rate_2_A_p_4

the final form

eq_Rp4_Ap4_2c:= eq_Rp4_Ap4_2b | eq_Rp4_Ap4_2a

dcRp4dt_2_A_p_4 = RL_p_4*k_2_A_p_4

 

 

 

R* <=> R''''

Constants: k_1_B_1_p_4 (forward), k_2_B_1_p_4 (reverse).

 

Equations subgroup: B1p4

 

a forward reaction rate  for the transition

eq_Rp4_B1p4_1a:= Rate_1_B_1_p_4 = k_1_B_1_p_4*R_s

Rate_1_B_1_p_4 = R_s*k_1_B_1_p_4

     a partial conversion rate of R'''' in this transition

molecularity:=1:
eq_Rp4_B1p4_1b:= dcRp4dt_1_B_1_p_4 = molecularity*Rate_1_B_1_p_4

dcRp4dt_1_B_1_p_4 = Rate_1_B_1_p_4

the final form

eq_Rp4_B1p4_1c:= eq_Rp4_B1p4_1b | eq_Rp4_B1p4_1a

dcRp4dt_1_B_1_p_4 = R_s*k_1_B_1_p_4

 

a reverse reaction rate for the transition

eq_Rp4_B1p4_2a:= Rate_2_B_1_p_4 = k_2_B_1_p_4*R_p_4

Rate_2_B_1_p_4 = R_p_4*k_2_B_1_p_4

     a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp4_B1p4_2b:= dcRp4dt_2_B_1_p_4 = molecularity*Rate_2_B_1_p_4

dcRp4dt_2_B_1_p_4 = -Rate_2_B_1_p_4

The final form

eq_Rp4_B1p4_2c:= eq_Rp4_B1p4_2b | eq_Rp4_B1p4_2a

dcRp4dt_2_B_1_p_4 = -R_p_4*k_2_B_1_p_4

 

 

 

R' <=> R''''

Constants: k_1_C_1_p_1_4 (forward), k_2_C_1_p_1_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p14

 

     a forward reaction rate  for the transition

eq_Rp4_C1p14_1a:= eq_Rp1_C1p14_1a

Rate_1_C_1_p_1_4 = R_p_1*k_1_C_1_p_1_4

     a partial conversion rate of R'''' in this transition

molecularity:=1:
eq_Rp4_C1p14_1b:= dcRp4dt_1_C_1_p_1_4 = molecularity*Rate_1_C_1_p_1_4

dcRp4dt_1_C_1_p_1_4 = Rate_1_C_1_p_1_4

    the final form

eq_Rp4_C1p14_1c:= eq_Rp4_C1p14_1b | eq_Rp4_C1p14_1a

dcRp4dt_1_C_1_p_1_4 = R_p_1*k_1_C_1_p_1_4

 

 

a reverse reaction rate for the transition

eq_Rp4_C1p14_2a:= eq_Rp1_C1p14_2a

Rate_2_C_1_p_1_4 = R_p_4*k_2_C_1_p_1_4

a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp4_C1p14_2b:= dcRp4dt_2_C_1_p_1_4 = molecularity*Rate_2_C_1_p_1_4

dcRp4dt_2_C_1_p_1_4 = -Rate_2_C_1_p_1_4

the final form

eq_Rp4_C1p14_2c:= eq_Rp4_C1p14_2b | eq_Rp4_C1p14_2a

dcRp4dt_2_C_1_p_1_4 = -R_p_4*k_2_C_1_p_1_4

 

 

 

 

 

R'' <=> R''''

Constants: k_1_C_1_p_2_4 (forward), k_2_C_1_p_2_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p24

 

 

   a forward reaction rate  for the transition

eq_Rp4_C1p24_1a:= eq_Rp2_C1p24_1a

Rate_1_C_1_p_2_4 = R_p_2*k_1_C_1_p_2_4

     a partial conversion rate of R'''' in this transition

molecularity:=1:
eq_Rp4_C1p24_1b:= dcRp4dt_1_C_1_p_2_4 = molecularity*Rate_1_C_1_p_2_4

dcRp4dt_1_C_1_p_2_4 = Rate_1_C_1_p_2_4

    the final form

eq_Rp4_C1p24_1c:= eq_Rp4_C1p24_1b | eq_Rp4_C1p24_1a

dcRp4dt_1_C_1_p_2_4 = R_p_2*k_1_C_1_p_2_4

 

 

a reverse reaction rate for the transition

eq_Rp4_C1p24_2a:= eq_Rp2_C1p24_2a

Rate_2_C_1_p_2_4 = R_p_4*k_2_C_1_p_2_4

a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp4_C1p24_2b:= dcRp4dt_2_C_1_p_2_4 = molecularity*Rate_2_C_1_p_2_4

dcRp4dt_2_C_1_p_2_4 = -Rate_2_C_1_p_2_4

the final form

eq_Rp4_C1p24_2c:= eq_Rp4_C1p24_2b | eq_Rp4_C1p24_2a

dcRp4dt_2_C_1_p_2_4 = -R_p_4*k_2_C_1_p_2_4

 

 

 

 

 

 

R''' <=> R''''

Constants: k_1_C_1_p_3_4 (forward), k_2_C_1_p_3_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p34

 

   a forward reaction rate  for the transition

eq_Rp4_C1p34_1a:= eq_Rp3_C1p34_1a

Rate_1_C_1_p_3_4 = R_p_3*k_1_C_1_p_3_4

     a partial conversion rate of R'''' in this transition

molecularity:=1:
eq_Rp4_C1p34_1b:= dcRp4dt_1_C_1_p_3_4 = molecularity*Rate_1_C_1_p_3_4

dcRp4dt_1_C_1_p_3_4 = Rate_1_C_1_p_3_4

    the final form

eq_Rp4_C1p34_1c:= eq_Rp4_C1p34_1b | eq_Rp4_C1p34_1a

dcRp4dt_1_C_1_p_3_4 = R_p_3*k_1_C_1_p_3_4

 

a reverse reaction rate for the transition

eq_Rp4_C1p34_2a:= eq_Rp3_C1p34_2a

Rate_2_C_1_p_3_4 = R_p_4*k_2_C_1_p_3_4

a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp4_C1p34_2b:= dcRp4dt_2_C_1_p_3_4 = molecularity*Rate_2_C_1_p_3_4

dcRp4dt_2_C_1_p_3_4 = -Rate_2_C_1_p_3_4

the final form

eq_Rp4_C1p34_2c:= eq_Rp4_C1p34_2b | eq_Rp4_C1p34_2a

dcRp4dt_2_C_1_p_3_4 = -R_p_4*k_2_C_1_p_3_4

 

 

 

 

R'''' <=> R'''''

Constants: k_1_C_1_p_4_5 (forward), k_2_C_1_p_4_5 (reverse).

 

Equations subgroup: C1p45

 

a forward reaction rate  for the transition

eq_Rp4_C1p45_1a:= Rate_1_C_1_p_4_5 =  k_1_C_1_p_4_5*R_p_4

Rate_1_C_1_p_4_5 = R_p_4*k_1_C_1_p_4_5

a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp4_C1p45_1b:= dcRp4dt_1_C_1_p_4_5 = molecularity*Rate_1_C_1_p_4_5

dcRp4dt_1_C_1_p_4_5 = -Rate_1_C_1_p_4_5

the final form

eq_Rp4_C1p45_1c:= eq_Rp4_C1p45_1b | eq_Rp4_C1p45_1a

dcRp4dt_1_C_1_p_4_5 = -R_p_4*k_1_C_1_p_4_5

 

 

a reverse reaction rate for the transition

eq_Rp4_C1p45_2a:= Rate_2_C_1_p_4_5 =  k_2_C_1_p_4_5*R_p_5

Rate_2_C_1_p_4_5 = R_p_5*k_2_C_1_p_4_5

  a partial conversion rate of R'''' in this transition

molecularity:=1:
eq_Rp4_C1p45_2b:= dcRp4dt_2_C_1_p_4_5 = molecularity*Rate_2_C_1_p_4_5

dcRp4dt_2_C_1_p_4_5 = Rate_2_C_1_p_4_5

the final form

eq_Rp4_C1p45_2c:= eq_Rp4_C1p45_2b | eq_Rp4_C1p45_2a

dcRp4dt_2_C_1_p_4_5 = R_p_5*k_2_C_1_p_4_5

 

 

 

 

Summary of partial conversion rates for the species

eq_Rp4_Ap4_1c;eq_Rp4_Ap4_2c;

dcRp4dt_1_A_p_4 = -L*R_p_4*k_1_A_p_4
dcRp4dt_2_A_p_4 = RL_p_4*k_2_A_p_4

eq_Rp4_B1p4_1c;eq_Rp4_B1p4_2c

dcRp4dt_1_B_1_p_4 = R_s*k_1_B_1_p_4
dcRp4dt_2_B_1_p_4 = -R_p_4*k_2_B_1_p_4

eq_Rp4_C1p14_1c;eq_Rp4_C1p14_2c;
eq_Rp4_C1p24_1c;eq_Rp4_C1p24_2c;
eq_Rp4_C1p34_1c;eq_Rp4_C1p34_2c;
eq_Rp4_C1p45_1c;eq_Rp4_C1p45_2c;

dcRp4dt_1_C_1_p_1_4 = R_p_1*k_1_C_1_p_1_4
dcRp4dt_2_C_1_p_1_4 = -R_p_4*k_2_C_1_p_1_4
dcRp4dt_1_C_1_p_2_4 = R_p_2*k_1_C_1_p_2_4
dcRp4dt_2_C_1_p_2_4 = -R_p_4*k_2_C_1_p_2_4
dcRp4dt_1_C_1_p_3_4 = R_p_3*k_1_C_1_p_3_4
dcRp4dt_2_C_1_p_3_4 = -R_p_4*k_2_C_1_p_3_4
dcRp4dt_1_C_1_p_4_5 = -R_p_4*k_1_C_1_p_4_5
dcRp4dt_2_C_1_p_4_5 = R_p_5*k_2_C_1_p_4_5

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL, 2U-R-RL , 3U-R-RL - not needed (do not have R'''' species)

 

 

 

4U-R-RL

dcRp4dt_N = dcRp4dt_1_A_p_4 + dcRp4dt_2_A_p_4 +\
dcRp4dt_1_B_1_p_4 + dcRp4dt_2_B_1_p_4  +\
dcRp4dt_1_C_1_p_1_4 + dcRp4dt_2_C_1_p_1_4 +\
dcRp4dt_1_C_1_p_2_4 + dcRp4dt_2_C_1_p_2_4 +\
dcRp4dt_1_C_1_p_3_4 + dcRp4dt_2_C_1_p_3_4  ;

dcRp4dt_N = dcRp4dt_1_A_p_4 + dcRp4dt_2_A_p_4 + dcRp4dt_1_B_1_p_4 + dcRp4dt_2_B_1_p_4 + dcRp4dt_1_C_1_p_1_4 + dcRp4dt_1_C_1_p_2_4 + dcRp4dt_1_C_1_p_3_4 + dcRp4dt_2_C_1_p_1_4 + dcRp4dt_2_C_1_p_2_4 + dcRp4dt_2_C_1_p_3_4

Substitute (use all equations)

eq_Rp4_N__4U_R_RL:= % |\
eq_Rp4_Ap4_1c | eq_Rp4_Ap4_2c |\
eq_Rp4_B1p4_1c | eq_Rp4_B1p4_2c |\
eq_Rp4_C1p14_1c | eq_Rp4_C1p14_2c |\
eq_Rp4_C1p24_1c | eq_Rp4_C1p24_2c |\
eq_Rp4_C1p34_1c | eq_Rp4_C1p34_2c |\
eq_Rp4_C1p45_1c | eq_Rp4_C1p45_2c;

dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 - L*R_p_4*k_1_A_p_4

 

 

 

5U-R-RL

dcRp4dt_N = dcRp4dt_1_A_p_4 + dcRp4dt_2_A_p_4 +\
dcRp4dt_1_B_1_p_4 + dcRp4dt_2_B_1_p_4  +\
dcRp4dt_1_C_1_p_1_4 + dcRp4dt_2_C_1_p_1_4 +\
dcRp4dt_1_C_1_p_2_4 + dcRp4dt_2_C_1_p_2_4 +\
dcRp4dt_1_C_1_p_3_4 + dcRp4dt_2_C_1_p_3_4  +\
dcRp4dt_1_C_1_p_4_5 + dcRp4dt_2_C_1_p_4_5  ;

dcRp4dt_N = dcRp4dt_1_A_p_4 + dcRp4dt_2_A_p_4 + dcRp4dt_1_B_1_p_4 + dcRp4dt_2_B_1_p_4 + dcRp4dt_1_C_1_p_1_4 + dcRp4dt_1_C_1_p_2_4 + dcRp4dt_1_C_1_p_3_4 + dcRp4dt_1_C_1_p_4_5 + dcRp4dt_2_C_1_p_1_4 + dcRp4dt_2_C_1_p_2_4 + dcRp4dt_2_C_1_p_3_4 + dcRp4dt_2_C_1_p_4_5

Substitute (use all equations)

eq_Rp4_N__5U_R_RL:= % |\
eq_Rp4_Ap4_1c | eq_Rp4_Ap4_2c |\
eq_Rp4_B1p4_1c | eq_Rp4_B1p4_2c |\
eq_Rp4_C1p14_1c | eq_Rp4_C1p14_2c |\
eq_Rp4_C1p24_1c | eq_Rp4_C1p24_2c |\
eq_Rp4_C1p34_1c | eq_Rp4_C1p34_2c |\
eq_Rp4_C1p45_1c | eq_Rp4_C1p45_2c;

dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_1_C_1_p_4_5 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_4_5 - L*R_p_4*k_1_A_p_4

 

Summary equations for R''''

eq_Rp4_N__4U_R_RL

dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 - L*R_p_4*k_1_A_p_4

eq_Rp4_N__5U_R_RL

dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_1_C_1_p_4_5 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_4_5 - L*R_p_4*k_1_A_p_4

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

 

 

Species: R'''''

Equations group: Rp5 

 

R'''''+L<=>RL'''''

Constants: k_1_A_p_5 (forward), k_2_A_p_5 (reverse).

 

Equations subgroup: Ap5

 

 

a forward reaction rate

eq_Rp5_Ap5_1a:= Rate_1_A_p_5 = k_1_A_p_5*R_p_5*L

Rate_1_A_p_5 = L*R_p_5*k_1_A_p_5

a partial conversion rate of R''''' in this transition

molecularity:=-1:
eq_Rp5_Ap5_1b:= dcRp5dt_1_A_p_5 = molecularity*Rate_1_A_p_5

dcRp5dt_1_A_p_5 = -Rate_1_A_p_5

the final form

eq_Rp5_Ap5_1c:= eq_Rp5_Ap5_1b | eq_Rp5_Ap5_1a

dcRp5dt_1_A_p_5 = -L*R_p_5*k_1_A_p_5

 

 

a reverse reaction rate for the transition

eq_Rp5_Ap5_2a:= Rate_2_A_p_5 = k_2_A_p_5*RL_p_5

Rate_2_A_p_5 = RL_p_5*k_2_A_p_5

a partial conversion rate of R''''' in this transition

molecularity:=1:
eq_Rp5_Ap5_2b:= dcRp5dt_2_A_p_5 = molecularity*Rate_2_A_p_5

dcRp5dt_2_A_p_5 = Rate_2_A_p_5

the final form

eq_Rp5_Ap5_2c:= eq_Rp5_Ap5_2b | eq_Rp5_Ap5_2a

dcRp5dt_2_A_p_5 = RL_p_5*k_2_A_p_5

 

 

 

 

R* <=> R'''''

Constants: k_1_B_1_p_5 (forward), k_2_B_1_p_5 (reverse).

 

Equations subgroup: B1p5

 

a forward reaction rate  for the transition

eq_Rp5_B1p5_1a:= Rate_1_B_1_p_5 = k_1_B_1_p_5*R_s

Rate_1_B_1_p_5 = R_s*k_1_B_1_p_5

     a partial conversion rate of R''''' in this transition

molecularity:=1:
eq_Rp5_B1p5_1b:= dcRp5dt_1_B_1_p_5 = molecularity*Rate_1_B_1_p_5

dcRp5dt_1_B_1_p_5 = Rate_1_B_1_p_5

the final form

eq_Rp5_B1p5_1c:= eq_Rp5_B1p5_1b | eq_Rp5_B1p5_1a

dcRp5dt_1_B_1_p_5 = R_s*k_1_B_1_p_5

 

a reverse reaction rate for the transition

eq_Rp5_B1p5_2a:= Rate_2_B_1_p_5 = k_2_B_1_p_5*R_p_5

Rate_2_B_1_p_5 = R_p_5*k_2_B_1_p_5

     a partial conversion rate of R'''' in this transition

molecularity:=-1:
eq_Rp5_B1p5_2b:= dcRp5dt_2_B_1_p_5 = molecularity*Rate_2_B_1_p_5

dcRp5dt_2_B_1_p_5 = -Rate_2_B_1_p_5

The final form

eq_Rp5_B1p5_2c:= eq_Rp5_B1p5_2b | eq_Rp5_B1p5_2a

dcRp5dt_2_B_1_p_5 = -R_p_5*k_2_B_1_p_5

 

 

 

 

R' <=> R'''''

Constants: k_1_C_1_p_1_5 (forward), k_2_C_1_p_1_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p15

 

    a forward reaction rate  for the transition

eq_Rp5_C1p15_1a:= eq_Rp1_C1p15_1a

Rate_1_C_1_p_1_5 = R_p_1*k_1_C_1_p_1_5

    a partial conversion rate of R''''' in this transition

molecularity:=1:
eq_Rp5_C1p15_1b:= dcRp5dt_1_C_1_p_1_5 = molecularity*Rate_1_C_1_p_1_5

dcRp5dt_1_C_1_p_1_5 = Rate_1_C_1_p_1_5

    the final form

eq_Rp5_C1p15_1c:= eq_Rp5_C1p15_1b | eq_Rp5_C1p15_1a

dcRp5dt_1_C_1_p_1_5 = R_p_1*k_1_C_1_p_1_5

 

a reverse reaction rate for the transition

eq_Rp5_C1p15_2a:= eq_Rp1_C1p15_2a

Rate_2_C_1_p_1_5 = R_p_5*k_2_C_1_p_1_5

  a partial conversion rate of R''''' in this transition

molecularity:=-1:
eq_Rp5_C1p15_2b:= dcRp5dt_2_C_1_p_1_5 = molecularity*Rate_2_C_1_p_1_5

dcRp5dt_2_C_1_p_1_5 = -Rate_2_C_1_p_1_5

the final form

eq_Rp5_C1p15_2c:= eq_Rp5_C1p15_2b | eq_Rp5_C1p15_2a

dcRp5dt_2_C_1_p_1_5 = -R_p_5*k_2_C_1_p_1_5

 

 

 

 

R'' <=> R'''''

Constants: k_1_C_1_p_2_5 (forward), k_2_C_1_p_2_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p25

 

   a forward reaction rate  for the transition

eq_Rp5_C1p25_1a:= eq_Rp2_C1p25_1a

Rate_1_C_1_p_2_5 = R_p_2*k_1_C_1_p_2_5

   a partial conversion rate of R''''' in this transition

molecularity:=1:
eq_Rp5_C1p25_1b:= dcRp5dt_1_C_1_p_2_5 = molecularity*Rate_1_C_1_p_2_5

dcRp5dt_1_C_1_p_2_5 = Rate_1_C_1_p_2_5

    the final form

eq_Rp5_C1p25_1c:= eq_Rp5_C1p25_1b | eq_Rp5_C1p25_1a

dcRp5dt_1_C_1_p_2_5 = R_p_2*k_1_C_1_p_2_5

 

a reverse reaction rate for the transition

eq_Rp5_C1p25_2a:= eq_Rp2_C1p25_2a

Rate_2_C_1_p_2_5 = R_p_5*k_2_C_1_p_2_5

  a partial conversion rate of R''''' in this transition

molecularity:=-1:
eq_Rp5_C1p25_2b:= dcRp5dt_2_C_1_p_2_5 = molecularity*Rate_2_C_1_p_2_5

dcRp5dt_2_C_1_p_2_5 = -Rate_2_C_1_p_2_5

the final form

eq_Rp5_C1p25_2c:= eq_Rp5_C1p25_2b | eq_Rp5_C1p25_2a

dcRp5dt_2_C_1_p_2_5 = -R_p_5*k_2_C_1_p_2_5

 

 

 

 

R''' <=> R'''''

Constants: k_1_C_1_p_3_5 (forward), k_2_C_1_p_3_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p35

 

   a forward reaction rate  for the transition

eq_Rp5_C1p35_1a:= eq_Rp3_C1p35_1a

Rate_1_C_1_p_3_5 = R_p_3*k_1_C_1_p_3_5

   a partial conversion rate of R''''' in this transition

molecularity:=1:
eq_Rp5_C1p35_1b:= dcRp5dt_1_C_1_p_3_5 = molecularity*Rate_1_C_1_p_3_5

dcRp5dt_1_C_1_p_3_5 = Rate_1_C_1_p_3_5

   the final form

eq_Rp5_C1p35_1c:= eq_Rp5_C1p35_1b | eq_Rp5_C1p35_1a

dcRp5dt_1_C_1_p_3_5 = R_p_3*k_1_C_1_p_3_5

 

a reverse reaction rate for the transition

eq_Rp5_C1p35_2a:= eq_Rp3_C1p35_2a

Rate_2_C_1_p_3_5 = R_p_5*k_2_C_1_p_3_5

  a partial conversion rate of R''''' in this transition

molecularity:=-1:
eq_Rp5_C1p35_2b:= dcRp5dt_2_C_1_p_3_5 = molecularity*Rate_2_C_1_p_3_5

dcRp5dt_2_C_1_p_3_5 = -Rate_2_C_1_p_3_5

the final form

eq_Rp5_C1p35_2c:= eq_Rp5_C1p35_2b | eq_Rp5_C1p35_2a

dcRp5dt_2_C_1_p_3_5 = -R_p_5*k_2_C_1_p_3_5

 

 

 

 

R'''' <=> R'''''

Constants: k_1_C_1_p_3_5 (forward), k_2_C_1_p_3_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C1p45

 

   a forward reaction rate  for the transition

eq_Rp5_C1p45_1a:= eq_Rp4_C1p45_1a

Rate_1_C_1_p_4_5 = R_p_4*k_1_C_1_p_4_5

   a partial conversion rate of R''''' in this transition

molecularity:=1:
eq_Rp5_C1p45_1b:= dcRp5dt_1_C_1_p_4_5 = molecularity*Rate_1_C_1_p_4_5

dcRp5dt_1_C_1_p_4_5 = Rate_1_C_1_p_4_5

  the final form

eq_Rp5_C1p45_1c:= eq_Rp5_C1p45_1b | eq_Rp5_C1p45_1a

dcRp5dt_1_C_1_p_4_5 = R_p_4*k_1_C_1_p_4_5

 

a reverse reaction rate for the transition

eq_Rp5_C1p45_2a:= eq_Rp4_C1p45_2a

Rate_2_C_1_p_4_5 = R_p_5*k_2_C_1_p_4_5

  a partial conversion rate of R''''' in this transition

molecularity:=-1:
eq_Rp5_C1p45_2b:= dcRp5dt_2_C_1_p_4_5 = molecularity*Rate_2_C_1_p_4_5

dcRp5dt_2_C_1_p_4_5 = -Rate_2_C_1_p_4_5

the final form

eq_Rp5_C1p45_2c:= eq_Rp5_C1p45_2b | eq_Rp5_C1p45_2a

dcRp5dt_2_C_1_p_4_5 = -R_p_5*k_2_C_1_p_4_5

 

 

 

Summary of partial conversion rates for the species

eq_Rp5_Ap5_1c;eq_Rp5_Ap5_2c;

dcRp5dt_1_A_p_5 = -L*R_p_5*k_1_A_p_5
dcRp5dt_2_A_p_5 = RL_p_5*k_2_A_p_5

eq_Rp5_B1p5_1c;eq_Rp5_B1p5_2c

dcRp5dt_1_B_1_p_5 = R_s*k_1_B_1_p_5
dcRp5dt_2_B_1_p_5 = -R_p_5*k_2_B_1_p_5

eq_Rp5_C1p15_1c;eq_Rp5_C1p15_2c;
eq_Rp5_C1p25_1c;eq_Rp5_C1p25_2c;
eq_Rp5_C1p35_1c;eq_Rp5_C1p35_2c;
eq_Rp5_C1p45_1c;eq_Rp5_C1p45_2c;

dcRp5dt_1_C_1_p_1_5 = R_p_1*k_1_C_1_p_1_5
dcRp5dt_2_C_1_p_1_5 = -R_p_5*k_2_C_1_p_1_5
dcRp5dt_1_C_1_p_2_5 = R_p_2*k_1_C_1_p_2_5
dcRp5dt_2_C_1_p_2_5 = -R_p_5*k_2_C_1_p_2_5
dcRp5dt_1_C_1_p_3_5 = R_p_3*k_1_C_1_p_3_5
dcRp5dt_2_C_1_p_3_5 = -R_p_5*k_2_C_1_p_3_5
dcRp5dt_1_C_1_p_4_5 = R_p_4*k_1_C_1_p_4_5
dcRp5dt_2_C_1_p_4_5 = -R_p_5*k_2_C_1_p_4_5

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL, 2U-R-RL, 3U-R-RL, 4U-R-RL  - not needed (do not have R'''' species)

 

 

 

5U-R-RL

dcRp5dt_N = dcRp5dt_1_A_p_5 + dcRp5dt_2_A_p_5 +\
dcRp5dt_1_B_1_p_5 + dcRp5dt_2_B_1_p_5  +\
dcRp5dt_1_C_1_p_1_5 + dcRp5dt_2_C_1_p_1_5 +\
dcRp5dt_1_C_1_p_2_5 + dcRp5dt_2_C_1_p_2_5 +\
dcRp5dt_1_C_1_p_3_5 + dcRp5dt_2_C_1_p_3_5 +\
dcRp5dt_1_C_1_p_4_5 + dcRp5dt_2_C_1_p_4_5  ;

dcRp5dt_N = dcRp5dt_1_A_p_5 + dcRp5dt_2_A_p_5 + dcRp5dt_1_B_1_p_5 + dcRp5dt_2_B_1_p_5 + dcRp5dt_1_C_1_p_1_5 + dcRp5dt_1_C_1_p_2_5 + dcRp5dt_1_C_1_p_3_5 + dcRp5dt_1_C_1_p_4_5 + dcRp5dt_2_C_1_p_1_5 + dcRp5dt_2_C_1_p_2_5 + dcRp5dt_2_C_1_p_3_5 + dcRp5dt_2_C_1_p_4_5

Substitute (use all equations)

eq_Rp5_N__5U_R_RL:= % |\
eq_Rp5_Ap5_1c | eq_Rp5_Ap5_2c |\
eq_Rp5_B1p5_1c | eq_Rp5_B1p5_2c |\
eq_Rp5_C1p15_1c | eq_Rp5_C1p15_2c |\
eq_Rp5_C1p25_1c | eq_Rp5_C1p25_2c |\
eq_Rp5_C1p35_1c | eq_Rp5_C1p35_2c |\
eq_Rp5_C1p45_1c | eq_Rp5_C1p45_2c;

dcRp5dt_N = RL_p_5*k_2_A_p_5 - R_p_5*k_2_B_1_p_5 + R_s*k_1_B_1_p_5 + R_p_1*k_1_C_1_p_1_5 + R_p_2*k_1_C_1_p_2_5 + R_p_3*k_1_C_1_p_3_5 + R_p_4*k_1_C_1_p_4_5 - R_p_5*k_2_C_1_p_1_5 - R_p_5*k_2_C_1_p_2_5 - R_p_5*k_2_C_1_p_3_5 - R_p_5*k_2_C_1_p_4_5 - L*R_p_5*k_1_A_p_5

 

 

 

Summary equations for R'''''

eq_Rp5_N__5U_R_RL

dcRp5dt_N = RL_p_5*k_2_A_p_5 - R_p_5*k_2_B_1_p_5 + R_s*k_1_B_1_p_5 + R_p_1*k_1_C_1_p_1_5 + R_p_2*k_1_C_1_p_2_5 + R_p_3*k_1_C_1_p_3_5 + R_p_4*k_1_C_1_p_4_5 - R_p_5*k_2_C_1_p_1_5 - R_p_5*k_2_C_1_p_2_5 - R_p_5*k_2_C_1_p_3_5 - R_p_5*k_2_C_1_p_4_5 - L*R_p_5*k_1_A_p_5

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

Species: RL'

Equations group: RLp1 

 

 

 

 

R'+L<=>RL'

Constants: k_1_A_p_1 (forward), k_2_A_p_1 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: Ap1

 

 

a forward reaction rate

eq_RLp1_Ap1_1a:= eq_Rp1_Ap1_1a

Rate_1_A_p_1 = L*R_p_1*k_1_A_p_1

a partial conversion rate of RL' in this transition

molecularity:=1:
eq_RLp1_Ap1_1b:= dcRLp1dt_1_A_p_1 = molecularity*Rate_1_A_p_1

dcRLp1dt_1_A_p_1 = Rate_1_A_p_1

The final form

eq_RLp1_Ap1_1c:= eq_RLp1_Ap1_1b | eq_RLp1_Ap1_1a

dcRLp1dt_1_A_p_1 = L*R_p_1*k_1_A_p_1

 

a reverse reaction rate for the transition

eq_RLp1_Ap1_2a:= eq_Rp1_Ap1_2a

Rate_2_A_p_1 = RL_p_1*k_2_A_p_1

a partial conversion rate of RL' in this transition

molecularity:=-1:
eq_RLp1_Ap1_2b:= dcRLp1dt_2_A_p_1 = molecularity*Rate_2_A_p_1

dcRLp1dt_2_A_p_1 = -Rate_2_A_p_1

The final form

eq_RLp1_Ap1_2c:= eq_RLp1_Ap1_2b | eq_RLp1_Ap1_2a

dcRLp1dt_2_A_p_1 = -RL_p_1*k_2_A_p_1

 

 

 

 

RL' <=> RL*

Constants: k_1_B_2_p_1 (forward), k_2_B_2_p_1 (reverse).

 

Equations subgroup: B2p1

 

a forward reaction rate  for the transition

eq_RLp1_B2p1_1a:= Rate_1_B_2_p_1 = k_1_B_2_p_1*RL_p_1

Rate_1_B_2_p_1 = RL_p_1*k_1_B_2_p_1

a partial conversion rate of RL' in this transition

molecularity:=-1:
eq_RLp1_B2p1_1b:= dcRLp1dt_1_B_2_p_1 = molecularity*Rate_1_B_2_p_1

dcRLp1dt_1_B_2_p_1 = -Rate_1_B_2_p_1

The final form

eq_RLp1_B2p1_1c:= eq_RLp1_B2p1_1b | eq_RLp1_B2p1_1a

dcRLp1dt_1_B_2_p_1 = -RL_p_1*k_1_B_2_p_1

 

a reverse reaction rate for the transition

eq_RLp1_B2p1_2a:= Rate_2_B_2_p_1 = k_2_B_2_p_1*RL_s

Rate_2_B_2_p_1 = RL_s*k_2_B_2_p_1

    a partial conversion rate of RL' in this transition

molecularity:=1:
eq_RLp1_B2p1_2b:= dcRLp1dt_2_B_2_p_1 = molecularity*Rate_2_B_2_p_1

dcRLp1dt_2_B_2_p_1 = Rate_2_B_2_p_1

The final form

eq_RLp1_B2p1_2c:= eq_RLp1_B2p1_2b | eq_RLp1_B2p1_2a

dcRLp1dt_2_B_2_p_1 = RL_s*k_2_B_2_p_1

 

 

 

RL' <=> RL''

Constants: k_1_C_2_p_1_2 (forward), k_2_C_2_p_1_2 (reverse).

 

Equations subgroup: C2p12

 

a forward reaction rate  for the transition

eq_RLp1_C2p12_1a:= Rate_1_C_2_p_1_2 =  k_1_C_2_p_1_2*RL_p_1

Rate_1_C_2_p_1_2 = RL_p_1*k_1_C_2_p_1_2

a partial conversion rate of RL' in this transition

molecularity:=-1:
eq_RLp1_C2p12_1b:= dcRLp1dt_1_C_2_p_1_2 = molecularity*Rate_1_C_2_p_1_2

dcRLp1dt_1_C_2_p_1_2 = -Rate_1_C_2_p_1_2

The final form

eq_RLp1_C2p12_1c:= eq_RLp1_C2p12_1b | eq_RLp1_C2p12_1a

dcRLp1dt_1_C_2_p_1_2 = -RL_p_1*k_1_C_2_p_1_2

 

a reverse reaction rate for the transition

eq_RLp1_C2p12_2a:= Rate_2_C_2_p_1_2 =  k_2_C_2_p_1_2*RL_p_2

Rate_2_C_2_p_1_2 = RL_p_2*k_2_C_2_p_1_2

a partial conversion rate of RL' in this transition

molecularity:=1:
eq_RLp1_C2p12_2b:= dcRLp1dt_2_C_2_p_1_2 = molecularity*Rate_2_C_2_p_1_2

dcRLp1dt_2_C_2_p_1_2 = Rate_2_C_2_p_1_2

The final form

eq_RLp1_C2p12_2c:= eq_RLp1_C2p12_2b | eq_RLp1_C2p12_2a

dcRLp1dt_2_C_2_p_1_2 = RL_p_2*k_2_C_2_p_1_2

 

 

 

 

RL' <=> RL'''

Constants: k_1_C_2_p_1_3 (forward), k_2_C_2_p_1_3 (reverse).

 

Equations subgroup: C2p13

 

a forward reaction rate  for the transition

eq_RLp1_C2p13_1a:= Rate_1_C_2_p_1_3 =  k_1_C_2_p_1_3*RL_p_1

Rate_1_C_2_p_1_3 = RL_p_1*k_1_C_2_p_1_3

a partial conversion rate of RL' in this transition

molecularity:=-1:
eq_RLp1_C2p13_1b:= dcRLp1dt_1_C_2_p_1_3 = molecularity*Rate_1_C_2_p_1_3

dcRLp1dt_1_C_2_p_1_3 = -Rate_1_C_2_p_1_3

The final form

eq_RLp1_C2p13_1c:= eq_RLp1_C2p13_1b | eq_RLp1_C2p13_1a

dcRLp1dt_1_C_2_p_1_3 = -RL_p_1*k_1_C_2_p_1_3

 

a reverse reaction rate for the transition

eq_RLp1_C2p13_2a:= Rate_2_C_2_p_1_3 =  k_2_C_2_p_1_3*RL_p_3

Rate_2_C_2_p_1_3 = RL_p_3*k_2_C_2_p_1_3

a partial conversion rate of RL' in this transition

molecularity:=1:
eq_RLp1_C2p13_2b:= dcRLp1dt_2_C_2_p_1_3 = molecularity*Rate_2_C_2_p_1_3

dcRLp1dt_2_C_2_p_1_3 = Rate_2_C_2_p_1_3

The final form

eq_RLp1_C2p13_2c:= eq_RLp1_C2p13_2b | eq_RLp1_C2p13_2a

dcRLp1dt_2_C_2_p_1_3 = RL_p_3*k_2_C_2_p_1_3

 

 

 

RL' <=> RL''''

Constants: k_1_C_2_p_1_4 (forward), k_2_C_2_p_1_4 (reverse).

 

Equations subgroup: C2p14

 

a forward reaction rate  for the transition

eq_RLp1_C2p14_1a:= Rate_1_C_2_p_1_4 =  k_1_C_2_p_1_4*RL_p_1

Rate_1_C_2_p_1_4 = RL_p_1*k_1_C_2_p_1_4

a partial conversion rate of RL' in this transition

molecularity:=-1:
eq_RLp1_C2p14_1b:= dcRLp1dt_1_C_2_p_1_4 = molecularity*Rate_1_C_2_p_1_4

dcRLp1dt_1_C_2_p_1_4 = -Rate_1_C_2_p_1_4

The final form

eq_RLp1_C2p14_1c:= eq_RLp1_C2p14_1b | eq_RLp1_C2p14_1a

dcRLp1dt_1_C_2_p_1_4 = -RL_p_1*k_1_C_2_p_1_4

 

a reverse reaction rate for the transition

eq_RLp1_C2p14_2a:= Rate_2_C_2_p_1_4 =  k_2_C_2_p_1_4*RL_p_4

Rate_2_C_2_p_1_4 = RL_p_4*k_2_C_2_p_1_4

a partial conversion rate of RL' in this transition

molecularity:=1:
eq_RLp1_C2p14_2b:= dcRLp1dt_2_C_2_p_1_4 = molecularity*Rate_2_C_2_p_1_4

dcRLp1dt_2_C_2_p_1_4 = Rate_2_C_2_p_1_4

The final form

eq_RLp1_C2p14_2c:= eq_RLp1_C2p14_2b | eq_RLp1_C2p14_2a

dcRLp1dt_2_C_2_p_1_4 = RL_p_4*k_2_C_2_p_1_4

 

 

 

 

RL' <=> RL'''''

Constants: k_1_C_2_p_1_5 (forward), k_2_C_2_p_1_5 (reverse).

 

Equations subgroup: C2p15

 

a forward reaction rate  for the transition

eq_RLp1_C2p15_1a:= Rate_1_C_2_p_1_5 =  k_1_C_2_p_1_5*RL_p_1

Rate_1_C_2_p_1_5 = RL_p_1*k_1_C_2_p_1_5

a partial conversion rate of RL' in this transition

molecularity:=-1:
eq_RLp1_C2p15_1b:= dcRLp1dt_1_C_2_p_1_5 = molecularity*Rate_1_C_2_p_1_5

dcRLp1dt_1_C_2_p_1_5 = -Rate_1_C_2_p_1_5

The final form

eq_RLp1_C2p15_1c:= eq_RLp1_C2p15_1b | eq_RLp1_C2p15_1a

dcRLp1dt_1_C_2_p_1_5 = -RL_p_1*k_1_C_2_p_1_5

 

a reverse reaction rate for the transition

eq_RLp1_C2p15_2a:= Rate_2_C_2_p_1_5 =  k_2_C_2_p_1_5*RL_p_5

Rate_2_C_2_p_1_5 = RL_p_5*k_2_C_2_p_1_5

a partial conversion rate of RL' in this transition

molecularity:=1:
eq_RLp1_C2p15_2b:= dcRLp1dt_2_C_2_p_1_5 = molecularity*Rate_2_C_2_p_1_5

dcRLp1dt_2_C_2_p_1_5 = Rate_2_C_2_p_1_5

The final form

eq_RLp1_C2p15_2c:= eq_RLp1_C2p15_2b | eq_RLp1_C2p15_2a

dcRLp1dt_2_C_2_p_1_5 = RL_p_5*k_2_C_2_p_1_5

 

 

Summary of partial conversion rates for the species

eq_RLp1_Ap1_1c;eq_RLp1_Ap1_2c;

dcRLp1dt_1_A_p_1 = L*R_p_1*k_1_A_p_1
dcRLp1dt_2_A_p_1 = -RL_p_1*k_2_A_p_1

eq_RLp1_B2p1_1c;eq_RLp1_B2p1_2c

dcRLp1dt_1_B_2_p_1 = -RL_p_1*k_1_B_2_p_1
dcRLp1dt_2_B_2_p_1 = RL_s*k_2_B_2_p_1

eq_RLp1_C2p12_1c;eq_RLp1_C2p12_2c;
eq_RLp1_C2p13_1c;eq_RLp1_C2p13_2c;
eq_RLp1_C2p14_1c;eq_RLp1_C2p14_2c;
eq_RLp1_C2p15_1c;eq_RLp1_C2p15_2c;

dcRLp1dt_1_C_2_p_1_2 = -RL_p_1*k_1_C_2_p_1_2
dcRLp1dt_2_C_2_p_1_2 = RL_p_2*k_2_C_2_p_1_2
dcRLp1dt_1_C_2_p_1_3 = -RL_p_1*k_1_C_2_p_1_3
dcRLp1dt_2_C_2_p_1_3 = RL_p_3*k_2_C_2_p_1_3
dcRLp1dt_1_C_2_p_1_4 = -RL_p_1*k_1_C_2_p_1_4
dcRLp1dt_2_C_2_p_1_4 = RL_p_4*k_2_C_2_p_1_4
dcRLp1dt_1_C_2_p_1_5 = -RL_p_1*k_1_C_2_p_1_5
dcRLp1dt_2_C_2_p_1_5 = RL_p_5*k_2_C_2_p_1_5

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1

    Substitute (use all equations)

eq_RLp1_N__1U_R_RL:= % | eq_RLp1_Ap1_1c | eq_RLp1_Ap1_2c \
| eq_RLp1_B2p1_1c | eq_RLp1_B2p1_2c \
| eq_RLp1_C2p12_1c | eq_RLp1_C2p12_2c \
| eq_RLp1_C2p13_1c | eq_RLp1_C2p13_2c \
| eq_RLp1_C2p14_1c | eq_RLp1_C2p14_2c \
| eq_RLp1_C2p15_1c | eq_RLp1_C2p15_2c;

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 + L*R_p_1*k_1_A_p_1

 

 

 

2U-R-RL

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 +\
dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_2;

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 + dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_2

    Substitute (use all equations)

eq_RLp1_N__2U_R_RL:= % | eq_RLp1_Ap1_1c | eq_RLp1_Ap1_2c \
| eq_RLp1_B2p1_1c | eq_RLp1_B2p1_2c \
| eq_RLp1_C2p12_1c | eq_RLp1_C2p12_2c \
| eq_RLp1_C2p13_1c | eq_RLp1_C2p13_2c \
| eq_RLp1_C2p14_1c | eq_RLp1_C2p14_2c \
| eq_RLp1_C2p15_1c | eq_RLp1_C2p15_2c;

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 + RL_p_2*k_2_C_2_p_1_2 + L*R_p_1*k_1_A_p_1

 

 

 

3U-R-RL

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 +\
dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_2 +\
dcRLp1dt_1_C_2_p_1_3 + dcRLp1dt_2_C_2_p_1_3;

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 + dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_1_C_2_p_1_3 + dcRLp1dt_2_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_3

    Substitute (use all equations)

eq_RLp1_N__3U_R_RL:= % | eq_RLp1_Ap1_1c | eq_RLp1_Ap1_2c \
| eq_RLp1_B2p1_1c | eq_RLp1_B2p1_2c \
| eq_RLp1_C2p12_1c | eq_RLp1_C2p12_2c \
| eq_RLp1_C2p13_1c | eq_RLp1_C2p13_2c \
| eq_RLp1_C2p14_1c | eq_RLp1_C2p14_2c \
| eq_RLp1_C2p15_1c | eq_RLp1_C2p15_2c;

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + L*R_p_1*k_1_A_p_1

 

 

 

4U-R-RL

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 +\
dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_2 +\
dcRLp1dt_1_C_2_p_1_3 + dcRLp1dt_2_C_2_p_1_3 +\
dcRLp1dt_1_C_2_p_1_4 + dcRLp1dt_2_C_2_p_1_4;

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 + dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_1_C_2_p_1_3 + dcRLp1dt_1_C_2_p_1_4 + dcRLp1dt_2_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_3 + dcRLp1dt_2_C_2_p_1_4

    Substitute (use all equations)

eq_RLp1_N__4U_R_RL:= % | eq_RLp1_Ap1_1c | eq_RLp1_Ap1_2c \
| eq_RLp1_B2p1_1c | eq_RLp1_B2p1_2c \
| eq_RLp1_C2p12_1c | eq_RLp1_C2p12_2c \
| eq_RLp1_C2p13_1c | eq_RLp1_C2p13_2c \
| eq_RLp1_C2p14_1c | eq_RLp1_C2p14_2c \
| eq_RLp1_C2p15_1c | eq_RLp1_C2p15_2c;

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + L*R_p_1*k_1_A_p_1

 

 

5U-R-RL

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 +\
dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_2 +\
dcRLp1dt_1_C_2_p_1_3 + dcRLp1dt_2_C_2_p_1_3 +\
dcRLp1dt_1_C_2_p_1_4 + dcRLp1dt_2_C_2_p_1_4 +\
dcRLp1dt_1_C_2_p_1_5 + dcRLp1dt_2_C_2_p_1_5;

dcRLp1dt_N = dcRLp1dt_1_A_p_1 + dcRLp1dt_2_A_p_1 + dcRLp1dt_1_B_2_p_1 + dcRLp1dt_2_B_2_p_1 + dcRLp1dt_1_C_2_p_1_2 + dcRLp1dt_1_C_2_p_1_3 + dcRLp1dt_1_C_2_p_1_4 + dcRLp1dt_1_C_2_p_1_5 + dcRLp1dt_2_C_2_p_1_2 + dcRLp1dt_2_C_2_p_1_3 + dcRLp1dt_2_C_2_p_1_4 + dcRLp1dt_2_C_2_p_1_5

    Substitute (use all equations)

eq_RLp1_N__5U_R_RL:= % | eq_RLp1_Ap1_1c | eq_RLp1_Ap1_2c \
| eq_RLp1_B2p1_1c | eq_RLp1_B2p1_2c \
| eq_RLp1_C2p12_1c | eq_RLp1_C2p12_2c \
| eq_RLp1_C2p13_1c | eq_RLp1_C2p13_2c \
| eq_RLp1_C2p14_1c | eq_RLp1_C2p14_2c \
| eq_RLp1_C2p15_1c | eq_RLp1_C2p15_2c;

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 - RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + RL_p_5*k_2_C_2_p_1_5 + L*R_p_1*k_1_A_p_1

 


 

Summary equations for RL'

eq_RLp1_N__1U_R_RL

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 + L*R_p_1*k_1_A_p_1

eq_RLp1_N__2U_R_RL

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 + RL_p_2*k_2_C_2_p_1_2 + L*R_p_1*k_1_A_p_1

eq_RLp1_N__3U_R_RL

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + L*R_p_1*k_1_A_p_1

eq_RLp1_N__4U_R_RL

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + L*R_p_1*k_1_A_p_1

eq_RLp1_N__5U_R_RL

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 - RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + RL_p_5*k_2_C_2_p_1_5 + L*R_p_1*k_1_A_p_1

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

Species: RL''

Equations group: RLp2 

 

 

 

 

R''+L<=>RL''

Constants: k_1_A_p_2 (forward), k_2_A_p_2 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: Ap2

 

a forward reaction rate

eq_RLp2_Ap2_1a:= eq_Rp2_Ap2_1a

Rate_1_A_p_2 = L*R_p_2*k_1_A_p_2

a partial conversion rate of RL'' in this transition

molecularity:=1:
eq_RLp2_Ap2_1b:= dcRLp2dt_1_A_p_2 = molecularity*Rate_1_A_p_2

dcRLp2dt_1_A_p_2 = Rate_1_A_p_2

the final form

eq_RLp2_Ap2_1c:= eq_RLp2_Ap2_1b | eq_RLp2_Ap2_1a

dcRLp2dt_1_A_p_2 = L*R_p_2*k_1_A_p_2

 

 

a reverse reaction rate for the transition

eq_RLp2_Ap2_2a:= eq_Rp2_Ap2_2a

Rate_2_A_p_2 = RL_p_2*k_2_A_p_2

a partial conversion rate of RL'' in this transition

molecularity:=-1:
eq_RLp2_Ap2_2b:= dcRLp2dt_2_A_p_2 = molecularity*Rate_2_A_p_2

dcRLp2dt_2_A_p_2 = -Rate_2_A_p_2

the final form

eq_RLp2_Ap2_2c:= eq_RLp2_Ap2_2b | eq_RLp2_Ap2_2a

dcRLp2dt_2_A_p_2 = -RL_p_2*k_2_A_p_2

 

 

 

 

RL'' <=> RL*

Constants: k_1_B_2_p_2 (forward), k_2_B_2_p_2 (reverse).

 

Equations subgroup: B2p2

 

a forward reaction rate  for the transition

eq_RLp2_B2p2_1a:= Rate_1_B_2_p_2 = k_1_B_2_p_2*RL_p_2

Rate_1_B_2_p_2 = RL_p_2*k_1_B_2_p_2

a partial conversion rate of RL'' in this transition

molecularity:=-1:
eq_RLp2_B2p2_1b:= dcRLp2dt_1_B_2_p_2 = molecularity*Rate_1_B_2_p_2

dcRLp2dt_1_B_2_p_2 = -Rate_1_B_2_p_2

the final form

eq_RLp2_B2p2_1c:= eq_RLp2_B2p2_1b | eq_RLp2_B2p2_1a

dcRLp2dt_1_B_2_p_2 = -RL_p_2*k_1_B_2_p_2

 

a reverse reaction rate for the transition

eq_RLp2_B2p2_2a:= Rate_2_B_2_p_2 = k_2_B_2_p_2*RL_s

Rate_2_B_2_p_2 = RL_s*k_2_B_2_p_2

    a partial conversion rate of RL'' in this transition

molecularity:=1:
eq_RLp2_B2p2_2b:= dcRLp2dt_2_B_2_p_2 = molecularity*Rate_2_B_2_p_2

dcRLp2dt_2_B_2_p_2 = Rate_2_B_2_p_2

  the final form

eq_RLp2_B2p2_2c:= eq_RLp2_B2p2_2b | eq_RLp2_B2p2_2a

dcRLp2dt_2_B_2_p_2 = RL_s*k_2_B_2_p_2

 

 

 

RL' <=> RL''

Constants: k_1_C_2_p_1_2 (forward), k_2_C_2_p_1_2 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p12

a forward reaction rate  for the transition

eq_RLp2_C2p12_1a:= eq_RLp1_C2p12_1a

Rate_1_C_2_p_1_2 = RL_p_1*k_1_C_2_p_1_2

a partial conversion rate of RL'' in this transition

molecularity:=1:
eq_RLp2_C2p12_1b:= dcRLp2dt_1_C_2_p_1_2 = molecularity*Rate_1_C_2_p_1_2

dcRLp2dt_1_C_2_p_1_2 = Rate_1_C_2_p_1_2

the final form

eq_RLp2_C2p12_1c:= eq_RLp2_C2p12_1b | eq_RLp2_C2p12_1a

dcRLp2dt_1_C_2_p_1_2 = RL_p_1*k_1_C_2_p_1_2

 

a reverse reaction rate for the transition

eq_RLp2_C2p12_2a:= eq_RLp1_C2p12_2a

Rate_2_C_2_p_1_2 = RL_p_2*k_2_C_2_p_1_2

a partial conversion rate of RL'' in this transition

molecularity:=-1:
eq_RLp2_C2p12_2b:= dcRLp2dt_2_C_2_p_1_2 = molecularity*Rate_2_C_2_p_1_2

dcRLp2dt_2_C_2_p_1_2 = -Rate_2_C_2_p_1_2

the final form

eq_RLp2_C2p12_2c:= eq_RLp2_C2p12_2b | eq_RLp2_C2p12_2a

dcRLp2dt_2_C_2_p_1_2 = -RL_p_2*k_2_C_2_p_1_2

 

 

 

 

RL'' <=> RL'''

Constants: k_1_C_2_p_2_3 (forward), k_2_C_2_p_2_3 (reverse).

 

Equations subgroup: C2p23

 

a forward reaction rate  for the transition

eq_RLp2_C2p23_1a:= Rate_1_C_2_p_2_3 =  k_1_C_2_p_2_3*RL_p_2

Rate_1_C_2_p_2_3 = RL_p_2*k_1_C_2_p_2_3

a partial conversion rate of RL'' in this transition

molecularity:=-1:
eq_RLp2_C2p23_1b:= dcRLp2dt_1_C_2_p_2_3 = molecularity*Rate_1_C_2_p_2_3

dcRLp2dt_1_C_2_p_2_3 = -Rate_1_C_2_p_2_3

the final form

eq_RLp2_C2p23_1c:= eq_RLp2_C2p23_1b | eq_RLp2_C2p23_1a

dcRLp2dt_1_C_2_p_2_3 = -RL_p_2*k_1_C_2_p_2_3

 

a reverse reaction rate for the transition

eq_RLp2_C2p23_2a:= Rate_2_C_2_p_2_3 =  k_2_C_2_p_2_3*RL_p_3

Rate_2_C_2_p_2_3 = RL_p_3*k_2_C_2_p_2_3

a partial conversion rate of RL'' in this transition

molecularity:=1:
eq_RLp2_C2p23_2b:= dcRLp2dt_2_C_2_p_2_3 = molecularity*Rate_2_C_2_p_2_3

dcRLp2dt_2_C_2_p_2_3 = Rate_2_C_2_p_2_3

the final form

eq_RLp2_C2p23_2c:= eq_RLp2_C2p23_2b | eq_RLp2_C2p23_2a

dcRLp2dt_2_C_2_p_2_3 = RL_p_3*k_2_C_2_p_2_3

 

 

 

RL'' <=> RL''''

Constants: k_1_C_2_p_2_4 (forward), k_2_C_2_p_2_4 (reverse).

 

Equations subgroup: C2p24

 

a forward reaction rate  for the transition

eq_RLp2_C2p24_1a:= Rate_1_C_2_p_2_4 =  k_1_C_2_p_2_4*RL_p_2

Rate_1_C_2_p_2_4 = RL_p_2*k_1_C_2_p_2_4

a partial conversion rate of RL'' in this transition

molecularity:=-1:
eq_RLp2_C2p24_1b:= dcRLp2dt_1_C_2_p_2_4 = molecularity*Rate_1_C_2_p_2_4

dcRLp2dt_1_C_2_p_2_4 = -Rate_1_C_2_p_2_4

the final form

eq_RLp2_C2p24_1c:= eq_RLp2_C2p24_1b | eq_RLp2_C2p24_1a

dcRLp2dt_1_C_2_p_2_4 = -RL_p_2*k_1_C_2_p_2_4

 

a reverse reaction rate for the transition

eq_RLp2_C2p24_2a:= Rate_2_C_2_p_2_4 =  k_2_C_2_p_2_4*RL_p_4

Rate_2_C_2_p_2_4 = RL_p_4*k_2_C_2_p_2_4

a partial conversion rate of RL'' in this transition

molecularity:=1:
eq_RLp2_C2p24_2b:= dcRLp2dt_2_C_2_p_2_4 = molecularity*Rate_2_C_2_p_2_4

dcRLp2dt_2_C_2_p_2_4 = Rate_2_C_2_p_2_4

the final form

eq_RLp2_C2p24_2c:= eq_RLp2_C2p24_2b | eq_RLp2_C2p24_2a

dcRLp2dt_2_C_2_p_2_4 = RL_p_4*k_2_C_2_p_2_4

 

 

 

RL'' <=> RL'''''

Constants: k_1_C_2_p_2_5 (forward), k_2_C_2_p_2_5 (reverse).

 

Equations subgroup: C2p25

 

a forward reaction rate  for the transition

eq_RLp2_C2p25_1a:= Rate_1_C_2_p_2_5 =  k_1_C_2_p_2_5*RL_p_2

Rate_1_C_2_p_2_5 = RL_p_2*k_1_C_2_p_2_5

a partial conversion rate of RL'' in this transition

molecularity:=-1:
eq_RLp2_C2p25_1b:= dcRLp2dt_1_C_2_p_2_5 = molecularity*Rate_1_C_2_p_2_5

dcRLp2dt_1_C_2_p_2_5 = -Rate_1_C_2_p_2_5

the final form

eq_RLp2_C2p25_1c:= eq_RLp2_C2p25_1b | eq_RLp2_C2p25_1a

dcRLp2dt_1_C_2_p_2_5 = -RL_p_2*k_1_C_2_p_2_5

 

a reverse reaction rate for the transition

eq_RLp2_C2p25_2a:= Rate_2_C_2_p_2_5 =  k_2_C_2_p_2_5*RL_p_5

Rate_2_C_2_p_2_5 = RL_p_5*k_2_C_2_p_2_5

a partial conversion rate of RL'' in this transition

molecularity:=1:
eq_RLp2_C2p25_2b:= dcRLp2dt_2_C_2_p_2_5 = molecularity*Rate_2_C_2_p_2_5

dcRLp2dt_2_C_2_p_2_5 = Rate_2_C_2_p_2_5

the final form

eq_RLp2_C2p25_2c:= eq_RLp2_C2p25_2b | eq_RLp2_C2p25_2a

dcRLp2dt_2_C_2_p_2_5 = RL_p_5*k_2_C_2_p_2_5

 

 

Summary of partial conversion rates for the species

eq_RLp2_Ap2_1c;eq_RLp2_Ap2_2c;

dcRLp2dt_1_A_p_2 = L*R_p_2*k_1_A_p_2
dcRLp2dt_2_A_p_2 = -RL_p_2*k_2_A_p_2

eq_RLp2_B2p2_1c;eq_RLp2_B2p2_2c

dcRLp2dt_1_B_2_p_2 = -RL_p_2*k_1_B_2_p_2
dcRLp2dt_2_B_2_p_2 = RL_s*k_2_B_2_p_2

eq_RLp2_C2p12_1c;eq_RLp2_C2p12_2c;
eq_RLp2_C2p23_1c;eq_RLp2_C2p23_2c;
eq_RLp2_C2p24_1c;eq_RLp2_C2p24_2c;
eq_RLp2_C2p25_1c;eq_RLp2_C2p25_2c;

dcRLp2dt_1_C_2_p_1_2 = RL_p_1*k_1_C_2_p_1_2
dcRLp2dt_2_C_2_p_1_2 = -RL_p_2*k_2_C_2_p_1_2
dcRLp2dt_1_C_2_p_2_3 = -RL_p_2*k_1_C_2_p_2_3
dcRLp2dt_2_C_2_p_2_3 = RL_p_3*k_2_C_2_p_2_3
dcRLp2dt_1_C_2_p_2_4 = -RL_p_2*k_1_C_2_p_2_4
dcRLp2dt_2_C_2_p_2_4 = RL_p_4*k_2_C_2_p_2_4
dcRLp2dt_1_C_2_p_2_5 = -RL_p_2*k_1_C_2_p_2_5
dcRLp2dt_2_C_2_p_2_5 = RL_p_5*k_2_C_2_p_2_5

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL - not needed; no RL'' species

 

2U-R-RL

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 +\
dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_2_C_2_p_1_2;

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 + dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_2_C_2_p_1_2

    Substitute (use all equations)

eq_RLp2_N__2U_R_RL:= % | eq_RLp2_Ap2_1c | eq_RLp2_Ap2_2c \
| eq_RLp2_B2p2_1c | eq_RLp2_B2p2_2c \
| eq_RLp2_C2p12_1c | eq_RLp2_C2p12_2c \
| eq_RLp2_C2p23_1c | eq_RLp2_C2p23_2c \
| eq_RLp2_C2p24_1c | eq_RLp2_C2p24_2c \
| eq_RLp2_C2p25_1c | eq_RLp2_C2p25_2c;

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_2_C_2_p_1_2 + L*R_p_2*k_1_A_p_2

 

 

3U-R-RL

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 +\
dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_2_C_2_p_1_2 +\
dcRLp2dt_1_C_2_p_2_3 + dcRLp2dt_2_C_2_p_2_3;

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 + dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_1_C_2_p_2_3 + dcRLp2dt_2_C_2_p_1_2 + dcRLp2dt_2_C_2_p_2_3

    Substitute (use all equations)

eq_RLp2_N__3U_R_RL:= % | eq_RLp2_Ap2_1c | eq_RLp2_Ap2_2c \
| eq_RLp2_B2p2_1c | eq_RLp2_B2p2_2c \
| eq_RLp2_C2p12_1c | eq_RLp2_C2p12_2c \
| eq_RLp2_C2p23_1c | eq_RLp2_C2p23_2c \
| eq_RLp2_C2p24_1c | eq_RLp2_C2p24_2c \
| eq_RLp2_C2p25_1c | eq_RLp2_C2p25_2c;

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + L*R_p_2*k_1_A_p_2

 

 

4U-R-RL

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 +\
dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_2_C_2_p_1_2 +\
dcRLp2dt_1_C_2_p_2_3 + dcRLp2dt_2_C_2_p_2_3 +\
dcRLp2dt_1_C_2_p_2_4 + dcRLp2dt_2_C_2_p_2_4;

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 + dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_1_C_2_p_2_3 + dcRLp2dt_1_C_2_p_2_4 + dcRLp2dt_2_C_2_p_1_2 + dcRLp2dt_2_C_2_p_2_3 + dcRLp2dt_2_C_2_p_2_4

    Substitute (use all equations)

eq_RLp2_N__4U_R_RL:= % | eq_RLp2_Ap2_1c | eq_RLp2_Ap2_2c \
| eq_RLp2_B2p2_1c | eq_RLp2_B2p2_2c \
| eq_RLp2_C2p12_1c | eq_RLp2_C2p12_2c \
| eq_RLp2_C2p23_1c | eq_RLp2_C2p23_2c \
| eq_RLp2_C2p24_1c | eq_RLp2_C2p24_2c \
| eq_RLp2_C2p25_1c | eq_RLp2_C2p25_2c;

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + L*R_p_2*k_1_A_p_2

 

 

5U-R-RL

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 +\
dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_2_C_2_p_1_2 +\
dcRLp2dt_1_C_2_p_2_3 + dcRLp2dt_2_C_2_p_2_3 +\
dcRLp2dt_1_C_2_p_2_4 + dcRLp2dt_2_C_2_p_2_4 +\
dcRLp2dt_1_C_2_p_2_5 + dcRLp2dt_2_C_2_p_2_5;

dcRLp2dt_N = dcRLp2dt_1_A_p_2 + dcRLp2dt_2_A_p_2 + dcRLp2dt_1_B_2_p_2 + dcRLp2dt_2_B_2_p_2 + dcRLp2dt_1_C_2_p_1_2 + dcRLp2dt_1_C_2_p_2_3 + dcRLp2dt_1_C_2_p_2_4 + dcRLp2dt_1_C_2_p_2_5 + dcRLp2dt_2_C_2_p_1_2 + dcRLp2dt_2_C_2_p_2_3 + dcRLp2dt_2_C_2_p_2_4 + dcRLp2dt_2_C_2_p_2_5

    Substitute (use all equations)

eq_RLp2_N__5U_R_RL:= % | eq_RLp2_Ap2_1c | eq_RLp2_Ap2_2c \
| eq_RLp2_B2p2_1c | eq_RLp2_B2p2_2c \
| eq_RLp2_C2p12_1c | eq_RLp2_C2p12_2c \
| eq_RLp2_C2p23_1c | eq_RLp2_C2p23_2c \
| eq_RLp2_C2p24_1c | eq_RLp2_C2p24_2c \
| eq_RLp2_C2p25_1c | eq_RLp2_C2p25_2c;

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_1_C_2_p_2_5 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + RL_p_5*k_2_C_2_p_2_5 + L*R_p_2*k_1_A_p_2

 

 

Summary equations for RL''

eq_RLp2_N__2U_R_RL

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_2_C_2_p_1_2 + L*R_p_2*k_1_A_p_2

eq_RLp2_N__3U_R_RL

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + L*R_p_2*k_1_A_p_2

eq_RLp2_N__4U_R_RL

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + L*R_p_2*k_1_A_p_2

eq_RLp2_N__5U_R_RL

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_1_C_2_p_2_5 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + RL_p_5*k_2_C_2_p_2_5 + L*R_p_2*k_1_A_p_2

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

 

 

 

 

Species: RL'''

Equations group: RLp3 

 

 

 

 

R'''+L<=>RL'''

Constants: k_1_A_p_3 (forward), k_2_A_p_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: Ap3

 

a forward reaction rate

eq_RLp3_Ap3_1a:= eq_Rp3_Ap3_1a

Rate_1_A_p_3 = L*R_p_3*k_1_A_p_3

a partial conversion rate of RL''' in this transition

molecularity:=1:
eq_RLp3_Ap3_1b:= dcRLp3dt_1_A_p_3 = molecularity*Rate_1_A_p_3

dcRLp3dt_1_A_p_3 = Rate_1_A_p_3

the final form

eq_RLp3_Ap3_1c:= eq_RLp3_Ap3_1b | eq_RLp3_Ap3_1a

dcRLp3dt_1_A_p_3 = L*R_p_3*k_1_A_p_3

 

a reverse reaction rate for the transition

eq_RLp3_Ap3_2a:= eq_Rp3_Ap3_2a

Rate_2_A_p_3 = RL_p_3*k_2_A_p_3

  a partial conversion rate of RL''' in this transition

molecularity:=-1:
eq_RLp3_Ap3_2b:= dcRLp3dt_2_A_p_3 = molecularity*Rate_2_A_p_3

dcRLp3dt_2_A_p_3 = -Rate_2_A_p_3

  the final form

eq_RLp3_Ap3_2c:= eq_RLp3_Ap3_2b | eq_RLp3_Ap3_2a

dcRLp3dt_2_A_p_3 = -RL_p_3*k_2_A_p_3

 

 

 

 

RL''' <=> RL*

Constants: k_1_B_2_p_3 (forward), k_2_B_2_p_3 (reverse).

 

Equations subgroup: B2p3

 

a forward reaction rate  for the transition

eq_RLp3_B2p3_1a:= Rate_1_B_2_p_3 = k_1_B_2_p_3*RL_p_3

Rate_1_B_2_p_3 = RL_p_3*k_1_B_2_p_3

a partial conversion rate of RL''' in this transition

molecularity:=-1:
eq_RLp3_B2p3_1b:= dcRLp3dt_1_B_2_p_3 = molecularity*Rate_1_B_2_p_3

dcRLp3dt_1_B_2_p_3 = -Rate_1_B_2_p_3

the final form

eq_RLp3_B2p3_1c:= eq_RLp3_B2p3_1b | eq_RLp3_B2p3_1a

dcRLp3dt_1_B_2_p_3 = -RL_p_3*k_1_B_2_p_3

 

a reverse reaction rate for the transition

eq_RLp3_B2p3_2a:= Rate_2_B_2_p_3 = k_2_B_2_p_3*RL_s

Rate_2_B_2_p_3 = RL_s*k_2_B_2_p_3

     a partial conversion rate of RL''' in this transition

molecularity:=1:
eq_RLp3_B2p3_2b:= dcRLp3dt_2_B_2_p_3 = molecularity*Rate_2_B_2_p_3

dcRLp3dt_2_B_2_p_3 = Rate_2_B_2_p_3

   the final form

eq_RLp3_B2p3_2c:= eq_RLp3_B2p3_2b | eq_RLp3_B2p3_2a

dcRLp3dt_2_B_2_p_3 = RL_s*k_2_B_2_p_3

 

 

 

RL' <=> RL'''

Constants: k_1_C_2_p_1_3 (forward), k_2_C_2_p_1_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p13

 

a forward reaction rate  for the transition

eq_RLp3_C2p13_1a:= eq_RLp1_C2p13_1a

Rate_1_C_2_p_1_3 = RL_p_1*k_1_C_2_p_1_3

a partial conversion rate of RL''' in this transition

molecularity:=1:
eq_RLp3_C2p13_1b:= dcRLp3dt_1_C_2_p_1_3 = molecularity*Rate_1_C_2_p_1_3

dcRLp3dt_1_C_2_p_1_3 = Rate_1_C_2_p_1_3

the final form

eq_RLp3_C2p13_1c:= eq_RLp3_C2p13_1b | eq_RLp3_C2p13_1a

dcRLp3dt_1_C_2_p_1_3 = RL_p_1*k_1_C_2_p_1_3

 

a reverse reaction rate for the transition

eq_RLp3_C2p13_2a:= eq_RLp1_C2p13_2a

Rate_2_C_2_p_1_3 = RL_p_3*k_2_C_2_p_1_3

a partial conversion rate of RL''' in this transition

molecularity:=-1:
eq_RLp3_C2p13_2b:= dcRLp3dt_2_C_2_p_1_3 = molecularity*Rate_2_C_2_p_1_3

dcRLp3dt_2_C_2_p_1_3 = -Rate_2_C_2_p_1_3

the final form

eq_RLp3_C2p13_2c:= eq_RLp3_C2p13_2b | eq_RLp3_C2p13_2a

dcRLp3dt_2_C_2_p_1_3 = -RL_p_3*k_2_C_2_p_1_3

 

 

 

 

RL'' <=> RL'''

Constants: k_1_C_2_p_2_3 (forward), k_2_C_2_p_2_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p23

 

a forward reaction rate  for the transition

eq_RLp3_C2p23_1a:= eq_RLp2_C2p23_1a

Rate_1_C_2_p_2_3 = RL_p_2*k_1_C_2_p_2_3

a partial conversion rate of RL''' in this transition

molecularity:=1:
eq_RLp3_C2p23_1b:= dcRLp3dt_1_C_2_p_2_3 = molecularity*Rate_1_C_2_p_2_3

dcRLp3dt_1_C_2_p_2_3 = Rate_1_C_2_p_2_3

the final form

eq_RLp3_C2p23_1c:= eq_RLp3_C2p23_1b | eq_RLp3_C2p23_1a

dcRLp3dt_1_C_2_p_2_3 = RL_p_2*k_1_C_2_p_2_3

 

a reverse reaction rate for the transition

eq_RLp3_C2p23_2a:= eq_RLp2_C2p23_2a

Rate_2_C_2_p_2_3 = RL_p_3*k_2_C_2_p_2_3

a partial conversion rate of RL''' in this transition

molecularity:=-1:
eq_RLp3_C2p23_2b:= dcRLp3dt_2_C_2_p_2_3 = molecularity*Rate_2_C_2_p_2_3

dcRLp3dt_2_C_2_p_2_3 = -Rate_2_C_2_p_2_3

the final form

eq_RLp3_C2p23_2c:= eq_RLp3_C2p23_2b | eq_RLp3_C2p23_2a

dcRLp3dt_2_C_2_p_2_3 = -RL_p_3*k_2_C_2_p_2_3

 

 

 

 

 

RL''' <=> RL''''

Constants: k_1_C_2_p_3_4 (forward), k_2_C_2_p_3_4 (reverse).

 

Equations subgroup: C2p34

 

a forward reaction rate  for the transition

eq_RLp3_C2p34_1a:= Rate_1_C_2_p_3_4 =  k_1_C_2_p_3_4*RL_p_3

Rate_1_C_2_p_3_4 = RL_p_3*k_1_C_2_p_3_4

  a partial conversion rate of RL''' in this transition

molecularity:=-1:
eq_RLp3_C2p34_1b:= dcRLp3dt_1_C_2_p_3_4 = molecularity*Rate_1_C_2_p_3_4

dcRLp3dt_1_C_2_p_3_4 = -Rate_1_C_2_p_3_4

the final form

eq_RLp3_C2p34_1c:= eq_RLp3_C2p34_1b | eq_RLp3_C2p34_1a

dcRLp3dt_1_C_2_p_3_4 = -RL_p_3*k_1_C_2_p_3_4

 

a reverse reaction rate for the transition

eq_RLp3_C2p34_2a:= Rate_2_C_2_p_3_4 =  k_2_C_2_p_3_4*RL_p_4

Rate_2_C_2_p_3_4 = RL_p_4*k_2_C_2_p_3_4

  a partial conversion rate of RL''' in this transition

molecularity:=1:
eq_RLp3_C2p34_2b:= dcRLp3dt_2_C_2_p_3_4 = molecularity*Rate_2_C_2_p_3_4

dcRLp3dt_2_C_2_p_3_4 = Rate_2_C_2_p_3_4

the final form

eq_RLp3_C2p34_2c:= eq_RLp3_C2p34_2b | eq_RLp3_C2p34_2a

dcRLp3dt_2_C_2_p_3_4 = RL_p_4*k_2_C_2_p_3_4

 

 

 

 

 

RL''' <=> RL'''''

Constants: k_1_C_2_p_3_5 (forward), k_2_C_2_p_3_5 (reverse).

 

Equations subgroup: C2p35

 

a forward reaction rate  for the transition

eq_RLp3_C2p35_1a:= Rate_1_C_2_p_3_5 =  k_1_C_2_p_3_5*RL_p_3

Rate_1_C_2_p_3_5 = RL_p_3*k_1_C_2_p_3_5

  a partial conversion rate of RL''' in this transition

molecularity:=-1:
eq_RLp3_C2p35_1b:= dcRLp3dt_1_C_2_p_3_5 = molecularity*Rate_1_C_2_p_3_5

dcRLp3dt_1_C_2_p_3_5 = -Rate_1_C_2_p_3_5

the final form

eq_RLp3_C2p35_1c:= eq_RLp3_C2p35_1b | eq_RLp3_C2p35_1a

dcRLp3dt_1_C_2_p_3_5 = -RL_p_3*k_1_C_2_p_3_5

 

a reverse reaction rate for the transition

eq_RLp3_C2p35_2a:= Rate_2_C_2_p_3_5 =  k_2_C_2_p_3_5*RL_p_5

Rate_2_C_2_p_3_5 = RL_p_5*k_2_C_2_p_3_5

  a partial conversion rate of RL''' in this transition

molecularity:=1:
eq_RLp3_C2p35_2b:= dcRLp3dt_2_C_2_p_3_5 = molecularity*Rate_2_C_2_p_3_5

dcRLp3dt_2_C_2_p_3_5 = Rate_2_C_2_p_3_5

the final form

eq_RLp3_C2p35_2c:= eq_RLp3_C2p35_2b | eq_RLp3_C2p35_2a

dcRLp3dt_2_C_2_p_3_5 = RL_p_5*k_2_C_2_p_3_5

 

 

Summary of partial conversion rates for the species

eq_RLp3_Ap3_1c;eq_RLp3_Ap3_2c;

dcRLp3dt_1_A_p_3 = L*R_p_3*k_1_A_p_3
dcRLp3dt_2_A_p_3 = -RL_p_3*k_2_A_p_3

eq_RLp3_B2p3_1c;eq_RLp3_B2p3_2c

dcRLp3dt_1_B_2_p_3 = -RL_p_3*k_1_B_2_p_3
dcRLp3dt_2_B_2_p_3 = RL_s*k_2_B_2_p_3

eq_RLp3_C2p13_1c;eq_RLp3_C2p13_2c;
eq_RLp3_C2p23_1c;eq_RLp3_C2p23_2c;
eq_RLp3_C2p34_1c;eq_RLp3_C2p34_2c;
eq_RLp3_C2p35_1c;eq_RLp3_C2p35_2c;

dcRLp3dt_1_C_2_p_1_3 = RL_p_1*k_1_C_2_p_1_3
dcRLp3dt_2_C_2_p_1_3 = -RL_p_3*k_2_C_2_p_1_3
dcRLp3dt_1_C_2_p_2_3 = RL_p_2*k_1_C_2_p_2_3
dcRLp3dt_2_C_2_p_2_3 = -RL_p_3*k_2_C_2_p_2_3
dcRLp3dt_1_C_2_p_3_4 = -RL_p_3*k_1_C_2_p_3_4
dcRLp3dt_2_C_2_p_3_4 = RL_p_4*k_2_C_2_p_3_4
dcRLp3dt_1_C_2_p_3_5 = -RL_p_3*k_1_C_2_p_3_5
dcRLp3dt_2_C_2_p_3_5 = RL_p_5*k_2_C_2_p_3_5

 

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL, 2U-R-RL - not needed; no RL''' species

 

 

3U-R-RL

dcRLp3dt_N = dcRLp3dt_1_A_p_3 + dcRLp3dt_2_A_p_3 + dcRLp3dt_1_B_2_p_3 + dcRLp3dt_2_B_2_p_3 +\
dcRLp3dt_1_C_2_p_1_3 + dcRLp3dt_2_C_2_p_1_3 +\
dcRLp3dt_1_C_2_p_2_3 + dcRLp3dt_2_C_2_p_2_3;

dcRLp3dt_N = dcRLp3dt_1_A_p_3 + dcRLp3dt_2_A_p_3 + dcRLp3dt_1_B_2_p_3 + dcRLp3dt_2_B_2_p_3 + dcRLp3dt_1_C_2_p_1_3 + dcRLp3dt_1_C_2_p_2_3 + dcRLp3dt_2_C_2_p_1_3 + dcRLp3dt_2_C_2_p_2_3

    Substitute (use all equations)

eq_RLp3_N__3U_R_RL:= % | eq_RLp3_Ap3_1c | eq_RLp3_Ap3_2c \
| eq_RLp3_B2p3_1c | eq_RLp3_B2p3_2c \
| eq_RLp3_C2p13_1c | eq_RLp3_C2p13_2c \
| eq_RLp3_C2p23_1c | eq_RLp3_C2p23_2c \
| eq_RLp3_C2p34_1c | eq_RLp3_C2p34_2c \
| eq_RLp3_C2p35_1c | eq_RLp3_C2p35_2c;

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + L*R_p_3*k_1_A_p_3

 

 

4U-R-RL

dcRLp3dt_N = dcRLp3dt_1_A_p_3 + dcRLp3dt_2_A_p_3 + dcRLp3dt_1_B_2_p_3 + dcRLp3dt_2_B_2_p_3 +\
dcRLp3dt_1_C_2_p_1_3 + dcRLp3dt_2_C_2_p_1_3 +\
dcRLp3dt_1_C_2_p_2_3 + dcRLp3dt_2_C_2_p_2_3+\
dcRLp3dt_1_C_2_p_3_4 + dcRLp3dt_2_C_2_p_3_4;

dcRLp3dt_N = dcRLp3dt_1_A_p_3 + dcRLp3dt_2_A_p_3 + dcRLp3dt_1_B_2_p_3 + dcRLp3dt_2_B_2_p_3 + dcRLp3dt_1_C_2_p_1_3 + dcRLp3dt_1_C_2_p_2_3 + dcRLp3dt_1_C_2_p_3_4 + dcRLp3dt_2_C_2_p_1_3 + dcRLp3dt_2_C_2_p_2_3 + dcRLp3dt_2_C_2_p_3_4

    Substitute (use all equations)

eq_RLp3_N__4U_R_RL:= % | eq_RLp3_Ap3_1c | eq_RLp3_Ap3_2c \
| eq_RLp3_B2p3_1c | eq_RLp3_B2p3_2c \
| eq_RLp3_C2p13_1c | eq_RLp3_C2p13_2c \
| eq_RLp3_C2p23_1c | eq_RLp3_C2p23_2c \
| eq_RLp3_C2p34_1c | eq_RLp3_C2p34_2c \
| eq_RLp3_C2p35_1c | eq_RLp3_C2p35_2c;

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + L*R_p_3*k_1_A_p_3

 

 

5U-R-RL

dcRLp3dt_N = dcRLp3dt_1_A_p_3 + dcRLp3dt_2_A_p_3 + dcRLp3dt_1_B_2_p_3 + dcRLp3dt_2_B_2_p_3 +\
dcRLp3dt_1_C_2_p_1_3 + dcRLp3dt_2_C_2_p_1_3 +\
dcRLp3dt_1_C_2_p_2_3 + dcRLp3dt_2_C_2_p_2_3 +\
dcRLp3dt_1_C_2_p_3_4 + dcRLp3dt_2_C_2_p_3_4 +\
dcRLp3dt_1_C_2_p_3_5 + dcRLp3dt_2_C_2_p_3_5;

dcRLp3dt_N = dcRLp3dt_1_A_p_3 + dcRLp3dt_2_A_p_3 + dcRLp3dt_1_B_2_p_3 + dcRLp3dt_2_B_2_p_3 + dcRLp3dt_1_C_2_p_1_3 + dcRLp3dt_1_C_2_p_2_3 + dcRLp3dt_1_C_2_p_3_4 + dcRLp3dt_1_C_2_p_3_5 + dcRLp3dt_2_C_2_p_1_3 + dcRLp3dt_2_C_2_p_2_3 + dcRLp3dt_2_C_2_p_3_4 + dcRLp3dt_2_C_2_p_3_5

    Substitute (use all equations)

eq_RLp3_N__5U_R_RL:= % | eq_RLp3_Ap3_1c | eq_RLp3_Ap3_2c \
| eq_RLp3_B2p3_1c | eq_RLp3_B2p3_2c \
| eq_RLp3_C2p13_1c | eq_RLp3_C2p13_2c \
| eq_RLp3_C2p23_1c | eq_RLp3_C2p23_2c \
| eq_RLp3_C2p34_1c | eq_RLp3_C2p34_2c \
| eq_RLp3_C2p35_1c | eq_RLp3_C2p35_2c;

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_1_C_2_p_3_5 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_3_5 + L*R_p_3*k_1_A_p_3

 

 

 

 

Summary equations for RL'''

 

eq_RLp3_N__3U_R_RL

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + L*R_p_3*k_1_A_p_3

eq_RLp3_N__4U_R_RL

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + L*R_p_3*k_1_A_p_3

eq_RLp3_N__5U_R_RL

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_1_C_2_p_3_5 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_3_5 + L*R_p_3*k_1_A_p_3

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

Species: RL''''

Equations group: RLp4 

 

 

 

 

R''''+L<=>RL''''

Constants: k_1_A_p_4 (forward), k_2_A_p_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: Ap4

 

a forward reaction rate

eq_RLp4_Ap4_1a:= eq_Rp4_Ap4_1a

Rate_1_A_p_4 = L*R_p_4*k_1_A_p_4

  a partial conversion rate of RL'''' in this transition

molecularity:=1:
eq_RLp4_Ap4_1b:= dcRLp4dt_1_A_p_4 = molecularity*Rate_1_A_p_4

dcRLp4dt_1_A_p_4 = Rate_1_A_p_4

  the final form

eq_RLp4_Ap4_1c:= eq_RLp4_Ap4_1b | eq_RLp4_Ap4_1a

dcRLp4dt_1_A_p_4 = L*R_p_4*k_1_A_p_4

 

 

a reverse reaction rate for the transition

eq_RLp4_Ap4_2a:= eq_Rp4_Ap4_2a

Rate_2_A_p_4 = RL_p_4*k_2_A_p_4

a partial conversion rate of RL'''' in this transition

molecularity:=-1:
eq_RLp4_Ap4_2b:= dcRLp4dt_2_A_p_4 = molecularity*Rate_2_A_p_4

dcRLp4dt_2_A_p_4 = -Rate_2_A_p_4

the final form

eq_RLp4_Ap4_2c:= eq_RLp4_Ap4_2b | eq_RLp4_Ap4_2a

dcRLp4dt_2_A_p_4 = -RL_p_4*k_2_A_p_4

 

 

 

 

 

RL'''' <=> RL*

Constants: k_1_B_2_p_4 (forward), k_2_B_2_p_4 (reverse).

 

Equations subgroup: B2p4

 

a forward reaction rate  for the transition

eq_RLp4_B2p4_1a:= Rate_1_B_2_p_4 = k_1_B_2_p_4*RL_p_4

Rate_1_B_2_p_4 = RL_p_4*k_1_B_2_p_4

a partial conversion rate of RL'''' in this transition

molecularity:=-1:
eq_RLp4_B2p4_1b:= dcRLp4dt_1_B_2_p_4 = molecularity*Rate_1_B_2_p_4

dcRLp4dt_1_B_2_p_4 = -Rate_1_B_2_p_4

the final form

eq_RLp4_B2p4_1c:= eq_RLp4_B2p4_1b | eq_RLp4_B2p4_1a

dcRLp4dt_1_B_2_p_4 = -RL_p_4*k_1_B_2_p_4

 

a reverse reaction rate for the transition

eq_RLp4_B2p4_2a:= Rate_2_B_2_p_4 = k_2_B_2_p_4*RL_s

Rate_2_B_2_p_4 = RL_s*k_2_B_2_p_4

      a partial conversion rate of RL'''' in this transition

molecularity:=1:
eq_RLp4_B2p4_2b:= dcRLp4dt_2_B_2_p_4 = molecularity*Rate_2_B_2_p_4

dcRLp4dt_2_B_2_p_4 = Rate_2_B_2_p_4

     the final form

eq_RLp4_B2p4_2c:= eq_RLp4_B2p4_2b | eq_RLp4_B2p4_2a

dcRLp4dt_2_B_2_p_4 = RL_s*k_2_B_2_p_4

 

 

 

RL' <=> RL''''

Constants: k_1_C_2_p_1_4 (forward), k_2_C_2_p_1_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p14

 

a forward reaction rate  for the transition

eq_RLp4_C2p14_1a:= eq_RLp1_C2p14_1a

Rate_1_C_2_p_1_4 = RL_p_1*k_1_C_2_p_1_4

  a partial conversion rate of RL'''' in this transition

molecularity:=1:
eq_RLp4_C2p14_1b:= dcRLp4dt_1_C_2_p_1_4 = molecularity*Rate_1_C_2_p_1_4

dcRLp4dt_1_C_2_p_1_4 = Rate_1_C_2_p_1_4

the final form

eq_RLp4_C2p14_1c:= eq_RLp4_C2p14_1b | eq_RLp4_C2p14_1a

dcRLp4dt_1_C_2_p_1_4 = RL_p_1*k_1_C_2_p_1_4

 

a reverse reaction rate for the transition

eq_RLp4_C2p14_2a:= eq_RLp1_C2p14_2a

Rate_2_C_2_p_1_4 = RL_p_4*k_2_C_2_p_1_4

a partial conversion rate of RL'''' in this transition

molecularity:=-1:
eq_RLp4_C2p14_2b:= dcRLp4dt_2_C_2_p_1_4 = molecularity*Rate_2_C_2_p_1_4

dcRLp4dt_2_C_2_p_1_4 = -Rate_2_C_2_p_1_4

  the final form

eq_RLp4_C2p14_2c:= eq_RLp4_C2p14_2b | eq_RLp4_C2p14_2a

dcRLp4dt_2_C_2_p_1_4 = -RL_p_4*k_2_C_2_p_1_4

 

 

 

 

RL'' <=> RL''''

Constants: k_1_C_2_p_2_4 (forward), k_2_C_2_p_2_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p24

 

a forward reaction rate  for the transition

eq_RLp4_C2p24_1a:= eq_RLp2_C2p24_1a

Rate_1_C_2_p_2_4 = RL_p_2*k_1_C_2_p_2_4

  a partial conversion rate of RL'''' in this transition

molecularity:=1:
eq_RLp4_C2p24_1b:= dcRLp4dt_1_C_2_p_2_4 = molecularity*Rate_1_C_2_p_2_4

dcRLp4dt_1_C_2_p_2_4 = Rate_1_C_2_p_2_4

the final form

eq_RLp4_C2p24_1c:= eq_RLp4_C2p24_1b | eq_RLp4_C2p24_1a

dcRLp4dt_1_C_2_p_2_4 = RL_p_2*k_1_C_2_p_2_4

 

a reverse reaction rate for the transition

eq_RLp4_C2p24_2a:= eq_RLp2_C2p24_2a

Rate_2_C_2_p_2_4 = RL_p_4*k_2_C_2_p_2_4

a partial conversion rate of RL'''' in this transition

molecularity:=-1:
eq_RLp4_C2p24_2b:= dcRLp4dt_2_C_2_p_2_4 = molecularity*Rate_2_C_2_p_2_4

dcRLp4dt_2_C_2_p_2_4 = -Rate_2_C_2_p_2_4

the final form

eq_RLp4_C2p24_2c:= eq_RLp4_C2p24_2b | eq_RLp4_C2p24_2a

dcRLp4dt_2_C_2_p_2_4 = -RL_p_4*k_2_C_2_p_2_4

 

 

 

RL''' <=> RL''''

Constants: k_1_C_2_p_3_4 (forward), k_2_C_2_p_3_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p34

 

a forward reaction rate  for the transition

eq_RLp4_C2p34_1a:= eq_RLp3_C2p34_1a

Rate_1_C_2_p_3_4 = RL_p_3*k_1_C_2_p_3_4

  a partial conversion rate of RL'''' in this transition

molecularity:=1:
eq_RLp4_C2p34_1b:= dcRLp4dt_1_C_2_p_3_4 = molecularity*Rate_1_C_2_p_3_4

dcRLp4dt_1_C_2_p_3_4 = Rate_1_C_2_p_3_4

the final form

eq_RLp4_C2p34_1c:= eq_RLp4_C2p34_1b | eq_RLp4_C2p34_1a

dcRLp4dt_1_C_2_p_3_4 = RL_p_3*k_1_C_2_p_3_4

 

a reverse reaction rate for the transition

eq_RLp4_C2p34_2a:= eq_RLp3_C2p34_2a

Rate_2_C_2_p_3_4 = RL_p_4*k_2_C_2_p_3_4

a partial conversion rate of RL'''' in this transition

molecularity:=-1:
eq_RLp4_C2p34_2b:= dcRLp4dt_2_C_2_p_3_4 = molecularity*Rate_2_C_2_p_3_4

dcRLp4dt_2_C_2_p_3_4 = -Rate_2_C_2_p_3_4

the final form

eq_RLp4_C2p34_2c:= eq_RLp4_C2p34_2b | eq_RLp4_C2p34_2a

dcRLp4dt_2_C_2_p_3_4 = -RL_p_4*k_2_C_2_p_3_4

 

 

 

 

RL'''' <=> RL'''''

Constants: k_1_C_2_p_4_5 (forward), k_2_C_2_p_4_5 (reverse).

 

Equations subgroup: C2p45

 

 

a forward reaction rate  for the transition

eq_RLp4_C2p45_1a:= Rate_1_C_2_p_4_5 =  k_1_C_2_p_4_5*RL_p_4

Rate_1_C_2_p_4_5 = RL_p_4*k_1_C_2_p_4_5

a partial conversion rate of RL'''' in this transition

molecularity:=-1:
eq_RLp4_C2p45_1b:= dcRLp4dt_1_C_2_p_4_5 = molecularity*Rate_1_C_2_p_4_5

dcRLp4dt_1_C_2_p_4_5 = -Rate_1_C_2_p_4_5

  the final form

eq_RLp4_C2p45_1c:= eq_RLp4_C2p45_1b | eq_RLp4_C2p45_1a

dcRLp4dt_1_C_2_p_4_5 = -RL_p_4*k_1_C_2_p_4_5

 

a reverse reaction rate for the transition

eq_RLp4_C2p45_2a:= Rate_2_C_2_p_4_5 =  k_2_C_2_p_4_5*RL_p_5

Rate_2_C_2_p_4_5 = RL_p_5*k_2_C_2_p_4_5

   a partial conversion rate of RL'''' in this transition

molecularity:=1:
eq_RLp4_C2p45_2b:= dcRLp4dt_2_C_2_p_4_5 = molecularity*Rate_2_C_2_p_4_5

dcRLp4dt_2_C_2_p_4_5 = Rate_2_C_2_p_4_5

  the final form

eq_RLp4_C2p45_2c:= eq_RLp4_C2p45_2b | eq_RLp4_C2p45_2a

dcRLp4dt_2_C_2_p_4_5 = RL_p_5*k_2_C_2_p_4_5

 

 

Summary of partial conversion rates for the species

eq_RLp4_Ap4_1c;eq_RLp4_Ap4_2c;

dcRLp4dt_1_A_p_4 = L*R_p_4*k_1_A_p_4
dcRLp4dt_2_A_p_4 = -RL_p_4*k_2_A_p_4

eq_RLp4_B2p4_1c;eq_RLp4_B2p4_2c

dcRLp4dt_1_B_2_p_4 = -RL_p_4*k_1_B_2_p_4
dcRLp4dt_2_B_2_p_4 = RL_s*k_2_B_2_p_4

eq_RLp4_C2p14_1c;eq_RLp4_C2p14_2c;
eq_RLp4_C2p24_1c;eq_RLp4_C2p24_2c;
eq_RLp4_C2p34_1c;eq_RLp4_C2p34_2c;
eq_RLp4_C2p45_1c;eq_RLp4_C2p45_2c;

dcRLp4dt_1_C_2_p_1_4 = RL_p_1*k_1_C_2_p_1_4
dcRLp4dt_2_C_2_p_1_4 = -RL_p_4*k_2_C_2_p_1_4
dcRLp4dt_1_C_2_p_2_4 = RL_p_2*k_1_C_2_p_2_4
dcRLp4dt_2_C_2_p_2_4 = -RL_p_4*k_2_C_2_p_2_4
dcRLp4dt_1_C_2_p_3_4 = RL_p_3*k_1_C_2_p_3_4
dcRLp4dt_2_C_2_p_3_4 = -RL_p_4*k_2_C_2_p_3_4
dcRLp4dt_1_C_2_p_4_5 = -RL_p_4*k_1_C_2_p_4_5
dcRLp4dt_2_C_2_p_4_5 = RL_p_5*k_2_C_2_p_4_5

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL, 2U-R-RL, 3U-R-RL - not needed; no RL'''' species

 

 

4U-R-RL

dcRLp4dt_N = dcRLp4dt_1_A_p_4 + dcRLp4dt_2_A_p_4 + dcRLp4dt_1_B_2_p_4 + dcRLp4dt_2_B_2_p_4 +\
dcRLp4dt_1_C_2_p_1_4 + dcRLp4dt_2_C_2_p_1_4 +\
dcRLp4dt_1_C_2_p_2_4 + dcRLp4dt_2_C_2_p_2_4 +\
dcRLp4dt_1_C_2_p_3_4 + dcRLp4dt_2_C_2_p_3_4;

dcRLp4dt_N = dcRLp4dt_1_A_p_4 + dcRLp4dt_2_A_p_4 + dcRLp4dt_1_B_2_p_4 + dcRLp4dt_2_B_2_p_4 + dcRLp4dt_1_C_2_p_1_4 + dcRLp4dt_1_C_2_p_2_4 + dcRLp4dt_1_C_2_p_3_4 + dcRLp4dt_2_C_2_p_1_4 + dcRLp4dt_2_C_2_p_2_4 + dcRLp4dt_2_C_2_p_3_4

    Substitute (use all equations)

eq_RLp4_N__4U_R_RL:= % | eq_RLp4_Ap4_1c | eq_RLp4_Ap4_2c \
| eq_RLp4_B2p4_1c | eq_RLp4_B2p4_2c \
| eq_RLp4_C2p14_1c | eq_RLp4_C2p14_2c \
| eq_RLp4_C2p24_1c | eq_RLp4_C2p24_2c \
| eq_RLp4_C2p34_1c | eq_RLp4_C2p34_2c \
| eq_RLp4_C2p45_1c | eq_RLp4_C2p45_2c;

dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + L*R_p_4*k_1_A_p_4

 

 

 

 

5U-R-RL

dcRLp4dt_N = dcRLp4dt_1_A_p_4 + dcRLp4dt_2_A_p_4 + dcRLp4dt_1_B_2_p_4 + dcRLp4dt_2_B_2_p_4 +\
dcRLp4dt_1_C_2_p_1_4 + dcRLp4dt_2_C_2_p_1_4 +\
dcRLp4dt_1_C_2_p_2_4 + dcRLp4dt_2_C_2_p_2_4 +\
dcRLp4dt_1_C_2_p_3_4 + dcRLp4dt_2_C_2_p_3_4 +\
dcRLp4dt_1_C_2_p_4_5 + dcRLp4dt_2_C_2_p_4_5;

dcRLp4dt_N = dcRLp4dt_1_A_p_4 + dcRLp4dt_2_A_p_4 + dcRLp4dt_1_B_2_p_4 + dcRLp4dt_2_B_2_p_4 + dcRLp4dt_1_C_2_p_1_4 + dcRLp4dt_1_C_2_p_2_4 + dcRLp4dt_1_C_2_p_3_4 + dcRLp4dt_1_C_2_p_4_5 + dcRLp4dt_2_C_2_p_1_4 + dcRLp4dt_2_C_2_p_2_4 + dcRLp4dt_2_C_2_p_3_4 + dcRLp4dt_2_C_2_p_4_5

    Substitute (use all equations)

eq_RLp4_N__5U_R_RL:= % | eq_RLp4_Ap4_1c | eq_RLp4_Ap4_2c \
| eq_RLp4_B2p4_1c | eq_RLp4_B2p4_2c \
| eq_RLp4_C2p14_1c | eq_RLp4_C2p14_2c \
| eq_RLp4_C2p24_1c | eq_RLp4_C2p24_2c \
| eq_RLp4_C2p34_1c | eq_RLp4_C2p34_2c \
| eq_RLp4_C2p45_1c | eq_RLp4_C2p45_2c;

dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_1_C_2_p_4_5 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_4_5 + L*R_p_4*k_1_A_p_4

 

 

 

 

Summary equations for RL''''

 

eq_RLp4_N__4U_R_RL

dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + L*R_p_4*k_1_A_p_4

eq_RLp4_N__5U_R_RL

dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_1_C_2_p_4_5 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_4_5 + L*R_p_4*k_1_A_p_4

 

 

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

Species: RL'''''

Equations group: RLp5 

 

 

 

 

R'''''+L<=>RL'''''

Constants: k_1_A_p_5 (forward), k_2_A_p_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: Ap5

 

a forward reaction rate

eq_RLp5_Ap5_1a:= eq_Rp5_Ap5_1a

Rate_1_A_p_5 = L*R_p_5*k_1_A_p_5

a partial conversion rate of RL''''' in this transition

molecularity:=1:
eq_RLp5_Ap5_1b:= dcRLp5dt_1_A_p_5 = molecularity*Rate_1_A_p_5

dcRLp5dt_1_A_p_5 = Rate_1_A_p_5

the final form

eq_RLp5_Ap5_1c:= eq_RLp5_Ap5_1b | eq_RLp5_Ap5_1a

dcRLp5dt_1_A_p_5 = L*R_p_5*k_1_A_p_5

 

a reverse reaction rate for the transition

eq_RLp5_Ap5_2a:= eq_Rp5_Ap5_2a

Rate_2_A_p_5 = RL_p_5*k_2_A_p_5

a partial conversion rate of RL''''' in this transition

molecularity:=-1:
eq_RLp5_Ap5_2b:= dcRLp5dt_2_A_p_5 = molecularity*Rate_2_A_p_5

dcRLp5dt_2_A_p_5 = -Rate_2_A_p_5

the final form

eq_RLp5_Ap5_2c:= eq_RLp5_Ap5_2b | eq_RLp5_Ap5_2a

dcRLp5dt_2_A_p_5 = -RL_p_5*k_2_A_p_5

 

 

 

 

 

RL''''' <=> RL*

Constants: k_1_B_2_p_5 (forward), k_2_B_2_p_5 (reverse).

 

Equations subgroup: B2p5

 

a forward reaction rate  for the transition

eq_RLp5_B2p5_1a:= Rate_1_B_2_p_5 = k_1_B_2_p_5*RL_p_5

Rate_1_B_2_p_5 = RL_p_5*k_1_B_2_p_5

a partial conversion rate of RL''''' in this transition

molecularity:=-1:
eq_RLp5_B2p5_1b:= dcRLp5dt_1_B_2_p_5 = molecularity*Rate_1_B_2_p_5

dcRLp5dt_1_B_2_p_5 = -Rate_1_B_2_p_5

the final form

eq_RLp5_B2p5_1c:= eq_RLp5_B2p5_1b | eq_RLp5_B2p5_1a

dcRLp5dt_1_B_2_p_5 = -RL_p_5*k_1_B_2_p_5

 

a reverse reaction rate for the transition

eq_RLp5_B2p5_2a:= Rate_2_B_2_p_5 = k_2_B_2_p_5*RL_s

Rate_2_B_2_p_5 = RL_s*k_2_B_2_p_5

      a partial conversion rate of RL''''' in this transition

molecularity:=1:
eq_RLp5_B2p5_2b:= dcRLp5dt_2_B_2_p_5 = molecularity*Rate_2_B_2_p_5

dcRLp5dt_2_B_2_p_5 = Rate_2_B_2_p_5

     the final form

eq_RLp5_B2p5_2c:= eq_RLp5_B2p5_2b | eq_RLp5_B2p5_2a

dcRLp5dt_2_B_2_p_5 = RL_s*k_2_B_2_p_5

 

 

 

 

RL' <=> RL'''''

Constants: k_1_C_2_p_1_5 (forward), k_2_C_2_p_1_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p15

 

a forward reaction rate  for the transition

eq_RLp5_C2p15_1a:= eq_RLp1_C2p15_1a

Rate_1_C_2_p_1_5 = RL_p_1*k_1_C_2_p_1_5

   a partial conversion rate of RL''''' in this transition

molecularity:=1:
eq_RLp5_C2p15_1b:= dcRLp5dt_1_C_2_p_1_5 = molecularity*Rate_1_C_2_p_1_5

dcRLp5dt_1_C_2_p_1_5 = Rate_1_C_2_p_1_5

  the final form

eq_RLp5_C2p15_1c:= eq_RLp5_C2p15_1b | eq_RLp5_C2p15_1a

dcRLp5dt_1_C_2_p_1_5 = RL_p_1*k_1_C_2_p_1_5

 

a reverse reaction rate for the transition

eq_RLp5_C2p15_2a:= eq_RLp1_C2p15_2a

Rate_2_C_2_p_1_5 = RL_p_5*k_2_C_2_p_1_5

  a partial conversion rate of RL''''' in this transition

molecularity:=-1:
eq_RLp5_C2p15_2b:= dcRLp5dt_2_C_2_p_1_5 = molecularity*Rate_2_C_2_p_1_5

dcRLp5dt_2_C_2_p_1_5 = -Rate_2_C_2_p_1_5

the final form

eq_RLp5_C2p15_2c:= eq_RLp5_C2p15_2b | eq_RLp5_C2p15_2a

dcRLp5dt_2_C_2_p_1_5 = -RL_p_5*k_2_C_2_p_1_5

 

 

 

RL'' <=> RL'''''

Constants: k_1_C_2_p_2_5 (forward), k_2_C_2_p_2_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p25

 

a forward reaction rate  for the transition

eq_RLp5_C2p25_1a:= eq_RLp2_C2p25_1a

Rate_1_C_2_p_2_5 = RL_p_2*k_1_C_2_p_2_5

a partial conversion rate of RL''''' in this transition

molecularity:=1:
eq_RLp5_C2p25_1b:= dcRLp5dt_1_C_2_p_2_5 = molecularity*Rate_1_C_2_p_2_5

dcRLp5dt_1_C_2_p_2_5 = Rate_1_C_2_p_2_5

  the final form

eq_RLp5_C2p25_1c:= eq_RLp5_C2p25_1b | eq_RLp5_C2p25_1a

dcRLp5dt_1_C_2_p_2_5 = RL_p_2*k_1_C_2_p_2_5

 

a reverse reaction rate for the transition

eq_RLp5_C2p25_2a:= eq_RLp2_C2p25_2a

Rate_2_C_2_p_2_5 = RL_p_5*k_2_C_2_p_2_5

  a partial conversion rate of RL''''' in this transition

molecularity:=-1:
eq_RLp5_C2p25_2b:= dcRLp5dt_2_C_2_p_2_5 = molecularity*Rate_2_C_2_p_2_5

dcRLp5dt_2_C_2_p_2_5 = -Rate_2_C_2_p_2_5

the final form

eq_RLp5_C2p25_2c:= eq_RLp5_C2p25_2b | eq_RLp5_C2p25_2a

dcRLp5dt_2_C_2_p_2_5 = -RL_p_5*k_2_C_2_p_2_5

 

 

 

 

RL''' <=> RL'''''

Constants: k_1_C_2_p_3_5 (forward), k_2_C_2_p_3_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p35

 

a forward reaction rate  for the transition

eq_RLp5_C2p35_1a:= eq_RLp3_C2p35_1a

Rate_1_C_2_p_3_5 = RL_p_3*k_1_C_2_p_3_5

a partial conversion rate of RL''''' in this transition

molecularity:=1:
eq_RLp5_C2p35_1b:= dcRLp5dt_1_C_2_p_3_5 = molecularity*Rate_1_C_2_p_3_5

dcRLp5dt_1_C_2_p_3_5 = Rate_1_C_2_p_3_5

  the final form

eq_RLp5_C2p35_1c:= eq_RLp5_C2p35_1b | eq_RLp5_C2p35_1a

dcRLp5dt_1_C_2_p_3_5 = RL_p_3*k_1_C_2_p_3_5

 

 

a reverse reaction rate for the transition

eq_RLp5_C2p35_2a:= eq_RLp3_C2p35_2a

Rate_2_C_2_p_3_5 = RL_p_5*k_2_C_2_p_3_5

  a partial conversion rate of RL''''' in this transition

molecularity:=-1:
eq_RLp5_C2p35_2b:= dcRLp5dt_2_C_2_p_3_5 = molecularity*Rate_2_C_2_p_3_5

dcRLp5dt_2_C_2_p_3_5 = -Rate_2_C_2_p_3_5

the final form

eq_RLp5_C2p35_2c:= eq_RLp5_C2p35_2b | eq_RLp5_C2p35_2a

dcRLp5dt_2_C_2_p_3_5 = -RL_p_5*k_2_C_2_p_3_5

 

 

 

 

 

 

RL'''' <=> RL'''''

Constants: k_1_C_2_p_4_5 (forward), k_2_C_2_p_4_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: C2p45

 

a forward reaction rate  for the transition

eq_RLp5_C2p45_1a:= eq_RLp4_C2p45_1a

Rate_1_C_2_p_4_5 = RL_p_4*k_1_C_2_p_4_5

a partial conversion rate of RL''''' in this transition

molecularity:=1:
eq_RLp5_C2p45_1b:= dcRLp5dt_1_C_2_p_4_5 = molecularity*Rate_1_C_2_p_4_5

dcRLp5dt_1_C_2_p_4_5 = Rate_1_C_2_p_4_5

  the final form

eq_RLp5_C2p45_1c:= eq_RLp5_C2p45_1b | eq_RLp5_C2p45_1a

dcRLp5dt_1_C_2_p_4_5 = RL_p_4*k_1_C_2_p_4_5

 

 

a reverse reaction rate for the transition

eq_RLp5_C2p45_2a:= eq_RLp4_C2p45_2a

Rate_2_C_2_p_4_5 = RL_p_5*k_2_C_2_p_4_5

  a partial conversion rate of RL''''' in this transition

molecularity:=-1:
eq_RLp5_C2p45_2b:= dcRLp5dt_2_C_2_p_4_5 = molecularity*Rate_2_C_2_p_4_5

dcRLp5dt_2_C_2_p_4_5 = -Rate_2_C_2_p_4_5

the final form

eq_RLp5_C2p45_2c:= eq_RLp5_C2p45_2b | eq_RLp5_C2p45_2a

dcRLp5dt_2_C_2_p_4_5 = -RL_p_5*k_2_C_2_p_4_5

 

 

 

Summary of partial conversion rates for the species

eq_RLp5_Ap5_1c;eq_RLp5_Ap5_2c;

dcRLp5dt_1_A_p_5 = L*R_p_5*k_1_A_p_5
dcRLp5dt_2_A_p_5 = -RL_p_5*k_2_A_p_5

eq_RLp5_B2p5_1c;eq_RLp5_B2p5_2c

dcRLp5dt_1_B_2_p_5 = -RL_p_5*k_1_B_2_p_5
dcRLp5dt_2_B_2_p_5 = RL_s*k_2_B_2_p_5

eq_RLp5_C2p15_1c;eq_RLp5_C2p15_2c;
eq_RLp5_C2p25_1c;eq_RLp5_C2p25_2c;
eq_RLp5_C2p35_1c;eq_RLp5_C2p35_2c;
eq_RLp5_C2p45_1c;eq_RLp5_C2p45_2c;

dcRLp5dt_1_C_2_p_1_5 = RL_p_1*k_1_C_2_p_1_5
dcRLp5dt_2_C_2_p_1_5 = -RL_p_5*k_2_C_2_p_1_5
dcRLp5dt_1_C_2_p_2_5 = RL_p_2*k_1_C_2_p_2_5
dcRLp5dt_2_C_2_p_2_5 = -RL_p_5*k_2_C_2_p_2_5
dcRLp5dt_1_C_2_p_3_5 = RL_p_3*k_1_C_2_p_3_5
dcRLp5dt_2_C_2_p_3_5 = -RL_p_5*k_2_C_2_p_3_5
dcRLp5dt_1_C_2_p_4_5 = RL_p_4*k_1_C_2_p_4_5
dcRLp5dt_2_C_2_p_4_5 = -RL_p_5*k_2_C_2_p_4_5

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

1U-R-RL, 2U-R-RL, 3U-R-RL, 4U-R-RL - not needed; no RL''''' species

 

 

5U-R-RL

dcRLp5dt_N = dcRLp5dt_1_A_p_5 + dcRLp5dt_2_A_p_5 + dcRLp5dt_1_B_2_p_5 + dcRLp5dt_2_B_2_p_5 +\
dcRLp5dt_1_C_2_p_1_5 + dcRLp5dt_2_C_2_p_1_5 +\
dcRLp5dt_1_C_2_p_2_5 + dcRLp5dt_2_C_2_p_2_5 +\
dcRLp5dt_1_C_2_p_3_5 + dcRLp5dt_2_C_2_p_3_5 +\
dcRLp5dt_1_C_2_p_4_5 + dcRLp5dt_2_C_2_p_4_5;

dcRLp5dt_N = dcRLp5dt_1_A_p_5 + dcRLp5dt_2_A_p_5 + dcRLp5dt_1_B_2_p_5 + dcRLp5dt_2_B_2_p_5 + dcRLp5dt_1_C_2_p_1_5 + dcRLp5dt_1_C_2_p_2_5 + dcRLp5dt_1_C_2_p_3_5 + dcRLp5dt_1_C_2_p_4_5 + dcRLp5dt_2_C_2_p_1_5 + dcRLp5dt_2_C_2_p_2_5 + dcRLp5dt_2_C_2_p_3_5 + dcRLp5dt_2_C_2_p_4_5

    Substitute (use all equations)

eq_RLp5_N__5U_R_RL:= % | eq_RLp5_Ap5_1c | eq_RLp5_Ap5_2c \
| eq_RLp5_B2p5_1c | eq_RLp5_B2p5_2c \
| eq_RLp5_C2p15_1c | eq_RLp5_C2p15_2c \
| eq_RLp5_C2p25_1c | eq_RLp5_C2p25_2c \
| eq_RLp5_C2p35_1c | eq_RLp5_C2p35_2c \
| eq_RLp5_C2p45_1c | eq_RLp5_C2p45_2c;

dcRLp5dt_N = RL_s*k_2_B_2_p_5 - RL_p_5*k_1_B_2_p_5 - RL_p_5*k_2_A_p_5 + RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_1_C_2_p_2_5 + RL_p_3*k_1_C_2_p_3_5 + RL_p_4*k_1_C_2_p_4_5 - RL_p_5*k_2_C_2_p_1_5 - RL_p_5*k_2_C_2_p_2_5 - RL_p_5*k_2_C_2_p_3_5 - RL_p_5*k_2_C_2_p_4_5 + L*R_p_5*k_1_A_p_5

 

Summary equations for RL'''''

 

eq_RLp5_N__5U_R_RL

dcRLp5dt_N = RL_s*k_2_B_2_p_5 - RL_p_5*k_1_B_2_p_5 - RL_p_5*k_2_A_p_5 + RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_1_C_2_p_2_5 + RL_p_3*k_1_C_2_p_3_5 + RL_p_4*k_1_C_2_p_4_5 - RL_p_5*k_2_C_2_p_1_5 - RL_p_5*k_2_C_2_p_2_5 - RL_p_5*k_2_C_2_p_3_5 - RL_p_5*k_2_C_2_p_4_5 + L*R_p_5*k_1_A_p_5

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

Species: R*

Equations group: Rs 

 

 

 

 

 

R* <=> R'

Constants: k_1_B_1_p_1 (forward), k_2_B_1_p_1 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B1p1

 

 

a forward reaction rate  for the transition

eq_Rs_B1p1_1a:= eq_Rp1_B1p1_1a

Rate_1_B_1_p_1 = R_s*k_1_B_1_p_1

a partial conversion rate of R* in this transition

molecularity:=-1:
eq_Rs_B1p1_1b:= dcRsdt_1_B_1_p_1 = molecularity*Rate_1_B_1_p_1

dcRsdt_1_B_1_p_1 = -Rate_1_B_1_p_1

the final form

eq_Rs_B1p1_1c:= eq_Rs_B1p1_1b | eq_Rs_B1p1_1a

dcRsdt_1_B_1_p_1 = -R_s*k_1_B_1_p_1

 

a reverse reaction rate for the transition

eq_Rs_B1p1_2a:=  eq_Rp1_B1p1_2a

Rate_2_B_1_p_1 = R_p_1*k_2_B_1_p_1

     a partial conversion rate of R* in this transition

molecularity:=1:
eq_Rs_B1p1_2b:= dcRsdt_2_B_1_p_1 = molecularity*Rate_2_B_1_p_1

dcRsdt_2_B_1_p_1 = Rate_2_B_1_p_1

the final form

eq_Rs_B1p1_2c:= eq_Rs_B1p1_2b | eq_Rs_B1p1_2a

dcRsdt_2_B_1_p_1 = R_p_1*k_2_B_1_p_1

 

 

R* <=> R''

Constants: k_1_B_1_p_2 (forward), k_2_B_1_p_2 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B1p2

 

a forward reaction rate  for the transition

eq_Rs_B1p2_1a:= eq_Rp2_B1p2_1a

Rate_1_B_1_p_2 = R_s*k_1_B_1_p_2

a partial conversion rate of R* in this transition

molecularity:=-1:
eq_Rs_B1p2_1b:= dcRsdt_1_B_1_p_2 = molecularity*Rate_1_B_1_p_2

dcRsdt_1_B_1_p_2 = -Rate_1_B_1_p_2

the final form

eq_Rs_B1p2_1c:= eq_Rs_B1p2_1b | eq_Rs_B1p2_1a

dcRsdt_1_B_1_p_2 = -R_s*k_1_B_1_p_2

 

a reverse reaction rate for the transition

eq_Rs_B1p2_2a:=  eq_Rp2_B1p2_2a

Rate_2_B_1_p_2 = R_p_2*k_2_B_1_p_2

    a partial conversion rate of R* in this transition

molecularity:=1:
eq_Rs_B1p2_2b:= dcRsdt_2_B_1_p_2 = molecularity*Rate_2_B_1_p_2

dcRsdt_2_B_1_p_2 = Rate_2_B_1_p_2

the final form

eq_Rs_B1p2_2c:= eq_Rs_B1p2_2b | eq_Rs_B1p2_2a

dcRsdt_2_B_1_p_2 = R_p_2*k_2_B_1_p_2

 

 

 

R* <=> R'''

Constants: k_1_B_1_p_3 (forward), k_2_B_1_p_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B1p3

 

 

a forward reaction rate  for the transition

eq_Rs_B1p3_1a:= eq_Rp3_B1p3_1a

Rate_1_B_1_p_3 = R_s*k_1_B_1_p_3

a partial conversion rate of R* in this transition

molecularity:=-1:
eq_Rs_B1p3_1b:= dcRsdt_1_B_1_p_3 = molecularity*Rate_1_B_1_p_3

dcRsdt_1_B_1_p_3 = -Rate_1_B_1_p_3

the final form

eq_Rs_B1p3_1c:= eq_Rs_B1p3_1b | eq_Rs_B1p3_1a

dcRsdt_1_B_1_p_3 = -R_s*k_1_B_1_p_3

 

a reverse reaction rate for the transition

eq_Rs_B1p3_2a:=  eq_Rp3_B1p3_2a

Rate_2_B_1_p_3 = R_p_3*k_2_B_1_p_3

    a partial conversion rate of R* in this transition

molecularity:=1:
eq_Rs_B1p3_2b:= dcRsdt_2_B_1_p_3 = molecularity*Rate_2_B_1_p_3

dcRsdt_2_B_1_p_3 = Rate_2_B_1_p_3

the final form

eq_Rs_B1p3_2c:= eq_Rs_B1p3_2b | eq_Rs_B1p3_2a

dcRsdt_2_B_1_p_3 = R_p_3*k_2_B_1_p_3

 

 

 

 

 

R* <=> R''''

Constants: k_1_B_1_p_4 (forward), k_2_B_1_p_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B1p4

 

a forward reaction rate  for the transition

eq_Rs_B1p4_1a:= eq_Rp4_B1p4_1a

Rate_1_B_1_p_4 = R_s*k_1_B_1_p_4

a partial conversion rate of R* in this transition

molecularity:=-1:
eq_Rs_B1p4_1b:= dcRsdt_1_B_1_p_4 = molecularity*Rate_1_B_1_p_4

dcRsdt_1_B_1_p_4 = -Rate_1_B_1_p_4

the final form

eq_Rs_B1p4_1c:= eq_Rs_B1p4_1b | eq_Rs_B1p4_1a

dcRsdt_1_B_1_p_4 = -R_s*k_1_B_1_p_4

 

a reverse reaction rate for the transition

eq_Rs_B1p4_2a:=  eq_Rp4_B1p4_2a

Rate_2_B_1_p_4 = R_p_4*k_2_B_1_p_4

    a partial conversion rate of R* in this transition

molecularity:=1:
eq_Rs_B1p4_2b:= dcRsdt_2_B_1_p_4 = molecularity*Rate_2_B_1_p_4

dcRsdt_2_B_1_p_4 = Rate_2_B_1_p_4

the final form

eq_Rs_B1p4_2c:= eq_Rs_B1p4_2b | eq_Rs_B1p4_2a

dcRsdt_2_B_1_p_4 = R_p_4*k_2_B_1_p_4

 

 

 

 

 

R* <=> R'''''

Constants: k_1_B_1_p_5 (forward), k_2_B_1_p_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B1p5

 

a forward reaction rate  for the transition

eq_Rs_B1p5_1a:= eq_Rp5_B1p5_1a

Rate_1_B_1_p_5 = R_s*k_1_B_1_p_5

a partial conversion rate of R* in this transition

molecularity:=-1:
eq_Rs_B1p5_1b:= dcRsdt_1_B_1_p_5 = molecularity*Rate_1_B_1_p_5

dcRsdt_1_B_1_p_5 = -Rate_1_B_1_p_5

the final form

eq_Rs_B1p5_1c:= eq_Rs_B1p5_1b | eq_Rs_B1p5_1a

dcRsdt_1_B_1_p_5 = -R_s*k_1_B_1_p_5

 

a reverse reaction rate for the transition

eq_Rs_B1p5_2a:=  eq_Rp5_B1p5_2a

Rate_2_B_1_p_5 = R_p_5*k_2_B_1_p_5

    a partial conversion rate of R* in this transition

molecularity:=1:
eq_Rs_B1p5_2b:= dcRsdt_2_B_1_p_5 = molecularity*Rate_2_B_1_p_5

dcRsdt_2_B_1_p_5 = Rate_2_B_1_p_5

the final form

eq_Rs_B1p5_2c:= eq_Rs_B1p5_2b | eq_Rs_B1p5_2a

dcRsdt_2_B_1_p_5 = R_p_5*k_2_B_1_p_5

 

 

 

 

 

Summary of partial conversion rates for the species

eq_Rs_B1p1_1c; eq_Rs_B1p1_2c;
eq_Rs_B1p2_1c; eq_Rs_B1p2_2c;
eq_Rs_B1p3_1c; eq_Rs_B1p3_2c;
eq_Rs_B1p4_1c; eq_Rs_B1p4_2c;
eq_Rs_B1p5_1c; eq_Rs_B1p5_2c;

dcRsdt_1_B_1_p_1 = -R_s*k_1_B_1_p_1
dcRsdt_2_B_1_p_1 = R_p_1*k_2_B_1_p_1
dcRsdt_1_B_1_p_2 = -R_s*k_1_B_1_p_2
dcRsdt_2_B_1_p_2 = R_p_2*k_2_B_1_p_2
dcRsdt_1_B_1_p_3 = -R_s*k_1_B_1_p_3
dcRsdt_2_B_1_p_3 = R_p_3*k_2_B_1_p_3
dcRsdt_1_B_1_p_4 = -R_s*k_1_B_1_p_4
dcRsdt_2_B_1_p_4 = R_p_4*k_2_B_1_p_4
dcRsdt_1_B_1_p_5 = -R_s*k_1_B_1_p_5
dcRsdt_2_B_1_p_5 = R_p_5*k_2_B_1_p_5

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

 

1U-R-RL

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_2_B_1_p_1 ;

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_2_B_1_p_1

   Substitute (use all equations)

eq_Rs_N__1U_R_RL:= % |  \
eq_Rs_B1p1_1c | eq_Rs_B1p1_2c | \
eq_Rs_B1p2_1c | eq_Rs_B1p2_2c | \
eq_Rs_B1p3_1c | eq_Rs_B1p3_2c | \
eq_Rs_B1p4_1c | eq_Rs_B1p4_2c | \
eq_Rs_B1p5_1c | eq_Rs_B1p5_2c ;

dcRsdt_N = R_p_1*k_2_B_1_p_1 - R_s*k_1_B_1_p_1

 

 

 

2U-R-RL

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_2_B_1_p_1 +\
dcRsdt_1_B_1_p_2 + dcRsdt_2_B_1_p_2;

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_1_B_1_p_2 + dcRsdt_2_B_1_p_1 + dcRsdt_2_B_1_p_2

   Substitute (use all equations)

eq_Rs_N__2U_R_RL:= % |  \
eq_Rs_B1p1_1c | eq_Rs_B1p1_2c | \
eq_Rs_B1p2_1c | eq_Rs_B1p2_2c | \
eq_Rs_B1p3_1c | eq_Rs_B1p3_2c | \
eq_Rs_B1p4_1c | eq_Rs_B1p4_2c | \
eq_Rs_B1p5_1c | eq_Rs_B1p5_2c ;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2

 

 

 

 

3U-R-RL

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_2_B_1_p_1 +\
dcRsdt_1_B_1_p_2 + dcRsdt_2_B_1_p_2 +\
dcRsdt_1_B_1_p_3 + dcRsdt_2_B_1_p_3;

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_1_B_1_p_2 + dcRsdt_1_B_1_p_3 + dcRsdt_2_B_1_p_1 + dcRsdt_2_B_1_p_2 + dcRsdt_2_B_1_p_3

   Substitute (use all equations)

eq_Rs_N__3U_R_RL:= % |  \
eq_Rs_B1p1_1c | eq_Rs_B1p1_2c | \
eq_Rs_B1p2_1c | eq_Rs_B1p2_2c | \
eq_Rs_B1p3_1c | eq_Rs_B1p3_2c | \
eq_Rs_B1p4_1c | eq_Rs_B1p4_2c | \
eq_Rs_B1p5_1c | eq_Rs_B1p5_2c ;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3

 

 

 

 

4U-R-RL

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_2_B_1_p_1 +\
dcRsdt_1_B_1_p_2 + dcRsdt_2_B_1_p_2 +\
dcRsdt_1_B_1_p_3 + dcRsdt_2_B_1_p_3 +\
dcRsdt_1_B_1_p_4 + dcRsdt_2_B_1_p_4;

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_1_B_1_p_2 + dcRsdt_1_B_1_p_3 + dcRsdt_1_B_1_p_4 + dcRsdt_2_B_1_p_1 + dcRsdt_2_B_1_p_2 + dcRsdt_2_B_1_p_3 + dcRsdt_2_B_1_p_4

   Substitute (use all equations)

eq_Rs_N__4U_R_RL:= % |  \
eq_Rs_B1p1_1c | eq_Rs_B1p1_2c | \
eq_Rs_B1p2_1c | eq_Rs_B1p2_2c | \
eq_Rs_B1p3_1c | eq_Rs_B1p3_2c | \
eq_Rs_B1p4_1c | eq_Rs_B1p4_2c | \
eq_Rs_B1p5_1c | eq_Rs_B1p5_2c ;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4

 

 

 

 

5U-R-RL

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_2_B_1_p_1 +\
dcRsdt_1_B_1_p_2 + dcRsdt_2_B_1_p_2 +\
dcRsdt_1_B_1_p_3 + dcRsdt_2_B_1_p_3 +\
dcRsdt_1_B_1_p_4 + dcRsdt_2_B_1_p_4 +\
dcRsdt_1_B_1_p_5 + dcRsdt_2_B_1_p_5;

dcRsdt_N = dcRsdt_1_B_1_p_1 + dcRsdt_1_B_1_p_2 + dcRsdt_1_B_1_p_3 + dcRsdt_1_B_1_p_4 + dcRsdt_1_B_1_p_5 + dcRsdt_2_B_1_p_1 + dcRsdt_2_B_1_p_2 + dcRsdt_2_B_1_p_3 + dcRsdt_2_B_1_p_4 + dcRsdt_2_B_1_p_5

   Substitute (use all equations)

eq_Rs_N__5U_R_RL:= % |  \
eq_Rs_B1p1_1c | eq_Rs_B1p1_2c | \
eq_Rs_B1p2_1c | eq_Rs_B1p2_2c | \
eq_Rs_B1p3_1c | eq_Rs_B1p3_2c | \
eq_Rs_B1p4_1c | eq_Rs_B1p4_2c | \
eq_Rs_B1p5_1c | eq_Rs_B1p5_2c ;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 + R_p_5*k_2_B_1_p_5 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4 - R_s*k_1_B_1_p_5

 

 

 

 

Summary equations for R*

 

eq_Rs_N__1U_R_RL

dcRsdt_N = R_p_1*k_2_B_1_p_1 - R_s*k_1_B_1_p_1

eq_Rs_N__2U_R_RL

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2

eq_Rs_N__3U_R_RL

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3

eq_Rs_N__4U_R_RL

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4

eq_Rs_N__5U_R_RL

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 + R_p_5*k_2_B_1_p_5 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4 - R_s*k_1_B_1_p_5

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Species: RL*

Equations group: RLs 

 

 

 

 

 

RL' <=> RL*

Constants: k_1_B_2_p_1 (forward), k_2_B_2_p_1 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B2p1

 

a forward reaction rate  for the transition

eq_RLs_B2p1_1a:= eq_RLp1_B2p1_1a

Rate_1_B_2_p_1 = RL_p_1*k_1_B_2_p_1

a partial conversion rate of RL* in this transition

molecularity:=1:
eq_RLs_B2p1_1b:= dcRLsdt_1_B_2_p_1 = molecularity*Rate_1_B_2_p_1

dcRLsdt_1_B_2_p_1 = Rate_1_B_2_p_1

the final form

eq_RLs_B2p1_1c:= eq_RLs_B2p1_1b | eq_RLs_B2p1_1a

dcRLsdt_1_B_2_p_1 = RL_p_1*k_1_B_2_p_1

 

a reverse reaction rate for the transition

eq_RLs_B2p1_2a:=  eq_RLp1_B2p1_2a

Rate_2_B_2_p_1 = RL_s*k_2_B_2_p_1

     a partial conversion rate of RL* in this transition

molecularity:=-1:
eq_RLs_B2p1_2b:= dcRLsdt_2_B_2_p_1 = molecularity*Rate_2_B_2_p_1

dcRLsdt_2_B_2_p_1 = -Rate_2_B_2_p_1

  the final form

eq_RLs_B2p1_2c:= eq_RLs_B2p1_2b | eq_RLs_B2p1_2a

dcRLsdt_2_B_2_p_1 = -RL_s*k_2_B_2_p_1

 

 

 

 

RL'' <=> RL*

Constants: k_1_B_2_p_2 (forward), k_2_B_2_p_2 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B2p2

 

 

a forward reaction rate  for the transition

eq_RLs_B2p2_1a:= eq_RLp2_B2p2_1a

Rate_1_B_2_p_2 = RL_p_2*k_1_B_2_p_2

a partial conversion rate of RL* in this transition

molecularity:=1:
eq_RLs_B2p2_1b:= dcRLsdt_1_B_2_p_2 = molecularity*Rate_1_B_2_p_2

dcRLsdt_1_B_2_p_2 = Rate_1_B_2_p_2

the final form

eq_RLs_B2p2_1c:= eq_RLs_B2p2_1b | eq_RLs_B2p2_1a

dcRLsdt_1_B_2_p_2 = RL_p_2*k_1_B_2_p_2

 

a reverse reaction rate for the transition

eq_RLs_B2p2_2a:=  eq_RLp2_B2p2_2a

Rate_2_B_2_p_2 = RL_s*k_2_B_2_p_2

    a partial conversion rate of RL* in this transition

molecularity:=-1:
eq_RLs_B2p2_2b:= dcRLsdt_2_B_2_p_2 = molecularity*Rate_2_B_2_p_2

dcRLsdt_2_B_2_p_2 = -Rate_2_B_2_p_2

  the final form

eq_RLs_B2p2_2c:= eq_RLs_B2p2_2b | eq_RLs_B2p2_2a

dcRLsdt_2_B_2_p_2 = -RL_s*k_2_B_2_p_2

 

 

 

RL''' <=> RL*

Constants: k_1_B_2_p_3 (forward), k_2_B_2_p_3 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B2p3

 

a forward reaction rate  for the transition

eq_RLs_B2p3_1a:= eq_RLp3_B2p3_1a

Rate_1_B_2_p_3 = RL_p_3*k_1_B_2_p_3

a partial conversion rate of RL* in this transition

molecularity:=1:
eq_RLs_B2p3_1b:= dcRLsdt_1_B_2_p_3 = molecularity*Rate_1_B_2_p_3

dcRLsdt_1_B_2_p_3 = Rate_1_B_2_p_3

the final form

eq_RLs_B2p3_1c:= eq_RLs_B2p3_1b | eq_RLs_B2p3_1a

dcRLsdt_1_B_2_p_3 = RL_p_3*k_1_B_2_p_3

 

a reverse reaction rate for the transition

eq_RLs_B2p3_2a:=  eq_RLp3_B2p3_2a

Rate_2_B_2_p_3 = RL_s*k_2_B_2_p_3

    a partial conversion rate of RL* in this transition

molecularity:=-1:
eq_RLs_B2p3_2b:= dcRLsdt_2_B_2_p_3 = molecularity*Rate_2_B_2_p_3

dcRLsdt_2_B_2_p_3 = -Rate_2_B_2_p_3

  the final form

eq_RLs_B2p3_2c:= eq_RLs_B2p3_2b | eq_RLs_B2p3_2a

dcRLsdt_2_B_2_p_3 = -RL_s*k_2_B_2_p_3

 

 

 

 

RL'''' <=> RL*

Constants: k_1_B_2_p_4 (forward), k_2_B_2_p_4 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B2p4

a forward reaction rate  for the transition

eq_RLs_B2p4_1a:= eq_RLp4_B2p4_1a

Rate_1_B_2_p_4 = RL_p_4*k_1_B_2_p_4

a partial conversion rate of RL* in this transition

molecularity:=1:
eq_RLs_B2p4_1b:= dcRLsdt_1_B_2_p_4 = molecularity*Rate_1_B_2_p_4

dcRLsdt_1_B_2_p_4 = Rate_1_B_2_p_4

the final form

eq_RLs_B2p4_1c:= eq_RLs_B2p4_1b | eq_RLs_B2p4_1a

dcRLsdt_1_B_2_p_4 = RL_p_4*k_1_B_2_p_4

 

 

a reverse reaction rate for the transition

eq_RLs_B2p4_2a:=  eq_RLp4_B2p4_2a

Rate_2_B_2_p_4 = RL_s*k_2_B_2_p_4

   a partial conversion rate of RL* in this transition

molecularity:=-1:
eq_RLs_B2p4_2b:= dcRLsdt_2_B_2_p_4 = molecularity*Rate_2_B_2_p_4

dcRLsdt_2_B_2_p_4 = -Rate_2_B_2_p_4

  the final form

eq_RLs_B2p4_2c:= eq_RLs_B2p4_2b | eq_RLs_B2p4_2a

dcRLsdt_2_B_2_p_4 = -RL_s*k_2_B_2_p_4

 

 

 

 

RL''''' <=> RL*

Constants: k_1_B_2_p_5 (forward), k_2_B_2_p_5 (reverse).

 

NOTE: Kinetic equations for this transition were already defined!

 

Equations subgroup: B2p5

 

a forward reaction rate  for the transition

eq_RLs_B2p5_1a:= eq_RLp5_B2p5_1a

Rate_1_B_2_p_5 = RL_p_5*k_1_B_2_p_5

a partial conversion rate of RL* in this transition

molecularity:=1:
eq_RLs_B2p5_1b:= dcRLsdt_1_B_2_p_5 = molecularity*Rate_1_B_2_p_5

dcRLsdt_1_B_2_p_5 = Rate_1_B_2_p_5

the final form

eq_RLs_B2p5_1c:= eq_RLs_B2p5_1b | eq_RLs_B2p5_1a

dcRLsdt_1_B_2_p_5 = RL_p_5*k_1_B_2_p_5

 

 

a reverse reaction rate for the transition

eq_RLs_B2p5_2a:=  eq_RLp5_B2p5_2a

Rate_2_B_2_p_5 = RL_s*k_2_B_2_p_5

     a partial conversion rate of RL* in this transition

molecularity:=-1:
eq_RLs_B2p5_2b:= dcRLsdt_2_B_2_p_5 = molecularity*Rate_2_B_2_p_5

dcRLsdt_2_B_2_p_5 = -Rate_2_B_2_p_5

  the final form

eq_RLs_B2p5_2c:= eq_RLs_B2p5_2b | eq_RLs_B2p5_2a

dcRLsdt_2_B_2_p_5 = -RL_s*k_2_B_2_p_5

 

 

 

 

 

Summary of partial conversion rates for the species

eq_RLs_B2p1_1c; eq_RLs_B2p1_2c;
eq_RLs_B2p2_1c; eq_RLs_B2p2_2c;
eq_RLs_B2p3_1c; eq_RLs_B2p3_2c;
eq_RLs_B2p4_1c; eq_RLs_B2p4_2c;
eq_RLs_B2p5_1c; eq_RLs_B2p5_2c;

dcRLsdt_1_B_2_p_1 = RL_p_1*k_1_B_2_p_1
dcRLsdt_2_B_2_p_1 = -RL_s*k_2_B_2_p_1
dcRLsdt_1_B_2_p_2 = RL_p_2*k_1_B_2_p_2
dcRLsdt_2_B_2_p_2 = -RL_s*k_2_B_2_p_2
dcRLsdt_1_B_2_p_3 = RL_p_3*k_1_B_2_p_3
dcRLsdt_2_B_2_p_3 = -RL_s*k_2_B_2_p_3
dcRLsdt_1_B_2_p_4 = RL_p_4*k_1_B_2_p_4
dcRLsdt_2_B_2_p_4 = -RL_s*k_2_B_2_p_4
dcRLsdt_1_B_2_p_5 = RL_p_5*k_1_B_2_p_5
dcRLsdt_2_B_2_p_5 = -RL_s*k_2_B_2_p_5

 

 

 

 

 

 

Net conversion rate for the species

I will create equations for all five versions of the mechanism.

 

 

 

 

1U-R-RL

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_2_B_2_p_1;

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_2_B_2_p_1

   Substitute (use all equations)

eq_RLs_N__1U_R_RL:= % |  \
eq_RLs_B2p1_1c | eq_RLs_B2p1_2c | \
eq_RLs_B2p2_1c | eq_RLs_B2p2_2c | \
eq_RLs_B2p3_1c | eq_RLs_B2p3_2c | \
eq_RLs_B2p4_1c | eq_RLs_B2p4_2c | \
eq_RLs_B2p5_1c | eq_RLs_B2p5_2c ;

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 - RL_s*k_2_B_2_p_1

 

 

 

 

2U-R-RL

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_2_B_2_p_1 +\
dcRLsdt_1_B_2_p_2 + dcRLsdt_2_B_2_p_2;

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_1_B_2_p_2 + dcRLsdt_2_B_2_p_1 + dcRLsdt_2_B_2_p_2

   Substitute (use all equations)

eq_RLs_N__2U_R_RL:= % |  \
eq_RLs_B2p1_1c | eq_RLs_B2p1_2c | \
eq_RLs_B2p2_1c | eq_RLs_B2p2_2c | \
eq_RLs_B2p3_1c | eq_RLs_B2p3_2c | \
eq_RLs_B2p4_1c | eq_RLs_B2p4_2c | \
eq_RLs_B2p5_1c | eq_RLs_B2p5_2c ;

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2

 

 

 

3U-R-RL

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_2_B_2_p_1 +\
dcRLsdt_1_B_2_p_2 + dcRLsdt_2_B_2_p_2 +\
dcRLsdt_1_B_2_p_3 + dcRLsdt_2_B_2_p_3;

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_1_B_2_p_2 + dcRLsdt_1_B_2_p_3 + dcRLsdt_2_B_2_p_1 + dcRLsdt_2_B_2_p_2 + dcRLsdt_2_B_2_p_3

   Substitute (use all equations)

eq_RLs_N__3U_R_RL:= % |  \
eq_RLs_B2p1_1c | eq_RLs_B2p1_2c | \
eq_RLs_B2p2_1c | eq_RLs_B2p2_2c | \
eq_RLs_B2p3_1c | eq_RLs_B2p3_2c | \
eq_RLs_B2p4_1c | eq_RLs_B2p4_2c | \
eq_RLs_B2p5_1c | eq_RLs_B2p5_2c ;

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3

 

 

 

 

4U-R-RL

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_2_B_2_p_1 +\
dcRLsdt_1_B_2_p_2 + dcRLsdt_2_B_2_p_2 +\
dcRLsdt_1_B_2_p_3 + dcRLsdt_2_B_2_p_3 +\
dcRLsdt_1_B_2_p_4 + dcRLsdt_2_B_2_p_4;

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_1_B_2_p_2 + dcRLsdt_1_B_2_p_3 + dcRLsdt_1_B_2_p_4 + dcRLsdt_2_B_2_p_1 + dcRLsdt_2_B_2_p_2 + dcRLsdt_2_B_2_p_3 + dcRLsdt_2_B_2_p_4

   Substitute (use all equations)

eq_RLs_N__4U_R_RL:= % |  \
eq_RLs_B2p1_1c | eq_RLs_B2p1_2c | \
eq_RLs_B2p2_1c | eq_RLs_B2p2_2c | \
eq_RLs_B2p3_1c | eq_RLs_B2p3_2c | \
eq_RLs_B2p4_1c | eq_RLs_B2p4_2c | \
eq_RLs_B2p5_1c | eq_RLs_B2p5_2c ;

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4

 

 

 

5U-R-RL

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_2_B_2_p_1 +\
dcRLsdt_1_B_2_p_2 + dcRLsdt_2_B_2_p_2 +\
dcRLsdt_1_B_2_p_3 + dcRLsdt_2_B_2_p_3 +\
dcRLsdt_1_B_2_p_4 + dcRLsdt_2_B_2_p_4 +\
dcRLsdt_1_B_2_p_5 + dcRLsdt_2_B_2_p_5;

dcRLsdt_N = dcRLsdt_1_B_2_p_1 + dcRLsdt_1_B_2_p_2 + dcRLsdt_1_B_2_p_3 + dcRLsdt_1_B_2_p_4 + dcRLsdt_1_B_2_p_5 + dcRLsdt_2_B_2_p_1 + dcRLsdt_2_B_2_p_2 + dcRLsdt_2_B_2_p_3 + dcRLsdt_2_B_2_p_4 + dcRLsdt_2_B_2_p_5

   Substitute (use all equations)

eq_RLs_N__5U_R_RL:= % |  \
eq_RLs_B2p1_1c | eq_RLs_B2p1_2c | \
eq_RLs_B2p2_1c | eq_RLs_B2p2_2c | \
eq_RLs_B2p3_1c | eq_RLs_B2p3_2c | \
eq_RLs_B2p4_1c | eq_RLs_B2p4_2c | \
eq_RLs_B2p5_1c | eq_RLs_B2p5_2c ;

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 + RL_p_5*k_1_B_2_p_5 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4 - RL_s*k_2_B_2_p_5

 

 

 

 

 

Summary equations for RL*

 

eq_RLs_N__1U_R_RL

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 - RL_s*k_2_B_2_p_1

eq_RLs_N__2U_R_RL

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2

eq_RLs_N__3U_R_RL

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3

eq_RLs_N__4U_R_RL

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4

eq_RLs_N__5U_R_RL

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 + RL_p_5*k_1_B_2_p_5 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4 - RL_s*k_2_B_2_p_5

 

 

Back to  Equations for each species

 

 

 

 

 

 

 

Expression in terms of spin (monomer) concentrations

 

=>>>  not needed here because we do not have oligomerization reactions.

 

 

 

 

 

 

Back to Contents

 

 

 

 

 

Control expession of K matrix for U-1R-RL mechanism using old order of species

 

 

This is a derivation for comparison with the existing U-R-RL mechanism matrix: order of species as
R, R*, RL, RL* =>
R', R*, RL', RL*

 

 

Summary list of the net rate equations for the mechanism

eq_Rp1_N__1U_R_RL;
eq_RLp1_N__1U_R_RL;
eq_Rs_N__1U_R_RL;
eq_RLs_N__1U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - L*R_p_1*k_1_A_p_1
dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 + L*R_p_1*k_1_A_p_1
dcRsdt_N = R_p_1*k_2_B_1_p_1 - R_s*k_1_B_1_p_1
dcRLsdt_N = RL_p_1*k_1_B_2_p_1 - RL_s*k_2_B_2_p_1

 

 

Assign sequential names to species

feq_1a:= R_p_1    = C1;
feq_1b:= R_s      = C2;
feq_1c:= RL_p_1   = C3;
feq_1d:= RL_s     = C4;

R_p_1 = C1
R_s = C2
RL_p_1 = C3
RL_s = C4

 

 

Assign the same order to net rate equations

feq_2a:= dcRp1dt_N      = dC1dt;
feq_2b:= dcRsdt_N    = dC2dt;
feq_2c:= dcRLp1dt_N     = dC3dt;
feq_2d:= dcRLsdt_N   = dC4dt;

dcRp1dt_N = dC1dt
dcRsdt_N = dC2dt
dcRLp1dt_N = dC3dt
dcRLsdt_N = dC4dt

 

 

Restate the equations in terms of new sequential species names (rename free ligand concentration too)

R'

eq_Rp1_N__1U_R_RL;
feq_3a:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - L*R_p_1*k_1_A_p_1
dC1dt = C3*k_2_A_p_1 + C2*k_1_B_1_p_1 - C1*k_2_B_1_p_1 - C1*Leq*k_1_A_p_1

R*

eq_Rs_N__1U_R_RL;
feq_3b:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRsdt_N = R_p_1*k_2_B_1_p_1 - R_s*k_1_B_1_p_1
dC2dt = C1*k_2_B_1_p_1 - C2*k_1_B_1_p_1

RL'

eq_RLp1_N__1U_R_RL;
feq_3c:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 + L*R_p_1*k_1_A_p_1
dC3dt = C4*k_2_B_2_p_1 - C3*k_1_B_2_p_1 - C3*k_2_A_p_1 + C1*Leq*k_1_A_p_1

RL*

eq_RLs_N__1U_R_RL;
feq_3d:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 - RL_s*k_2_B_2_p_1
dC4dt = C3*k_1_B_2_p_1 - C4*k_2_B_2_p_1

 

 

Prepare results for transfer to MATLAB

 

See Workflow for accurate extraction of the K matrix

 

 

 

Simple rules that allow catching mistakes in K matrix derivation:

   

   (1) a sum of each column should be zero (so each constant must appear with both positive and negative sign), and 

 

   (2) each row has to have complete pairs of constants (i.e., if k12

    appears there must be k21 in the same row with an opposite sign and so on).

K:=matrix(4,4,[
[   -k_2_B_1_p_1 -Leq*k_1_A_p_1, k_1_B_1_p_1, k_2_A_p_1, 0      ],
[ k_2_B_1_p_1,  -k_1_B_1_p_1, 0, 0      ],
[  Leq*k_1_A_p_1, 0 , -k_1_B_2_p_1 -k_2_A_p_1,   k_2_B_2_p_1    ],
[  0, 0, k_1_B_2_p_1, -k_2_B_2_p_1     ]
])

matrix([[- k_2_B_1_p_1 - Leq*k_1_A_p_1, k_1_B_1_p_1, k_2_A_p_1, 0], [k_2_B_1_p_1, -k_1_B_1_p_1, 0, 0], [Leq*k_1_A_p_1, 0, - k_2_A_p_1 - k_1_B_2_p_1, k_2_B_2_p_1], [0, 0, k_1_B_2_p_1, -k_2_B_2_p_1]])

 

Test the K matrix entry

 

Create a column vector of species concentrations

P:=matrix(4,1,[C1, C2, C3, C4])

matrix([[C1], [C2], [C3], [C4]])

Multiply K and P:

dCdt_manual_input:= K*P

matrix([[C3*k_2_A_p_1 + C2*k_1_B_1_p_1 - C1*(k_2_B_1_p_1 + Leq*k_1_A_p_1)], [C1*k_2_B_1_p_1 - C2*k_1_B_1_p_1], [C4*k_2_B_2_p_1 - C3*(k_2_A_p_1 + k_1_B_2_p_1) + C1*Leq*k_1_A_p_1], [C3*k_1_B_2_p_1 - C4*k_2_B_2_p_1]])

Collect right-hand-side parts of net rate equations expressed in sequential species names

dCdt_mupad:=matrix(4,1,[ rhs(feq_3a), rhs(feq_3b), rhs(feq_3c), rhs(feq_3d)])

matrix([[C3*k_2_A_p_1 + C2*k_1_B_1_p_1 - C1*k_2_B_1_p_1 - C1*Leq*k_1_A_p_1], [C1*k_2_B_1_p_1 - C2*k_1_B_1_p_1], [C4*k_2_B_2_p_1 - C3*k_1_B_2_p_1 - C3*k_2_A_p_1 + C1*Leq*k_1_A_p_1], [C3*k_1_B_2_p_1 - C4*k_2_B_2_p_1]])

 

Compare derivation result to manual input

dCdt_mupad=dCdt_manual_input:
normal(%);
bool(%)

matrix([[C3*k_2_A_p_1 + C2*k_1_B_1_p_1 - C1*k_2_B_1_p_1 - C1*Leq*k_1_A_p_1], [C1*k_2_B_1_p_1 - C2*k_1_B_1_p_1], [C4*k_2_B_2_p_1 - C3*k_1_B_2_p_1 - C3*k_2_A_p_1 + C1*Leq*k_1_A_p_1], [C3*k_1_B_2_p_1 - C4*k_2_B_2_p_1]]) = matrix([[C3*k_2_A_p_1 + C2*k_1_B_1_p_1 - C1*k_2_B_1_p_1 - C1*Leq*k_1_A_p_1], [C1*k_2_B_1_p_1 - C2*k_1_B_1_p_1], [C4*k_2_B_2_p_1 - C3*k_1_B_2_p_1 - C3*k_2_A_p_1 + C1*Leq*k_1_A_p_1], [C3*k_1_B_2_p_1 - C4*k_2_B_2_p_1]])
TRUE

 

 

Compare to:

/Users/kovrigin_laptop/Documents/Workspace/Global_Analysis/IDAP/Mathematical_models/NMR_line_shape_models/U_5R_RL/U_5R_RL.mn

 

/Users/kovrigin_laptop/Documents/Workspace/Global_Analysis/IDAP/Mathematical_models/NMR_line_shape_models/U_R_RL/U_R_RL.mn

 

Conclusion:
Typed K-matrix is correct and corresponds to U-R-RL matrix derived earlier for IDAP if A2 transition is removed.

 

 

Back to Contents

 

 

 

 

 

 

 

 

 

 

 

 

Expession of K matrix for U-1R-RL mechanism with current order of species

 

 

Order of species to allow for easy expansion of matrices:

R*, RL*, R', RL',  R'', RL'',  R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

Summary list of the net rate equations for the mechanism

eq_Rp1_N__1U_R_RL;
eq_RLp1_N__1U_R_RL;
eq_Rs_N__1U_R_RL;
eq_RLs_N__1U_R_RL

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - L*R_p_1*k_1_A_p_1
dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 + L*R_p_1*k_1_A_p_1
dcRsdt_N = R_p_1*k_2_B_1_p_1 - R_s*k_1_B_1_p_1
dcRLsdt_N = RL_p_1*k_1_B_2_p_1 - RL_s*k_2_B_2_p_1

 

Assign sequential names to species

feq_1a:= R_s        = C1;
feq_1b:= RL_s       = C2;
feq_1c:= R_p_1      = C3;
feq_1d:= RL_p_1     = C4;

R_s = C1
RL_s = C2
R_p_1 = C3
RL_p_1 = C4

 

 

Assign the same order to net rate equations

feq_2a:= dcRsdt_N      = dC1dt;
feq_2b:= dcRLsdt_N    = dC2dt;
feq_2c:= dcRp1dt_N     = dC3dt;
feq_2d:= dcRLp1dt_N   = dC4dt;

dcRsdt_N = dC1dt
dcRLsdt_N = dC2dt
dcRp1dt_N = dC3dt
dcRLp1dt_N = dC4dt

 

 

Restate the equations in terms of new sequential species names (rename free ligand concentration too)

R*

eq_Rs_N__1U_R_RL;
feq_3a:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRsdt_N = R_p_1*k_2_B_1_p_1 - R_s*k_1_B_1_p_1
dC1dt = C3*k_2_B_1_p_1 - C1*k_1_B_1_p_1

RL*

eq_RLs_N__1U_R_RL;
feq_3b:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 - RL_s*k_2_B_2_p_1
dC2dt = C4*k_1_B_2_p_1 - C2*k_2_B_2_p_1

R'

eq_Rp1_N__1U_R_RL;
feq_3c:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - L*R_p_1*k_1_A_p_1
dC3dt = C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*Leq*k_1_A_p_1

RL'

eq_RLp1_N__1U_R_RL;
feq_3d:= % | feq_1a | feq_1b | feq_1c | feq_2a | feq_2b | feq_2c |  feq_1d |  feq_2d |  L = Leq

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 + L*R_p_1*k_1_A_p_1
dC4dt = C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 + C3*Leq*k_1_A_p_1

 

 

 

Prepare results for transfer to MATLAB

 

See Workflow for accurate extraction of the K matrix

 

 

 

Simple rules that allow catching mistakes in K matrix derivation:

   

   (1) a sum of each column should be zero (so each constant must appear with both positive and negative sign), and 

 

   (2) each row has to have complete pairs of constants (i.e., if k12

    appears there must be k21 in the same row with an opposite sign and so on).

K:=matrix(4,4,[
[  -k_1_B_1_p_1,     0,              k_2_B_1_p_1, 0    ],
[      0,           -k_2_B_2_p_1,     0,          k_1_B_2_p_1  ],
[  k_1_B_1_p_1,     0,           -k_2_B_1_p_1 -Leq*k_1_A_p_1, k_2_A_p_1    ],
[    0,            k_2_B_2_p_1, Leq*k_1_A_p_1, -k_1_B_2_p_1 -k_2_A_p_1      ]
])

matrix([[-k_1_B_1_p_1, 0, k_2_B_1_p_1, 0], [0, -k_2_B_2_p_1, 0, k_1_B_2_p_1], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - Leq*k_1_A_p_1, k_2_A_p_1], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1]])

 

Test the K matrix entry

 

Create a column vector of species concentrations

P:=matrix(4,1,[C1, C2, C3, C4])

matrix([[C1], [C2], [C3], [C4]])

Multiply K and P:

dCdt_manual_input:= K*P

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_1], [C4*k_1_B_2_p_1 - C2*k_2_B_2_p_1], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*(k_2_B_1_p_1 + Leq*k_1_A_p_1)], [C2*k_2_B_2_p_1 - C4*(k_2_A_p_1 + k_1_B_2_p_1) + C3*Leq*k_1_A_p_1]])

 

Collect right-hand-side parts of net rate equations expressed in sequential species names

dCdt_mupad:=matrix(4,1,[ rhs(feq_3a), rhs(feq_3b), rhs(feq_3c), rhs(feq_3d)])

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_1], [C4*k_1_B_2_p_1 - C2*k_2_B_2_p_1], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 + C3*Leq*k_1_A_p_1]])

 

Compare derivation result to manual input

dCdt_mupad=dCdt_manual_input:
normal(%);
bool(%)

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_1], [C4*k_1_B_2_p_1 - C2*k_2_B_2_p_1], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 + C3*Leq*k_1_A_p_1]]) = matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_1], [C4*k_1_B_2_p_1 - C2*k_2_B_2_p_1], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 + C3*Leq*k_1_A_p_1]])
TRUE

Conclusion:
Typed K-matrix is correct

 

 

 

K matrix for the 1U-R-RL model with the new species order

K;

matrix([[-k_1_B_1_p_1, 0, k_2_B_1_p_1, 0], [0, -k_2_B_2_p_1, 0, k_1_B_2_p_1], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - Leq*k_1_A_p_1, k_2_A_p_1], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1]])

 

 

 

 

Back to Contents

 

 

 

 

 

 

 

 

 

Expession of K matrix for U-2R-RL mechanism

 

 

Order of species to allow for easy expansion of matrices:

R*, RL*, R', RL',  R'', RL'',  R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

Summary list of the net rate equations for the mechanism

eq_Rs_N__2U_R_RL;
eq_RLs_N__2U_R_RL;
eq_Rp1_N__2U_R_RL;
eq_RLp1_N__2U_R_RL;
eq_Rp2_N__2U_R_RL;
eq_Rp2_N__2U_R_RL;
eq_RLp2_N__2U_R_RL;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2
dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2
dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 + R_p_2*k_2_C_1_p_1_2 - L*R_p_1*k_1_A_p_1
dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 + RL_p_2*k_2_C_2_p_1_2 + L*R_p_1*k_1_A_p_1
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_2_C_1_p_1_2 - L*R_p_2*k_1_A_p_2
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_2_C_1_p_1_2 - L*R_p_2*k_1_A_p_2
dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_2_C_2_p_1_2 + L*R_p_2*k_1_A_p_2

 

 

Assign sequential names to species

feq_1a:= R_s        = C1;
feq_1b:= RL_s       = C2;
feq_1c:= R_p_1      = C3;
feq_1d:= RL_p_1     = C4;
feq_1e:= R_p_2      = C5;
feq_1f:= RL_p_2     = C6;

R_s = C1
RL_s = C2
R_p_1 = C3
RL_p_1 = C4
R_p_2 = C5
RL_p_2 = C6

 

Assign the same order to net rate equations

feq_2a:= dcRsdt_N      = dC1dt;
feq_2b:= dcRLsdt_N     = dC2dt;
feq_2c:= dcRp1dt_N     = dC3dt;
feq_2d:= dcRLp1dt_N    = dC4dt;
feq_2e:= dcRp2dt_N     = dC5dt;
feq_2f:= dcRLp2dt_N    = dC6dt;

dcRsdt_N = dC1dt
dcRLsdt_N = dC2dt
dcRp1dt_N = dC3dt
dcRLp1dt_N = dC4dt
dcRp2dt_N = dC5dt
dcRLp2dt_N = dC6dt

 

Restate the equations in terms of new sequential species names (rename free ligand concentration too)

R*

eq_Rs_N__2U_R_RL;
feq_3a:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  L = Leq

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2
dC1dt = C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2

RL*

eq_RLs_N__2U_R_RL;
feq_3b:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  L = Leq

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2
dC2dt = C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2

R'

eq_Rp1_N__2U_R_RL;
feq_3c:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  L = Leq

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 + R_p_2*k_2_C_1_p_1_2 - L*R_p_1*k_1_A_p_1
dC3dt = C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 + C5*k_2_C_1_p_1_2 - C3*Leq*k_1_A_p_1

RL'

eq_RLp1_N__2U_R_RL;
feq_3d:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  L = Leq

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 + RL_p_2*k_2_C_2_p_1_2 + L*R_p_1*k_1_A_p_1
dC4dt = C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 + C6*k_2_C_2_p_1_2 + C3*Leq*k_1_A_p_1

R''

eq_Rp2_N__2U_R_RL;
feq_3e:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  L = Leq

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_2_C_1_p_1_2 - L*R_p_2*k_1_A_p_2
dC5dt = C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_2_C_1_p_1_2 - C5*Leq*k_1_A_p_2

RL''

eq_RLp2_N__2U_R_RL;
feq_3f:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  L = Leq

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_2_C_2_p_1_2 + L*R_p_2*k_1_A_p_2
dC6dt = C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_2_C_2_p_1_2 + C5*Leq*k_1_A_p_2

 

 

Prepare results for transfer to MATLAB

 

See Workflow for accurate extraction of the K matrix

 

 

 

Simple rules that allow catching mistakes in K matrix derivation:

   

   (1) a sum of each column should be zero (so each constant must appear with both positive and negative sign), and 

 

   (2) each row has to have complete pairs of constants (i.e., if k12

    appears there must be k21 in the same row with an opposite sign and so on).

K:=matrix(6,6,[
[  -k_1_B_1_p_2 -k_1_B_1_p_1,0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0   ],
[ 0, -k_2_B_2_p_1 -k_2_B_2_p_2, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2       ],
[  k_1_B_1_p_1, 0, -k_2_B_1_p_1 -k_1_C_1_p_1_2 -Leq*k_1_A_p_1, k_2_A_p_1 , k_2_C_1_p_1_2, 0   ],
[    0, k_2_B_2_p_1, Leq*k_1_A_p_1,  -k_1_B_2_p_1 -k_2_A_p_1 -k_1_C_2_p_1_2, 0, k_2_C_2_p_1_2     ],
[  k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0,  -k_2_B_1_p_2 -k_2_C_1_p_1_2 -Leq*k_1_A_p_2,  k_2_A_p_2   ],
[    0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2,  -k_1_B_2_p_2 -k_2_A_p_2 -k_2_C_2_p_1_2     ]
])

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2, 0, k_2_C_2_p_1_2], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_2_C_2_p_1_2]])

 

Test the K matrix entry

 

Create a column vector of species concentrations

P:=matrix(6,1,[C1, C2, C3, C4, C5, C6])

matrix([[C1], [C2], [C3], [C4], [C5], [C6]])

  

Multiply K and P:

dCdt_manual_input:= K*P

matrix([[C3*k_2_B_1_p_1 + C5*k_2_B_1_p_2 - C1*(k_1_B_1_p_1 + k_1_B_1_p_2)], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 - C2*(k_2_B_2_p_1 + k_2_B_2_p_2)], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 + C5*k_2_C_1_p_1_2 - C3*(k_2_B_1_p_1 + k_1_C_1_p_1_2 + Leq*k_1_A_p_1)], [C2*k_2_B_2_p_1 + C6*k_2_C_2_p_1_2 - C4*(k_2_A_p_1 + k_1_B_2_p_1 + k_1_C_2_p_1_2) + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*(k_2_B_1_p_2 + k_2_C_1_p_1_2 + Leq*k_1_A_p_2)], [C2*k_2_B_2_p_2 + C4*k_1_C_2_p_1_2 - C6*(k_2_A_p_2 + k_1_B_2_p_2 + k_2_C_2_p_1_2) + C5*Leq*k_1_A_p_2]])

 

Collect right-hand-side parts of net rate equations expressed in sequential species names

dCdt_mupad:=matrix(6,1,[ rhs(feq_3a), rhs(feq_3b), rhs(feq_3c), rhs(feq_3d), rhs(feq_3e), rhs(feq_3f)])

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 + C5*k_2_C_1_p_1_2 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 + C6*k_2_C_2_p_1_2 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_2_C_1_p_1_2 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_2_C_2_p_1_2 + C5*Leq*k_1_A_p_2]])

Compare derivation result to manual input

dCdt_mupad=dCdt_manual_input:
normal(%);
bool(%)

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 + C5*k_2_C_1_p_1_2 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 + C6*k_2_C_2_p_1_2 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_2_C_1_p_1_2 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_2_C_2_p_1_2 + C5*Leq*k_1_A_p_2]]) = matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 + C5*k_2_C_1_p_1_2 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 + C6*k_2_C_2_p_1_2 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_2_C_1_p_1_2 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_2_C_2_p_1_2 + C5*Leq*k_1_A_p_2]])
TRUE

Conclusion:
Typed K-matrix is correct

 

 

K matrix for the 2U-R-RL model

K;

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2, 0, k_2_C_2_p_1_2], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_2_C_2_p_1_2]])

 

 

 

 

Back to Contents

 

 

 

 

 

 

 

 

Expession of K matrix for U-3R-RL mechanism

 

 

Order of species to allow for easy expansion of matrices:

R*, RL*, R', RL',  R'', RL'',  R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

Summary list of the net rate equations for the mechanism

eq_Rs_N__3U_R_RL;
eq_RLs_N__3U_R_RL;
eq_Rp1_N__3U_R_RL;
eq_RLp1_N__3U_R_RL;
eq_Rp2_N__3U_R_RL;
eq_Rp2_N__3U_R_RL;
eq_RLp2_N__3U_R_RL;
eq_Rp3_N__3U_R_RL;
eq_RLp3_N__3U_R_RL;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3
dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3
dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 - L*R_p_1*k_1_A_p_1
dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + L*R_p_1*k_1_A_p_1
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 - L*R_p_2*k_1_A_p_2
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 - L*R_p_2*k_1_A_p_2
dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + L*R_p_2*k_1_A_p_2
dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 - L*R_p_3*k_1_A_p_3
dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + L*R_p_3*k_1_A_p_3

 

 

Assign sequential names to species

feq_1a:= R_s        = C1;
feq_1b:= RL_s       = C2;
feq_1c:= R_p_1      = C3;
feq_1d:= RL_p_1     = C4;
feq_1e:= R_p_2      = C5;
feq_1f:= RL_p_2     = C6;
feq_1g:= R_p_3      = C7;
feq_1h:= RL_p_3     = C8;

R_s = C1
RL_s = C2
R_p_1 = C3
RL_p_1 = C4
R_p_2 = C5
RL_p_2 = C6
R_p_3 = C7
RL_p_3 = C8

 

Assign the same order to net rate equations

feq_2a:= dcRsdt_N      = dC1dt;
feq_2b:= dcRLsdt_N     = dC2dt;
feq_2c:= dcRp1dt_N     = dC3dt;
feq_2d:= dcRLp1dt_N    = dC4dt;
feq_2e:= dcRp2dt_N     = dC5dt;
feq_2f:= dcRLp2dt_N    = dC6dt;
feq_2g:= dcRp3dt_N     = dC7dt;
feq_2h:= dcRLp3dt_N    = dC8dt;

dcRsdt_N = dC1dt
dcRLsdt_N = dC2dt
dcRp1dt_N = dC3dt
dcRLp1dt_N = dC4dt
dcRp2dt_N = dC5dt
dcRLp2dt_N = dC6dt
dcRp3dt_N = dC7dt
dcRLp3dt_N = dC8dt

 

 

 

Restate the equations in terms of new sequential species names (rename free ligand concentration too)

R*

eq_Rs_N__3U_R_RL;
feq_3a:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3
dC1dt = C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3

 

RL*

eq_RLs_N__3U_R_RL;
feq_3b:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3
dC2dt = C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3

 

R'

eq_Rp1_N__3U_R_RL;
feq_3c:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 - L*R_p_1*k_1_A_p_1
dC3dt = C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 - C3*Leq*k_1_A_p_1

 

RL'

eq_RLp1_N__3U_R_RL;
feq_3d:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + L*R_p_1*k_1_A_p_1
dC4dt = C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C3*Leq*k_1_A_p_1

 

R''

eq_Rp2_N__3U_R_RL;
feq_3e:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 - L*R_p_2*k_1_A_p_2
dC5dt = C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 - C5*Leq*k_1_A_p_2

 

RL''

eq_RLp2_N__3U_R_RL;
feq_3f:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq 

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + L*R_p_2*k_1_A_p_2
dC6dt = C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C5*Leq*k_1_A_p_2

 

R'''

eq_Rp3_N__3U_R_RL;
feq_3g:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 - L*R_p_3*k_1_A_p_3
dC7dt = C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 - C7*Leq*k_1_A_p_3

 

RL'''

eq_RLp3_N__3U_R_RL;
feq_3h:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  L = Leq

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + L*R_p_3*k_1_A_p_3
dC8dt = C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C7*Leq*k_1_A_p_3

 

Prepare results for transfer to MATLAB

 

See Workflow for accurate extraction of the K matrix

 

 

 

Simple rules that allow catching mistakes in K matrix derivation:

   

   (1) a sum of each column should be zero (so each constant must appear with both positive and negative sign), and 

 

   (2) each row has to have complete pairs of constants (i.e., if k12

    appears there must be k21 in the same row with an opposite sign and so on).

K:=matrix(8,8,[
[ -k_1_B_1_p_2 -k_1_B_1_p_3 -k_1_B_1_p_1, 0, k_2_B_1_p_1, 0, +k_2_B_1_p_2, 0, +k_2_B_1_p_3, 0  ],
[  0, -k_2_B_2_p_1 -k_2_B_2_p_2 -k_2_B_2_p_3, 0, k_1_B_2_p_1, 0, +k_1_B_2_p_2, 0, +k_1_B_2_p_3     ],
[  +k_1_B_1_p_1, 0, -k_2_B_1_p_1 -k_1_C_1_p_1_2 -k_1_C_1_p_1_3 -Leq*k_1_A_p_1, k_2_A_p_1, +k_2_C_1_p_1_2, 0, +k_2_C_1_p_1_3, 0  ],
[  0, k_2_B_2_p_1, +Leq*k_1_A_p_1,  -k_1_B_2_p_1 -k_2_A_p_1 -k_1_C_2_p_1_2 -k_1_C_2_p_1_3, 0, +k_2_C_2_p_1_2, 0, +k_2_C_2_p_1_3   ],
[  +k_1_B_1_p_2, 0,+k_1_C_1_p_1_2, 0, -k_2_B_1_p_2  -k_1_C_1_p_2_3 -k_2_C_1_p_1_2 -Leq*k_1_A_p_2, k_2_A_p_2,  +k_2_C_1_p_2_3, 0  ],
[  0, k_2_B_2_p_2, 0, +k_1_C_2_p_1_2, +Leq*k_1_A_p_2,  -k_1_B_2_p_2 -k_2_A_p_2 -k_1_C_2_p_2_3 -k_2_C_2_p_1_2, 0, +k_2_C_2_p_2_3   ],
[   k_1_B_1_p_3, 0, +k_1_C_1_p_1_3, 0, +k_1_C_1_p_2_3, 0,   -k_2_B_1_p_3  -k_2_C_1_p_1_3 -k_2_C_1_p_2_3 -Leq*k_1_A_p_3, k_2_A_p_3  ],
[  0, k_2_B_2_p_3, 0, +k_1_C_2_p_1_3, 0,  +k_1_C_2_p_2_3,  +Leq*k_1_A_p_3, -k_1_B_2_p_3 -k_2_A_p_3 -k_2_C_2_p_1_3 -k_2_C_2_p_2_3   ]
])

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2 - k_1_B_1_p_3, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0, k_2_B_1_p_3, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2 - k_2_B_2_p_3, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2, 0, k_1_B_2_p_3], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - k_1_C_1_p_1_3 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0, k_2_C_1_p_1_3, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2 - k_1_C_2_p_1_3, 0, k_2_C_2_p_1_2, 0, k_2_C_2_p_1_3], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_1_C_1_p_2_3 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2, k_2_C_1_p_2_3, 0], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_1_C_2_p_2_3 - k_2_C_2_p_1_2, 0, k_2_C_2_p_2_3], [k_1_B_1_p_3, 0, k_1_C_1_p_1_3, 0, k_1_C_1_p_2_3, 0, - k_2_B_1_p_3 - k_2_C_1_p_1_3 - k_2_C_1_p_2_3 - Leq*k_1_A_p_3, k_2_A_p_3], [0, k_2_B_2_p_3, 0, k_1_C_2_p_1_3, 0, k_1_C_2_p_2_3, Leq*k_1_A_p_3, - k_2_A_p_3 - k_1_B_2_p_3 - k_2_C_2_p_1_3 - k_2_C_2_p_2_3]])

 

Test the K matrix entry

 

Create a column vector of species concentrations

P:=matrix(8,1,[C1, C2, C3, C4, C5, C6, C7, C8])

matrix([[C1], [C2], [C3], [C4], [C5], [C6], [C7], [C8]])

 

Multiply K and P:

dCdt_manual_input:= K*P

matrix([[C3*k_2_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 - C1*(k_1_B_1_p_1 + k_1_B_1_p_2 + k_1_B_1_p_3)], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 - C2*(k_2_B_2_p_1 + k_2_B_2_p_2 + k_2_B_2_p_3)], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 - C3*(k_2_B_1_p_1 + k_1_C_1_p_1_2 + k_1_C_1_p_1_3 + Leq*k_1_A_p_1)], [C2*k_2_B_2_p_1 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 - C4*(k_2_A_p_1 + k_1_B_2_p_1 + k_1_C_2_p_1_2 + k_1_C_2_p_1_3) + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 + C3*k_1_C_1_p_1_2 + C7*k_2_C_1_p_2_3 - C5*(k_2_B_1_p_2 + k_1_C_1_p_2_3 + k_2_C_1_p_1_2 + Leq*k_1_A_p_2)], [C2*k_2_B_2_p_2 + C4*k_1_C_2_p_1_2 + C8*k_2_C_2_p_2_3 - C6*(k_2_A_p_2 + k_1_B_2_p_2 + k_1_C_2_p_2_3 + k_2_C_2_p_1_2) + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*(k_2_B_1_p_3 + k_2_C_1_p_1_3 + k_2_C_1_p_2_3 + Leq*k_1_A_p_3)], [C2*k_2_B_2_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*(k_2_A_p_3 + k_1_B_2_p_3 + k_2_C_2_p_1_3 + k_2_C_2_p_2_3) + C7*Leq*k_1_A_p_3]])

 

 

Collect right-hand-side parts of net rate equations expressed in sequential species names

dCdt_mupad:=matrix(8,1,[ rhs(feq_3a), rhs(feq_3b), rhs(feq_3c), rhs(feq_3d), rhs(feq_3e), rhs(feq_3f), rhs(feq_3g), rhs(feq_3h)])

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C7*Leq*k_1_A_p_3]])

 

Compare derivation result to manual input

dCdt_mupad=dCdt_manual_input:
normal(%);
bool(%)

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C7*Leq*k_1_A_p_3]]) = matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C7*Leq*k_1_A_p_3]])
TRUE

 

Conclusion:
Typed K-matrix is correct

 

 

K matrix for the 3U-R-RL model

K;

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2 - k_1_B_1_p_3, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0, k_2_B_1_p_3, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2 - k_2_B_2_p_3, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2, 0, k_1_B_2_p_3], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - k_1_C_1_p_1_3 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0, k_2_C_1_p_1_3, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2 - k_1_C_2_p_1_3, 0, k_2_C_2_p_1_2, 0, k_2_C_2_p_1_3], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_1_C_1_p_2_3 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2, k_2_C_1_p_2_3, 0], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_1_C_2_p_2_3 - k_2_C_2_p_1_2, 0, k_2_C_2_p_2_3], [k_1_B_1_p_3, 0, k_1_C_1_p_1_3, 0, k_1_C_1_p_2_3, 0, - k_2_B_1_p_3 - k_2_C_1_p_1_3 - k_2_C_1_p_2_3 - Leq*k_1_A_p_3, k_2_A_p_3], [0, k_2_B_2_p_3, 0, k_1_C_2_p_1_3, 0, k_1_C_2_p_2_3, Leq*k_1_A_p_3, - k_2_A_p_3 - k_1_B_2_p_3 - k_2_C_2_p_1_3 - k_2_C_2_p_2_3]])

 

 

 

 

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Expession of K matrix for U-4R-RL mechanism

 

 

Order of species to allow for easy expansion of matrices:

R*, RL*, R', RL',  R'', RL'',  R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

 

Summary list of the net rate equations for the mechanism

eq_Rs_N__4U_R_RL;
eq_RLs_N__4U_R_RL;
eq_Rp1_N__4U_R_RL;
eq_RLp1_N__4U_R_RL;
eq_Rp2_N__4U_R_RL;
eq_Rp2_N__4U_R_RL;
eq_RLp2_N__4U_R_RL;
eq_Rp3_N__4U_R_RL;
eq_RLp3_N__4U_R_RL;
eq_Rp4_N__4U_R_RL;
eq_RLp4_N__4U_R_RL;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4
dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4
dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 - L*R_p_1*k_1_A_p_1
dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + L*R_p_1*k_1_A_p_1
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 - L*R_p_2*k_1_A_p_2
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 - L*R_p_2*k_1_A_p_2
dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + L*R_p_2*k_1_A_p_2
dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 - L*R_p_3*k_1_A_p_3
dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + L*R_p_3*k_1_A_p_3
dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 - L*R_p_4*k_1_A_p_4
dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + L*R_p_4*k_1_A_p_4

 

Assign sequential names to species

feq_1a:= R_s        = C1;
feq_1b:= RL_s       = C2;
feq_1c:= R_p_1      = C3;
feq_1d:= RL_p_1     = C4;
feq_1e:= R_p_2      = C5;
feq_1f:= RL_p_2     = C6;
feq_1g:= R_p_3      = C7;
feq_1h:= RL_p_3     = C8;
feq_1i:= R_p_4      = C9;
feq_1j:= RL_p_4     = C10;

R_s = C1
RL_s = C2
R_p_1 = C3
RL_p_1 = C4
R_p_2 = C5
RL_p_2 = C6
R_p_3 = C7
RL_p_3 = C8
R_p_4 = C9
RL_p_4 = C10

 

 

Assign the same order to net rate equations

feq_2a:= dcRsdt_N      = dC1dt;
feq_2b:= dcRLsdt_N     = dC2dt;
feq_2c:= dcRp1dt_N     = dC3dt;
feq_2d:= dcRLp1dt_N    = dC4dt;
feq_2e:= dcRp2dt_N     = dC5dt;
feq_2f:= dcRLp2dt_N    = dC6dt;
feq_2g:= dcRp3dt_N     = dC7dt;
feq_2h:= dcRLp3dt_N    = dC8dt;
feq_2i:= dcRp4dt_N     = dC9dt;
feq_2j:= dcRLp4dt_N    = dC10dt;

dcRsdt_N = dC1dt
dcRLsdt_N = dC2dt
dcRp1dt_N = dC3dt
dcRLp1dt_N = dC4dt
dcRp2dt_N = dC5dt
dcRLp2dt_N = dC6dt
dcRp3dt_N = dC7dt
dcRLp3dt_N = dC8dt
dcRp4dt_N = dC9dt
dcRLp4dt_N = dC10dt

 

 

 

Restate the equations in terms of new sequential species names (rename free ligand concentration too)

R*

eq_Rs_N__4U_R_RL;
feq_3a:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4
dC1dt = C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4

 

RL*

eq_RLs_N__4U_R_RL;
feq_3b:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4
dC2dt = C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4

 

R'

eq_Rp1_N__4U_R_RL;
feq_3c:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 - L*R_p_1*k_1_A_p_1
dC3dt = C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 - C3*Leq*k_1_A_p_1

 

RL'

eq_RLp1_N__4U_R_RL;
feq_3d:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + L*R_p_1*k_1_A_p_1
dC4dt = C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C3*Leq*k_1_A_p_1

 

R''

eq_Rp2_N__4U_R_RL;
feq_3e:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 - L*R_p_2*k_1_A_p_2
dC5dt = C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 - C5*Leq*k_1_A_p_2

 

RL''

eq_RLp2_N__4U_R_RL;
feq_3f:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + L*R_p_2*k_1_A_p_2
dC6dt = C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C5*Leq*k_1_A_p_2

 

 

R'''

eq_Rp3_N__4U_R_RL;
feq_3g:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 - L*R_p_3*k_1_A_p_3
dC7dt = C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 - C7*Leq*k_1_A_p_3

 

RL'''

eq_RLp3_N__4U_R_RL;
feq_3h:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + L*R_p_3*k_1_A_p_3
dC8dt = C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C7*Leq*k_1_A_p_3

 

R''''

eq_Rp4_N__4U_R_RL;
feq_3i:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 - L*R_p_4*k_1_A_p_4
dC9dt = C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 - C9*Leq*k_1_A_p_4

 

 

RL''''

eq_RLp4_N__4U_R_RL;
feq_3j:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  L = Leq

dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + L*R_p_4*k_1_A_p_4
dC10dt = C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C9*Leq*k_1_A_p_4

 

 

Prepare results for transfer to MATLAB

 

See Workflow for accurate extraction of the K matrix

 

 

 

Simple rules that allow catching mistakes in K matrix derivation:

   

   (1) a sum of each column should be zero (so each constant must appear with both positive and negative sign), and 

 

   (2) each row has to have complete pairs of constants (i.e., if k12

    appears there must be k21 in the same row with an opposite sign and so on).

K:=matrix(10,10,[
[ -k_1_B_1_p_2 -k_1_B_1_p_3 -k_1_B_1_p_4 -k_1_B_1_p_1, 0,  k_2_B_1_p_1, 0,   +k_2_B_1_p_2, 0, +k_2_B_1_p_3, 0, +k_2_B_1_p_4 ,0 ],
[  0, -k_2_B_2_p_1 -k_2_B_2_p_2 -k_2_B_2_p_3 -k_2_B_2_p_4, 0, k_1_B_2_p_1, 0, +k_1_B_2_p_2, 0, +k_1_B_2_p_3, 0, +k_1_B_2_p_4  ],
[  +k_1_B_1_p_1, 0, -k_2_B_1_p_1 -k_1_C_1_p_1_2 -k_1_C_1_p_1_3 -k_1_C_1_p_1_4 -Leq*k_1_A_p_1,  k_2_A_p_1, +k_2_C_1_p_1_2, 0, +k_2_C_1_p_1_3,0, +k_2_C_1_p_1_4,0  ],
[ 0, k_2_B_2_p_1, +Leq*k_1_A_p_1,  -k_1_B_2_p_1 -k_2_A_p_1 -k_1_C_2_p_1_2 -k_1_C_2_p_1_3 -k_1_C_2_p_1_4, 0, +k_2_C_2_p_1_2, 0, +k_2_C_2_p_1_3, 0, +k_2_C_2_p_1_4  ],
[  +k_1_B_1_p_2, 0, +k_1_C_1_p_1_2, 0, -k_2_B_1_p_2 -k_1_C_1_p_2_3 -k_1_C_1_p_2_4 -k_2_C_1_p_1_2 -Leq*k_1_A_p_2, k_2_A_p_2, +k_2_C_1_p_2_3, 0, +k_2_C_1_p_2_4,0  ],
[ 0, k_2_B_2_p_2, 0, +k_1_C_2_p_1_2, +Leq*k_1_A_p_2, -k_1_B_2_p_2 -k_2_A_p_2 -k_1_C_2_p_2_3 -k_1_C_2_p_2_4 -k_2_C_2_p_1_2, 0, +k_2_C_2_p_2_3, 0, +k_2_C_2_p_2_4  ],
[ +k_1_B_1_p_3, 0, +k_1_C_1_p_1_3, 0, +k_1_C_1_p_2_3, 0, -k_2_B_1_p_3 -k_1_C_1_p_3_4 -k_2_C_1_p_1_3 -k_2_C_1_p_2_3 -Leq*k_1_A_p_3, k_2_A_p_3, +k_2_C_1_p_3_4, 0  ],
[  0, k_2_B_2_p_3, 0, +k_1_C_2_p_1_3, 0, +k_1_C_2_p_2_3, +Leq*k_1_A_p_3, -k_1_B_2_p_3 -k_2_A_p_3 -k_1_C_2_p_3_4 -k_2_C_2_p_1_3 -k_2_C_2_p_2_3, 0, +k_2_C_2_p_3_4  ],
[ +k_1_B_1_p_4, 0, +k_1_C_1_p_1_4, 0, +k_1_C_1_p_2_4, 0, +k_1_C_1_p_3_4, 0, -k_2_B_1_p_4 -k_2_C_1_p_1_4 -k_2_C_1_p_2_4 -k_2_C_1_p_3_4 -Leq*k_1_A_p_4,  k_2_A_p_4  ],
[  0, k_2_B_2_p_4, 0, +k_1_C_2_p_1_4, 0, +k_1_C_2_p_2_4, 0, +k_1_C_2_p_3_4, +Leq*k_1_A_p_4,  -k_1_B_2_p_4 -k_2_A_p_4 -k_2_C_2_p_1_4 -k_2_C_2_p_2_4 -k_2_C_2_p_3_4 ]
])

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2 - k_1_B_1_p_3 - k_1_B_1_p_4, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0, k_2_B_1_p_3, 0, k_2_B_1_p_4, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2 - k_2_B_2_p_3 - k_2_B_2_p_4, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2, 0, k_1_B_2_p_3, 0, k_1_B_2_p_4], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - k_1_C_1_p_1_3 - k_1_C_1_p_1_4 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0, k_2_C_1_p_1_3, 0, k_2_C_1_p_1_4, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2 - k_1_C_2_p_1_3 - k_1_C_2_p_1_4, 0, k_2_C_2_p_1_2, 0, k_2_C_2_p_1_3, 0, k_2_C_2_p_1_4], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_1_C_1_p_2_3 - k_1_C_1_p_2_4 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2, k_2_C_1_p_2_3, 0, k_2_C_1_p_2_4, 0], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_1_C_2_p_2_3 - k_1_C_2_p_2_4 - k_2_C_2_p_1_2, 0, k_2_C_2_p_2_3, 0, k_2_C_2_p_2_4], [k_1_B_1_p_3, 0, k_1_C_1_p_1_3, 0, k_1_C_1_p_2_3, 0, - k_2_B_1_p_3 - k_1_C_1_p_3_4 - k_2_C_1_p_1_3 - k_2_C_1_p_2_3 - Leq*k_1_A_p_3, k_2_A_p_3, k_2_C_1_p_3_4, 0], [0, k_2_B_2_p_3, 0, k_1_C_2_p_1_3, 0, k_1_C_2_p_2_3, Leq*k_1_A_p_3, - k_2_A_p_3 - k_1_B_2_p_3 - k_1_C_2_p_3_4 - k_2_C_2_p_1_3 - k_2_C_2_p_2_3, 0, k_2_C_2_p_3_4], [k_1_B_1_p_4, 0, k_1_C_1_p_1_4, 0, k_1_C_1_p_2_4, 0, k_1_C_1_p_3_4, 0, - k_2_B_1_p_4 - k_2_C_1_p_1_4 - k_2_C_1_p_2_4 - k_2_C_1_p_3_4 - Leq*k_1_A_p_4, k_2_A_p_4], [0, k_2_B_2_p_4, 0, k_1_C_2_p_1_4, 0, k_1_C_2_p_2_4, 0, k_1_C_2_p_3_4, Leq*k_1_A_p_4, - k_2_A_p_4 - k_1_B_2_p_4 - k_2_C_2_p_1_4 - k_2_C_2_p_2_4 - k_2_C_2_p_3_4]])

 

 

Test the K matrix entry

 

Create a column vector of species concentrations

P:=matrix(10,1,[C1, C2, C3, C4, C5, C6, C7, C8, C9, C10])

matrix([[C1], [C2], [C3], [C4], [C5], [C6], [C7], [C8], [C9], [C10]])

Multiply K and P:

dCdt_manual_input:= K*P

matrix([[C3*k_2_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4 - C1*(k_1_B_1_p_1 + k_1_B_1_p_2 + k_1_B_1_p_3 + k_1_B_1_p_4)], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 - C2*(k_2_B_2_p_1 + k_2_B_2_p_2 + k_2_B_2_p_3 + k_2_B_2_p_4)], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 - C3*(k_2_B_1_p_1 + k_1_C_1_p_1_2 + k_1_C_1_p_1_3 + k_1_C_1_p_1_4 + Leq*k_1_A_p_1)], [C2*k_2_B_2_p_1 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 - C4*(k_2_A_p_1 + k_1_B_2_p_1 + k_1_C_2_p_1_2 + k_1_C_2_p_1_3 + k_1_C_2_p_1_4) + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 + C3*k_1_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 - C5*(k_2_B_1_p_2 + k_1_C_1_p_2_3 + k_1_C_1_p_2_4 + k_2_C_1_p_1_2 + Leq*k_1_A_p_2)], [C2*k_2_B_2_p_2 + C4*k_1_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 - C6*(k_2_A_p_2 + k_1_B_2_p_2 + k_1_C_2_p_2_3 + k_1_C_2_p_2_4 + k_2_C_2_p_1_2) + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 + C9*k_2_C_1_p_3_4 - C7*(k_2_B_1_p_3 + k_1_C_1_p_3_4 + k_2_C_1_p_1_3 + k_2_C_1_p_2_3 + Leq*k_1_A_p_3)], [C2*k_2_B_2_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 + C10*k_2_C_2_p_3_4 - C8*(k_2_A_p_3 + k_1_B_2_p_3 + k_1_C_2_p_3_4 + k_2_C_2_p_1_3 + k_2_C_2_p_2_3) + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*(k_2_B_1_p_4 + k_2_C_1_p_1_4 + k_2_C_1_p_2_4 + k_2_C_1_p_3_4 + Leq*k_1_A_p_4)], [C2*k_2_B_2_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*(k_2_A_p_4 + k_1_B_2_p_4 + k_2_C_2_p_1_4 + k_2_C_2_p_2_4 + k_2_C_2_p_3_4) + C9*Leq*k_1_A_p_4]])

 

Collect right-hand-side parts of net rate equations expressed in sequential species names

dCdt_mupad:=matrix(10,1,[ rhs(feq_3a), rhs(feq_3b), rhs(feq_3c), rhs(feq_3d), rhs(feq_3e), rhs(feq_3f), rhs(feq_3g), rhs(feq_3h), rhs(feq_3i), rhs(feq_3j)])

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 - C9*Leq*k_1_A_p_4], [C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C9*Leq*k_1_A_p_4]])

Compare derivation result to manual input

dCdt_mupad=dCdt_manual_input:
normal(%);
bool(%)

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 - C9*Leq*k_1_A_p_4], [C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C9*Leq*k_1_A_p_4]]) = matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 - C9*Leq*k_1_A_p_4], [C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C9*Leq*k_1_A_p_4]])
TRUE

 

Conclusion:
Typed K-matrix is correct

 

 

K matrix for the 4U-R-RL model

K;

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2 - k_1_B_1_p_3 - k_1_B_1_p_4, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0, k_2_B_1_p_3, 0, k_2_B_1_p_4, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2 - k_2_B_2_p_3 - k_2_B_2_p_4, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2, 0, k_1_B_2_p_3, 0, k_1_B_2_p_4], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - k_1_C_1_p_1_3 - k_1_C_1_p_1_4 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0, k_2_C_1_p_1_3, 0, k_2_C_1_p_1_4, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2 - k_1_C_2_p_1_3 - k_1_C_2_p_1_4, 0, k_2_C_2_p_1_2, 0, k_2_C_2_p_1_3, 0, k_2_C_2_p_1_4], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_1_C_1_p_2_3 - k_1_C_1_p_2_4 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2, k_2_C_1_p_2_3, 0, k_2_C_1_p_2_4, 0], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_1_C_2_p_2_3 - k_1_C_2_p_2_4 - k_2_C_2_p_1_2, 0, k_2_C_2_p_2_3, 0, k_2_C_2_p_2_4], [k_1_B_1_p_3, 0, k_1_C_1_p_1_3, 0, k_1_C_1_p_2_3, 0, - k_2_B_1_p_3 - k_1_C_1_p_3_4 - k_2_C_1_p_1_3 - k_2_C_1_p_2_3 - Leq*k_1_A_p_3, k_2_A_p_3, k_2_C_1_p_3_4, 0], [0, k_2_B_2_p_3, 0, k_1_C_2_p_1_3, 0, k_1_C_2_p_2_3, Leq*k_1_A_p_3, - k_2_A_p_3 - k_1_B_2_p_3 - k_1_C_2_p_3_4 - k_2_C_2_p_1_3 - k_2_C_2_p_2_3, 0, k_2_C_2_p_3_4], [k_1_B_1_p_4, 0, k_1_C_1_p_1_4, 0, k_1_C_1_p_2_4, 0, k_1_C_1_p_3_4, 0, - k_2_B_1_p_4 - k_2_C_1_p_1_4 - k_2_C_1_p_2_4 - k_2_C_1_p_3_4 - Leq*k_1_A_p_4, k_2_A_p_4], [0, k_2_B_2_p_4, 0, k_1_C_2_p_1_4, 0, k_1_C_2_p_2_4, 0, k_1_C_2_p_3_4, Leq*k_1_A_p_4, - k_2_A_p_4 - k_1_B_2_p_4 - k_2_C_2_p_1_4 - k_2_C_2_p_2_4 - k_2_C_2_p_3_4]])

 

 

 

 

Back to Contents

 

 

 

 

 

 

 

 

 

 

 

 

Expession of K matrix for U-5R-RL mechanism

 

 

Order of species to allow for easy expansion of matrices:

R*, RL*, R', RL',  R'', RL'',  R''', RL''',  R'''', RL'''',  R''''', RL'''''

 

 

Summary list of the net rate equations for the mechanism

eq_Rs_N__5U_R_RL;
eq_RLs_N__5U_R_RL;
eq_Rp1_N__5U_R_RL;
eq_RLp1_N__5U_R_RL;
eq_Rp2_N__5U_R_RL;
eq_Rp2_N__5U_R_RL;
eq_RLp2_N__5U_R_RL;
eq_Rp3_N__5U_R_RL;
eq_RLp3_N__5U_R_RL;
eq_Rp4_N__5U_R_RL;
eq_RLp4_N__5U_R_RL;
eq_Rp5_N__5U_R_RL;
eq_RLp5_N__5U_R_RL;

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 + R_p_5*k_2_B_1_p_5 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4 - R_s*k_1_B_1_p_5
dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 + RL_p_5*k_1_B_2_p_5 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4 - RL_s*k_2_B_2_p_5
dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 - R_p_1*k_1_C_1_p_1_5 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 + R_p_5*k_2_C_1_p_1_5 - L*R_p_1*k_1_A_p_1
dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 - RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + RL_p_5*k_2_C_2_p_1_5 + L*R_p_1*k_1_A_p_1
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_1_C_1_p_2_5 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 + R_p_5*k_2_C_1_p_2_5 - L*R_p_2*k_1_A_p_2
dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_1_C_1_p_2_5 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 + R_p_5*k_2_C_1_p_2_5 - L*R_p_2*k_1_A_p_2
dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_1_C_2_p_2_5 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + RL_p_5*k_2_C_2_p_2_5 + L*R_p_2*k_1_A_p_2
dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_1_C_1_p_3_5 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_3_5 - L*R_p_3*k_1_A_p_3
dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_1_C_2_p_3_5 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_3_5 + L*R_p_3*k_1_A_p_3
dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_1_C_1_p_4_5 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_4_5 - L*R_p_4*k_1_A_p_4
dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_1_C_2_p_4_5 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_4_5 + L*R_p_4*k_1_A_p_4
dcRp5dt_N = RL_p_5*k_2_A_p_5 - R_p_5*k_2_B_1_p_5 + R_s*k_1_B_1_p_5 + R_p_1*k_1_C_1_p_1_5 + R_p_2*k_1_C_1_p_2_5 + R_p_3*k_1_C_1_p_3_5 + R_p_4*k_1_C_1_p_4_5 - R_p_5*k_2_C_1_p_1_5 - R_p_5*k_2_C_1_p_2_5 - R_p_5*k_2_C_1_p_3_5 - R_p_5*k_2_C_1_p_4_5 - L*R_p_5*k_1_A_p_5
dcRLp5dt_N = RL_s*k_2_B_2_p_5 - RL_p_5*k_1_B_2_p_5 - RL_p_5*k_2_A_p_5 + RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_1_C_2_p_2_5 + RL_p_3*k_1_C_2_p_3_5 + RL_p_4*k_1_C_2_p_4_5 - RL_p_5*k_2_C_2_p_1_5 - RL_p_5*k_2_C_2_p_2_5 - RL_p_5*k_2_C_2_p_3_5 - RL_p_5*k_2_C_2_p_4_5 + L*R_p_5*k_1_A_p_5

 

Assign sequential names to species

feq_1a:= R_s        = C1;
feq_1b:= RL_s       = C2;
feq_1c:= R_p_1      = C3;
feq_1d:= RL_p_1     = C4;
feq_1e:= R_p_2      = C5;
feq_1f:= RL_p_2     = C6;
feq_1g:= R_p_3      = C7;
feq_1h:= RL_p_3     = C8;
feq_1i:= R_p_4      = C9;
feq_1j:= RL_p_4     = C10;
feq_1k:= R_p_5      = C11;
feq_1l:= RL_p_5     = C12;

R_s = C1
RL_s = C2
R_p_1 = C3
RL_p_1 = C4
R_p_2 = C5
RL_p_2 = C6
R_p_3 = C7
RL_p_3 = C8
R_p_4 = C9
RL_p_4 = C10
R_p_5 = C11
RL_p_5 = C12

Assign the same order to net rate equations

feq_2a:= dcRsdt_N      = dC1dt;
feq_2b:= dcRLsdt_N     = dC2dt;
feq_2c:= dcRp1dt_N     = dC3dt;
feq_2d:= dcRLp1dt_N    = dC4dt;
feq_2e:= dcRp2dt_N     = dC5dt;
feq_2f:= dcRLp2dt_N    = dC6dt;
feq_2g:= dcRp3dt_N     = dC7dt;
feq_2h:= dcRLp3dt_N    = dC8dt;
feq_2i:= dcRp4dt_N     = dC9dt;
feq_2j:= dcRLp4dt_N    = dC10dt;
feq_2k:= dcRp5dt_N     = dC11dt;
feq_2l:= dcRLp5dt_N    = dC12dt;

dcRsdt_N = dC1dt
dcRLsdt_N = dC2dt
dcRp1dt_N = dC3dt
dcRLp1dt_N = dC4dt
dcRp2dt_N = dC5dt
dcRLp2dt_N = dC6dt
dcRp3dt_N = dC7dt
dcRLp3dt_N = dC8dt
dcRp4dt_N = dC9dt
dcRLp4dt_N = dC10dt
dcRp5dt_N = dC11dt
dcRLp5dt_N = dC12dt

 

 

Restate the equations in terms of new sequential species names (rename free ligand concentration too)

R*

eq_Rs_N__5U_R_RL;
feq_3a:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRsdt_N = R_p_1*k_2_B_1_p_1 + R_p_2*k_2_B_1_p_2 + R_p_3*k_2_B_1_p_3 + R_p_4*k_2_B_1_p_4 + R_p_5*k_2_B_1_p_5 - R_s*k_1_B_1_p_1 - R_s*k_1_B_1_p_2 - R_s*k_1_B_1_p_3 - R_s*k_1_B_1_p_4 - R_s*k_1_B_1_p_5
dC1dt = C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_5 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4 + C11*k_2_B_1_p_5

 

RL*

eq_RLs_N__5U_R_RL;
feq_3b:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRLsdt_N = RL_p_1*k_1_B_2_p_1 + RL_p_2*k_1_B_2_p_2 + RL_p_3*k_1_B_2_p_3 + RL_p_4*k_1_B_2_p_4 - RL_s*k_2_B_2_p_1 - RL_s*k_2_B_2_p_2 + RL_p_5*k_1_B_2_p_5 - RL_s*k_2_B_2_p_3 - RL_s*k_2_B_2_p_4 - RL_s*k_2_B_2_p_5
dC2dt = C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 + C12*k_1_B_2_p_5 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4 - C2*k_2_B_2_p_5

 

R'

eq_Rp1_N__5U_R_RL;
feq_3c:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRp1dt_N = RL_p_1*k_2_A_p_1 - R_p_1*k_2_B_1_p_1 + R_s*k_1_B_1_p_1 - R_p_1*k_1_C_1_p_1_2 - R_p_1*k_1_C_1_p_1_3 - R_p_1*k_1_C_1_p_1_4 - R_p_1*k_1_C_1_p_1_5 + R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_1_3 + R_p_4*k_2_C_1_p_1_4 + R_p_5*k_2_C_1_p_1_5 - L*R_p_1*k_1_A_p_1
dC3dt = C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 - C3*k_1_C_1_p_1_5 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 + C11*k_2_C_1_p_1_5 - C3*Leq*k_1_A_p_1

 

RL'

eq_RLp1_N__5U_R_RL;
feq_3d:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRLp1dt_N = RL_s*k_2_B_2_p_1 - RL_p_1*k_1_B_2_p_1 - RL_p_1*k_2_A_p_1 - RL_p_1*k_1_C_2_p_1_2 - RL_p_1*k_1_C_2_p_1_3 - RL_p_1*k_1_C_2_p_1_4 - RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_1_3 + RL_p_4*k_2_C_2_p_1_4 + RL_p_5*k_2_C_2_p_1_5 + L*R_p_1*k_1_A_p_1
dC4dt = C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 - C4*k_1_C_2_p_1_5 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C12*k_2_C_2_p_1_5 + C3*Leq*k_1_A_p_1

 

R''

eq_Rp2_N__5U_R_RL;
feq_3e:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRp2dt_N = RL_p_2*k_2_A_p_2 - R_p_2*k_2_B_1_p_2 + R_s*k_1_B_1_p_2 + R_p_1*k_1_C_1_p_1_2 - R_p_2*k_1_C_1_p_2_3 - R_p_2*k_1_C_1_p_2_4 - R_p_2*k_1_C_1_p_2_5 - R_p_2*k_2_C_1_p_1_2 + R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_2_4 + R_p_5*k_2_C_1_p_2_5 - L*R_p_2*k_1_A_p_2
dC5dt = C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_1_C_1_p_2_5 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 + C11*k_2_C_1_p_2_5 - C5*Leq*k_1_A_p_2

 

RL''

eq_RLp2_N__5U_R_RL;
feq_3f:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRLp2dt_N = RL_s*k_2_B_2_p_2 - RL_p_2*k_1_B_2_p_2 - RL_p_2*k_2_A_p_2 + RL_p_1*k_1_C_2_p_1_2 - RL_p_2*k_1_C_2_p_2_3 - RL_p_2*k_1_C_2_p_2_4 - RL_p_2*k_1_C_2_p_2_5 - RL_p_2*k_2_C_2_p_1_2 + RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_2_4 + RL_p_5*k_2_C_2_p_2_5 + L*R_p_2*k_1_A_p_2
dC6dt = C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_1_C_2_p_2_5 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C12*k_2_C_2_p_2_5 + C5*Leq*k_1_A_p_2

 

R'''

eq_Rp3_N__5U_R_RL;
feq_3g:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRp3dt_N = RL_p_3*k_2_A_p_3 - R_p_3*k_2_B_1_p_3 + R_s*k_1_B_1_p_3 + R_p_1*k_1_C_1_p_1_3 + R_p_2*k_1_C_1_p_2_3 - R_p_3*k_1_C_1_p_3_4 - R_p_3*k_1_C_1_p_3_5 - R_p_3*k_2_C_1_p_1_3 - R_p_3*k_2_C_1_p_2_3 + R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_3_5 - L*R_p_3*k_1_A_p_3
dC7dt = C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_1_C_1_p_3_5 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_3_5 - C7*Leq*k_1_A_p_3

 

RL'''

eq_RLp3_N__5U_R_RL;
feq_3h:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRLp3dt_N = RL_s*k_2_B_2_p_3 - RL_p_3*k_1_B_2_p_3 - RL_p_3*k_2_A_p_3 + RL_p_1*k_1_C_2_p_1_3 + RL_p_2*k_1_C_2_p_2_3 - RL_p_3*k_1_C_2_p_3_4 - RL_p_3*k_1_C_2_p_3_5 - RL_p_3*k_2_C_2_p_1_3 - RL_p_3*k_2_C_2_p_2_3 + RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_3_5 + L*R_p_3*k_1_A_p_3
dC8dt = C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_1_C_2_p_3_5 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_3_5 + C7*Leq*k_1_A_p_3

 

R''''

eq_Rp4_N__5U_R_RL;
feq_3i:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRp4dt_N = RL_p_4*k_2_A_p_4 - R_p_4*k_2_B_1_p_4 + R_s*k_1_B_1_p_4 + R_p_1*k_1_C_1_p_1_4 + R_p_2*k_1_C_1_p_2_4 + R_p_3*k_1_C_1_p_3_4 - R_p_4*k_1_C_1_p_4_5 - R_p_4*k_2_C_1_p_1_4 - R_p_4*k_2_C_1_p_2_4 - R_p_4*k_2_C_1_p_3_4 + R_p_5*k_2_C_1_p_4_5 - L*R_p_4*k_1_A_p_4
dC9dt = C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_1_C_1_p_4_5 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_4_5 - C9*Leq*k_1_A_p_4

 

RL''''

eq_RLp4_N__5U_R_RL;
feq_3j:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRLp4dt_N = RL_s*k_2_B_2_p_4 - RL_p_4*k_1_B_2_p_4 - RL_p_4*k_2_A_p_4 + RL_p_1*k_1_C_2_p_1_4 + RL_p_2*k_1_C_2_p_2_4 + RL_p_3*k_1_C_2_p_3_4 - RL_p_4*k_1_C_2_p_4_5 - RL_p_4*k_2_C_2_p_1_4 - RL_p_4*k_2_C_2_p_2_4 - RL_p_4*k_2_C_2_p_3_4 + RL_p_5*k_2_C_2_p_4_5 + L*R_p_4*k_1_A_p_4
dC10dt = C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_1_C_2_p_4_5 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_4_5 + C9*Leq*k_1_A_p_4

 

R'''''

eq_Rp5_N__5U_R_RL;
feq_3k:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRp5dt_N = RL_p_5*k_2_A_p_5 - R_p_5*k_2_B_1_p_5 + R_s*k_1_B_1_p_5 + R_p_1*k_1_C_1_p_1_5 + R_p_2*k_1_C_1_p_2_5 + R_p_3*k_1_C_1_p_3_5 + R_p_4*k_1_C_1_p_4_5 - R_p_5*k_2_C_1_p_1_5 - R_p_5*k_2_C_1_p_2_5 - R_p_5*k_2_C_1_p_3_5 - R_p_5*k_2_C_1_p_4_5 - L*R_p_5*k_1_A_p_5
dC11dt = C12*k_2_A_p_5 + C1*k_1_B_1_p_5 - C11*k_2_B_1_p_5 + C3*k_1_C_1_p_1_5 + C5*k_1_C_1_p_2_5 + C7*k_1_C_1_p_3_5 + C9*k_1_C_1_p_4_5 - C11*k_2_C_1_p_1_5 - C11*k_2_C_1_p_2_5 - C11*k_2_C_1_p_3_5 - C11*k_2_C_1_p_4_5 - C11*Leq*k_1_A_p_5

 

RL'''''

eq_RLp5_N__5U_R_RL;
feq_3l:= % |\
  feq_1a | feq_2a | \
  feq_1b | feq_2b | \
  feq_1c | feq_2c | \
  feq_1d | feq_2d | \
  feq_1e | feq_2e | \
  feq_1f | feq_2f | \
  feq_1g | feq_2g | \
  feq_1h | feq_2h | \
  feq_1i | feq_2i | \
  feq_1j | feq_2j | \
  feq_1k | feq_2k | \
  feq_1l | feq_2l | \
  L = Leq

dcRLp5dt_N = RL_s*k_2_B_2_p_5 - RL_p_5*k_1_B_2_p_5 - RL_p_5*k_2_A_p_5 + RL_p_1*k_1_C_2_p_1_5 + RL_p_2*k_1_C_2_p_2_5 + RL_p_3*k_1_C_2_p_3_5 + RL_p_4*k_1_C_2_p_4_5 - RL_p_5*k_2_C_2_p_1_5 - RL_p_5*k_2_C_2_p_2_5 - RL_p_5*k_2_C_2_p_3_5 - RL_p_5*k_2_C_2_p_4_5 + L*R_p_5*k_1_A_p_5
dC12dt = C2*k_2_B_2_p_5 - C12*k_1_B_2_p_5 - C12*k_2_A_p_5 + C4*k_1_C_2_p_1_5 + C6*k_1_C_2_p_2_5 + C8*k_1_C_2_p_3_5 + C10*k_1_C_2_p_4_5 - C12*k_2_C_2_p_1_5 - C12*k_2_C_2_p_2_5 - C12*k_2_C_2_p_3_5 - C12*k_2_C_2_p_4_5 + C11*Leq*k_1_A_p_5

 

 

Prepare results for transfer to MATLAB

 

See Workflow for accurate extraction of the K matrix

 

 

 

Simple rules that allow catching mistakes in K matrix derivation:

   

   (1) a sum of each column should be zero (so each constant must appear with both positive and negative sign), and 

 

   (2) each row has to have complete pairs of constants (i.e., if k12

    appears there must be k21 in the same row with an opposite sign and so on).

K:=matrix(12,12,[
[  -k_1_B_1_p_2 -k_1_B_1_p_3 -k_1_B_1_p_4 -k_1_B_1_p_5 -k_1_B_1_p_1, 0, k_2_B_1_p_1, 0, +k_2_B_1_p_2, 0, +k_2_B_1_p_3, 0, +k_2_B_1_p_4, 0, +k_2_B_1_p_5, 0  ],
[ 0, -k_2_B_2_p_1 -k_2_B_2_p_2 -k_2_B_2_p_3 -k_2_B_2_p_4 -k_2_B_2_p_5, 0, k_1_B_2_p_1, 0, +k_1_B_2_p_2, 0, +k_1_B_2_p_3, 0, +k_1_B_2_p_4, 0, +k_1_B_2_p_5  ],
[ +k_1_B_1_p_1, 0, -k_2_B_1_p_1 -k_1_C_1_p_1_2 -k_1_C_1_p_1_3 -k_1_C_1_p_1_4 -k_1_C_1_p_1_5 -Leq*k_1_A_p_1, k_2_A_p_1, +k_2_C_1_p_1_2, 0, +k_2_C_1_p_1_3, 0, +k_2_C_1_p_1_4, 0, +k_2_C_1_p_1_5, 0  ],
[ 0, k_2_B_2_p_1, +Leq*k_1_A_p_1,  -k_1_B_2_p_1 -k_2_A_p_1 -k_1_C_2_p_1_2 -k_1_C_2_p_1_3 -k_1_C_2_p_1_4 -k_1_C_2_p_1_5, 0, +k_2_C_2_p_1_2, 0, +k_2_C_2_p_1_3, 0, +k_2_C_2_p_1_4, 0, +k_2_C_2_p_1_5   ],
[ +k_1_B_1_p_2, 0, +k_1_C_1_p_1_2, 0,  -k_2_B_1_p_2 -k_1_C_1_p_2_3 -k_1_C_1_p_2_4 -k_1_C_1_p_2_5 -k_2_C_1_p_1_2 -Leq*k_1_A_p_2, k_2_A_p_2, +k_2_C_1_p_2_3, 0, +k_2_C_1_p_2_4, 0, +k_2_C_1_p_2_5, 0  ],
[ 0, k_2_B_2_p_2, 0, +k_1_C_2_p_1_2,  +Leq*k_1_A_p_2, -k_1_B_2_p_2 -k_2_A_p_2 -k_1_C_2_p_2_3 -k_1_C_2_p_2_4 -k_1_C_2_p_2_5 -k_2_C_2_p_1_2, 0, +k_2_C_2_p_2_3, 0, +k_2_C_2_p_2_4, 0, +k_2_C_2_p_2_5  ],
[  +k_1_B_1_p_3, 0, +k_1_C_1_p_1_3, 0,+k_1_C_1_p_2_3, 0, -k_2_B_1_p_3  -k_1_C_1_p_3_4 -k_1_C_1_p_3_5 -k_2_C_1_p_1_3 -k_2_C_1_p_2_3 -Leq*k_1_A_p_3, k_2_A_p_3, +k_2_C_1_p_3_4, 0, +k_2_C_1_p_3_5, 0   ],
[ 0, k_2_B_2_p_3, 0, +k_1_C_2_p_1_3, 0, +k_1_C_2_p_2_3, +Leq*k_1_A_p_3, -k_1_B_2_p_3 -k_2_A_p_3 -k_1_C_2_p_3_4 -k_1_C_2_p_3_5 -k_2_C_2_p_1_3 -k_2_C_2_p_2_3, 0, +k_2_C_2_p_3_4, 0, +k_2_C_2_p_3_5  ],
[  +k_1_B_1_p_4, 0, +k_1_C_1_p_1_4, 0, +k_1_C_1_p_2_4, 0, +k_1_C_1_p_3_4, 0, -k_2_B_1_p_4 -k_1_C_1_p_4_5 -k_2_C_1_p_1_4 -k_2_C_1_p_2_4 -k_2_C_1_p_3_4 -Leq*k_1_A_p_4, k_2_A_p_4, +k_2_C_1_p_4_5, 0   ],
[  0, k_2_B_2_p_4, 0, +k_1_C_2_p_1_4, 0, +k_1_C_2_p_2_4, 0, +k_1_C_2_p_3_4,  +Leq*k_1_A_p_4, -k_1_B_2_p_4 -k_2_A_p_4 -k_1_C_2_p_4_5 -k_2_C_2_p_1_4 -k_2_C_2_p_2_4 -k_2_C_2_p_3_4, 0, +k_2_C_2_p_4_5  ],
[   +k_1_B_1_p_5, 0, +k_1_C_1_p_1_5, 0, +k_1_C_1_p_2_5, 0, +k_1_C_1_p_3_5, 0, +k_1_C_1_p_4_5, 0, -k_2_B_1_p_5 -k_2_C_1_p_1_5 -k_2_C_1_p_2_5 -k_2_C_1_p_3_5 -k_2_C_1_p_4_5 -Leq*k_1_A_p_5, k_2_A_p_5 ],
[  0, k_2_B_2_p_5, 0, +k_1_C_2_p_1_5, 0, +k_1_C_2_p_2_5, 0, +k_1_C_2_p_3_5, 0, +k_1_C_2_p_4_5,  +Leq*k_1_A_p_5, -k_1_B_2_p_5 -k_2_A_p_5 -k_2_C_2_p_1_5 -k_2_C_2_p_2_5 -k_2_C_2_p_3_5 -k_2_C_2_p_4_5 ]
])

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2 - k_1_B_1_p_3 - k_1_B_1_p_4 - k_1_B_1_p_5, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0, k_2_B_1_p_3, 0, k_2_B_1_p_4, 0, k_2_B_1_p_5, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2 - k_2_B_2_p_3 - k_2_B_2_p_4 - k_2_B_2_p_5, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2, 0, k_1_B_2_p_3, 0, k_1_B_2_p_4, 0, k_1_B_2_p_5], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - k_1_C_1_p_1_3 - k_1_C_1_p_1_4 - k_1_C_1_p_1_5 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0, k_2_C_1_p_1_3, 0, k_2_C_1_p_1_4, 0, k_2_C_1_p_1_5, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2 - k_1_C_2_p_1_3 - k_1_C_2_p_1_4 - k_1_C_2_p_1_5, 0, k_2_C_2_p_1_2, 0, k_2_C_2_p_1_3, 0, k_2_C_2_p_1_4, 0, k_2_C_2_p_1_5], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_1_C_1_p_2_3 - k_1_C_1_p_2_4 - k_1_C_1_p_2_5 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2, k_2_C_1_p_2_3, 0, k_2_C_1_p_2_4, 0, k_2_C_1_p_2_5, 0], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_1_C_2_p_2_3 - k_1_C_2_p_2_4 - k_1_C_2_p_2_5 - k_2_C_2_p_1_2, 0, k_2_C_2_p_2_3, 0, k_2_C_2_p_2_4, 0, k_2_C_2_p_2_5], [k_1_B_1_p_3, 0, k_1_C_1_p_1_3, 0, k_1_C_1_p_2_3, 0, - k_2_B_1_p_3 - k_1_C_1_p_3_4 - k_1_C_1_p_3_5 - k_2_C_1_p_1_3 - k_2_C_1_p_2_3 - Leq*k_1_A_p_3, k_2_A_p_3, k_2_C_1_p_3_4, 0, k_2_C_1_p_3_5, 0], [0, k_2_B_2_p_3, 0, k_1_C_2_p_1_3, 0, k_1_C_2_p_2_3, Leq*k_1_A_p_3, - k_2_A_p_3 - k_1_B_2_p_3 - k_1_C_2_p_3_4 - k_1_C_2_p_3_5 - k_2_C_2_p_1_3 - k_2_C_2_p_2_3, 0, k_2_C_2_p_3_4, 0, k_2_C_2_p_3_5], [k_1_B_1_p_4, 0, k_1_C_1_p_1_4, 0, k_1_C_1_p_2_4, 0, k_1_C_1_p_3_4, 0, - k_2_B_1_p_4 - k_1_C_1_p_4_5 - k_2_C_1_p_1_4 - k_2_C_1_p_2_4 - k_2_C_1_p_3_4 - Leq*k_1_A_p_4, k_2_A_p_4, k_2_C_1_p_4_5, 0], [0, k_2_B_2_p_4, 0, k_1_C_2_p_1_4, 0, k_1_C_2_p_2_4, 0, k_1_C_2_p_3_4, Leq*k_1_A_p_4, - k_2_A_p_4 - k_1_B_2_p_4 - k_1_C_2_p_4_5 - k_2_C_2_p_1_4 - k_2_C_2_p_2_4 - k_2_C_2_p_3_4, 0, k_2_C_2_p_4_5], [k_1_B_1_p_5, 0, k_1_C_1_p_1_5, 0, k_1_C_1_p_2_5, 0, k_1_C_1_p_3_5, 0, k_1_C_1_p_4_5, 0, - k_2_B_1_p_5 - k_2_C_1_p_1_5 - k_2_C_1_p_2_5 - k_2_C_1_p_3_5 - k_2_C_1_p_4_5 - Leq*k_1_A_p_5, k_2_A_p_5], [0, k_2_B_2_p_5, 0, k_1_C_2_p_1_5, 0, k_1_C_2_p_2_5, 0, k_1_C_2_p_3_5, 0, k_1_C_2_p_4_5, Leq*k_1_A_p_5, - k_2_A_p_5 - k_1_B_2_p_5 - k_2_C_2_p_1_5 - k_2_C_2_p_2_5 - k_2_C_2_p_3_5 - k_2_C_2_p_4_5]])

 

Test the K matrix entry

 

Create a column vector of species concentrations

P:=matrix(12,1,[C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12])

matrix([[C1], [C2], [C3], [C4], [C5], [C6], [C7], [C8], [C9], [C10], [C11], [C12]])

Multiply K and P:

dCdt_manual_input:= K*P

matrix([[C3*k_2_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4 + C11*k_2_B_1_p_5 - C1*(k_1_B_1_p_1 + k_1_B_1_p_2 + k_1_B_1_p_3 + k_1_B_1_p_4 + k_1_B_1_p_5)], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 + C12*k_1_B_2_p_5 - C2*(k_2_B_2_p_1 + k_2_B_2_p_2 + k_2_B_2_p_3 + k_2_B_2_p_4 + k_2_B_2_p_5)], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 + C11*k_2_C_1_p_1_5 - C3*(k_2_B_1_p_1 + k_1_C_1_p_1_2 + k_1_C_1_p_1_3 + k_1_C_1_p_1_4 + k_1_C_1_p_1_5 + Leq*k_1_A_p_1)], [C2*k_2_B_2_p_1 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C12*k_2_C_2_p_1_5 - C4*(k_2_A_p_1 + k_1_B_2_p_1 + k_1_C_2_p_1_2 + k_1_C_2_p_1_3 + k_1_C_2_p_1_4 + k_1_C_2_p_1_5) + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 + C3*k_1_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 + C11*k_2_C_1_p_2_5 - C5*(k_2_B_1_p_2 + k_1_C_1_p_2_3 + k_1_C_1_p_2_4 + k_1_C_1_p_2_5 + k_2_C_1_p_1_2 + Leq*k_1_A_p_2)], [C2*k_2_B_2_p_2 + C4*k_1_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C12*k_2_C_2_p_2_5 - C6*(k_2_A_p_2 + k_1_B_2_p_2 + k_1_C_2_p_2_3 + k_1_C_2_p_2_4 + k_1_C_2_p_2_5 + k_2_C_2_p_1_2) + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 + C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_3_5 - C7*(k_2_B_1_p_3 + k_1_C_1_p_3_4 + k_1_C_1_p_3_5 + k_2_C_1_p_1_3 + k_2_C_1_p_2_3 + Leq*k_1_A_p_3)], [C2*k_2_B_2_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_3_5 - C8*(k_2_A_p_3 + k_1_B_2_p_3 + k_1_C_2_p_3_4 + k_1_C_2_p_3_5 + k_2_C_2_p_1_3 + k_2_C_2_p_2_3) + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 + C11*k_2_C_1_p_4_5 - C9*(k_2_B_1_p_4 + k_1_C_1_p_4_5 + k_2_C_1_p_1_4 + k_2_C_1_p_2_4 + k_2_C_1_p_3_4 + Leq*k_1_A_p_4)], [C2*k_2_B_2_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 + C12*k_2_C_2_p_4_5 - C10*(k_2_A_p_4 + k_1_B_2_p_4 + k_1_C_2_p_4_5 + k_2_C_2_p_1_4 + k_2_C_2_p_2_4 + k_2_C_2_p_3_4) + C9*Leq*k_1_A_p_4], [C12*k_2_A_p_5 + C1*k_1_B_1_p_5 + C3*k_1_C_1_p_1_5 + C5*k_1_C_1_p_2_5 + C7*k_1_C_1_p_3_5 + C9*k_1_C_1_p_4_5 - C11*(k_2_B_1_p_5 + k_2_C_1_p_1_5 + k_2_C_1_p_2_5 + k_2_C_1_p_3_5 + k_2_C_1_p_4_5 + Leq*k_1_A_p_5)], [C2*k_2_B_2_p_5 + C4*k_1_C_2_p_1_5 + C6*k_1_C_2_p_2_5 + C8*k_1_C_2_p_3_5 + C10*k_1_C_2_p_4_5 - C12*(k_2_A_p_5 + k_1_B_2_p_5 + k_2_C_2_p_1_5 + k_2_C_2_p_2_5 + k_2_C_2_p_3_5 + k_2_C_2_p_4_5) + C11*Leq*k_1_A_p_5]])

Collect right-hand-side parts of net rate equations expressed in sequential species names

dCdt_mupad:=matrix(12,1,[ rhs(feq_3a), rhs(feq_3b), rhs(feq_3c), rhs(feq_3d), rhs(feq_3e), rhs(feq_3f), rhs(feq_3g), rhs(feq_3h), rhs(feq_3i), rhs(feq_3j), rhs(feq_3k), rhs(feq_3l)])

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_5 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4 + C11*k_2_B_1_p_5], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 + C12*k_1_B_2_p_5 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4 - C2*k_2_B_2_p_5], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 - C3*k_1_C_1_p_1_5 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 + C11*k_2_C_1_p_1_5 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 - C4*k_1_C_2_p_1_5 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C12*k_2_C_2_p_1_5 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_1_C_1_p_2_5 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 + C11*k_2_C_1_p_2_5 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_1_C_2_p_2_5 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C12*k_2_C_2_p_2_5 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_1_C_1_p_3_5 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_3_5 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_1_C_2_p_3_5 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_3_5 + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_1_C_1_p_4_5 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_4_5 - C9*Leq*k_1_A_p_4], [C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_1_C_2_p_4_5 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_4_5 + C9*Leq*k_1_A_p_4], [C12*k_2_A_p_5 + C1*k_1_B_1_p_5 - C11*k_2_B_1_p_5 + C3*k_1_C_1_p_1_5 + C5*k_1_C_1_p_2_5 + C7*k_1_C_1_p_3_5 + C9*k_1_C_1_p_4_5 - C11*k_2_C_1_p_1_5 - C11*k_2_C_1_p_2_5 - C11*k_2_C_1_p_3_5 - C11*k_2_C_1_p_4_5 - C11*Leq*k_1_A_p_5], [C2*k_2_B_2_p_5 - C12*k_1_B_2_p_5 - C12*k_2_A_p_5 + C4*k_1_C_2_p_1_5 + C6*k_1_C_2_p_2_5 + C8*k_1_C_2_p_3_5 + C10*k_1_C_2_p_4_5 - C12*k_2_C_2_p_1_5 - C12*k_2_C_2_p_2_5 - C12*k_2_C_2_p_3_5 - C12*k_2_C_2_p_4_5 + C11*Leq*k_1_A_p_5]])

Compare derivation result to manual input

dCdt_mupad=dCdt_manual_input:
normal(%);
bool(%)

matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_5 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4 + C11*k_2_B_1_p_5], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 + C12*k_1_B_2_p_5 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4 - C2*k_2_B_2_p_5], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 - C3*k_1_C_1_p_1_5 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 + C11*k_2_C_1_p_1_5 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 - C4*k_1_C_2_p_1_5 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C12*k_2_C_2_p_1_5 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_1_C_1_p_2_5 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 + C11*k_2_C_1_p_2_5 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_1_C_2_p_2_5 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C12*k_2_C_2_p_2_5 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_1_C_1_p_3_5 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_3_5 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_1_C_2_p_3_5 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_3_5 + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_1_C_1_p_4_5 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_4_5 - C9*Leq*k_1_A_p_4], [C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_1_C_2_p_4_5 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_4_5 + C9*Leq*k_1_A_p_4], [C12*k_2_A_p_5 + C1*k_1_B_1_p_5 - C11*k_2_B_1_p_5 + C3*k_1_C_1_p_1_5 + C5*k_1_C_1_p_2_5 + C7*k_1_C_1_p_3_5 + C9*k_1_C_1_p_4_5 - C11*k_2_C_1_p_1_5 - C11*k_2_C_1_p_2_5 - C11*k_2_C_1_p_3_5 - C11*k_2_C_1_p_4_5 - C11*Leq*k_1_A_p_5], [C2*k_2_B_2_p_5 - C12*k_1_B_2_p_5 - C12*k_2_A_p_5 + C4*k_1_C_2_p_1_5 + C6*k_1_C_2_p_2_5 + C8*k_1_C_2_p_3_5 + C10*k_1_C_2_p_4_5 - C12*k_2_C_2_p_1_5 - C12*k_2_C_2_p_2_5 - C12*k_2_C_2_p_3_5 - C12*k_2_C_2_p_4_5 + C11*Leq*k_1_A_p_5]]) = matrix([[C3*k_2_B_1_p_1 - C1*k_1_B_1_p_2 - C1*k_1_B_1_p_3 - C1*k_1_B_1_p_4 - C1*k_1_B_1_p_5 - C1*k_1_B_1_p_1 + C5*k_2_B_1_p_2 + C7*k_2_B_1_p_3 + C9*k_2_B_1_p_4 + C11*k_2_B_1_p_5], [C4*k_1_B_2_p_1 + C6*k_1_B_2_p_2 + C8*k_1_B_2_p_3 + C10*k_1_B_2_p_4 + C12*k_1_B_2_p_5 - C2*k_2_B_2_p_1 - C2*k_2_B_2_p_2 - C2*k_2_B_2_p_3 - C2*k_2_B_2_p_4 - C2*k_2_B_2_p_5], [C4*k_2_A_p_1 + C1*k_1_B_1_p_1 - C3*k_2_B_1_p_1 - C3*k_1_C_1_p_1_2 - C3*k_1_C_1_p_1_3 - C3*k_1_C_1_p_1_4 - C3*k_1_C_1_p_1_5 + C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_1_3 + C9*k_2_C_1_p_1_4 + C11*k_2_C_1_p_1_5 - C3*Leq*k_1_A_p_1], [C2*k_2_B_2_p_1 - C4*k_1_B_2_p_1 - C4*k_2_A_p_1 - C4*k_1_C_2_p_1_2 - C4*k_1_C_2_p_1_3 - C4*k_1_C_2_p_1_4 - C4*k_1_C_2_p_1_5 + C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_1_3 + C10*k_2_C_2_p_1_4 + C12*k_2_C_2_p_1_5 + C3*Leq*k_1_A_p_1], [C6*k_2_A_p_2 + C1*k_1_B_1_p_2 - C5*k_2_B_1_p_2 + C3*k_1_C_1_p_1_2 - C5*k_1_C_1_p_2_3 - C5*k_1_C_1_p_2_4 - C5*k_1_C_1_p_2_5 - C5*k_2_C_1_p_1_2 + C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_2_4 + C11*k_2_C_1_p_2_5 - C5*Leq*k_1_A_p_2], [C2*k_2_B_2_p_2 - C6*k_1_B_2_p_2 - C6*k_2_A_p_2 + C4*k_1_C_2_p_1_2 - C6*k_1_C_2_p_2_3 - C6*k_1_C_2_p_2_4 - C6*k_1_C_2_p_2_5 - C6*k_2_C_2_p_1_2 + C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_2_4 + C12*k_2_C_2_p_2_5 + C5*Leq*k_1_A_p_2], [C8*k_2_A_p_3 + C1*k_1_B_1_p_3 - C7*k_2_B_1_p_3 + C3*k_1_C_1_p_1_3 + C5*k_1_C_1_p_2_3 - C7*k_1_C_1_p_3_4 - C7*k_1_C_1_p_3_5 - C7*k_2_C_1_p_1_3 - C7*k_2_C_1_p_2_3 + C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_3_5 - C7*Leq*k_1_A_p_3], [C2*k_2_B_2_p_3 - C8*k_1_B_2_p_3 - C8*k_2_A_p_3 + C4*k_1_C_2_p_1_3 + C6*k_1_C_2_p_2_3 - C8*k_1_C_2_p_3_4 - C8*k_1_C_2_p_3_5 - C8*k_2_C_2_p_1_3 - C8*k_2_C_2_p_2_3 + C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_3_5 + C7*Leq*k_1_A_p_3], [C10*k_2_A_p_4 + C1*k_1_B_1_p_4 - C9*k_2_B_1_p_4 + C3*k_1_C_1_p_1_4 + C5*k_1_C_1_p_2_4 + C7*k_1_C_1_p_3_4 - C9*k_1_C_1_p_4_5 - C9*k_2_C_1_p_1_4 - C9*k_2_C_1_p_2_4 - C9*k_2_C_1_p_3_4 + C11*k_2_C_1_p_4_5 - C9*Leq*k_1_A_p_4], [C2*k_2_B_2_p_4 - C10*k_1_B_2_p_4 - C10*k_2_A_p_4 + C4*k_1_C_2_p_1_4 + C6*k_1_C_2_p_2_4 + C8*k_1_C_2_p_3_4 - C10*k_1_C_2_p_4_5 - C10*k_2_C_2_p_1_4 - C10*k_2_C_2_p_2_4 - C10*k_2_C_2_p_3_4 + C12*k_2_C_2_p_4_5 + C9*Leq*k_1_A_p_4], [C12*k_2_A_p_5 + C1*k_1_B_1_p_5 - C11*k_2_B_1_p_5 + C3*k_1_C_1_p_1_5 + C5*k_1_C_1_p_2_5 + C7*k_1_C_1_p_3_5 + C9*k_1_C_1_p_4_5 - C11*k_2_C_1_p_1_5 - C11*k_2_C_1_p_2_5 - C11*k_2_C_1_p_3_5 - C11*k_2_C_1_p_4_5 - C11*Leq*k_1_A_p_5], [C2*k_2_B_2_p_5 - C12*k_1_B_2_p_5 - C12*k_2_A_p_5 + C4*k_1_C_2_p_1_5 + C6*k_1_C_2_p_2_5 + C8*k_1_C_2_p_3_5 + C10*k_1_C_2_p_4_5 - C12*k_2_C_2_p_1_5 - C12*k_2_C_2_p_2_5 - C12*k_2_C_2_p_3_5 - C12*k_2_C_2_p_4_5 + C11*Leq*k_1_A_p_5]])
TRUE

 

Conclusion:
Typed K-matrix is correct

 

 

K matrix for the 5U-R-RL model

K;

matrix([[- k_1_B_1_p_1 - k_1_B_1_p_2 - k_1_B_1_p_3 - k_1_B_1_p_4 - k_1_B_1_p_5, 0, k_2_B_1_p_1, 0, k_2_B_1_p_2, 0, k_2_B_1_p_3, 0, k_2_B_1_p_4, 0, k_2_B_1_p_5, 0], [0, - k_2_B_2_p_1 - k_2_B_2_p_2 - k_2_B_2_p_3 - k_2_B_2_p_4 - k_2_B_2_p_5, 0, k_1_B_2_p_1, 0, k_1_B_2_p_2, 0, k_1_B_2_p_3, 0, k_1_B_2_p_4, 0, k_1_B_2_p_5], [k_1_B_1_p_1, 0, - k_2_B_1_p_1 - k_1_C_1_p_1_2 - k_1_C_1_p_1_3 - k_1_C_1_p_1_4 - k_1_C_1_p_1_5 - Leq*k_1_A_p_1, k_2_A_p_1, k_2_C_1_p_1_2, 0, k_2_C_1_p_1_3, 0, k_2_C_1_p_1_4, 0, k_2_C_1_p_1_5, 0], [0, k_2_B_2_p_1, Leq*k_1_A_p_1, - k_2_A_p_1 - k_1_B_2_p_1 - k_1_C_2_p_1_2 - k_1_C_2_p_1_3 - k_1_C_2_p_1_4 - k_1_C_2_p_1_5, 0, k_2_C_2_p_1_2, 0, k_2_C_2_p_1_3, 0, k_2_C_2_p_1_4, 0, k_2_C_2_p_1_5], [k_1_B_1_p_2, 0, k_1_C_1_p_1_2, 0, - k_2_B_1_p_2 - k_1_C_1_p_2_3 - k_1_C_1_p_2_4 - k_1_C_1_p_2_5 - k_2_C_1_p_1_2 - Leq*k_1_A_p_2, k_2_A_p_2, k_2_C_1_p_2_3, 0, k_2_C_1_p_2_4, 0, k_2_C_1_p_2_5, 0], [0, k_2_B_2_p_2, 0, k_1_C_2_p_1_2, Leq*k_1_A_p_2, - k_2_A_p_2 - k_1_B_2_p_2 - k_1_C_2_p_2_3 - k_1_C_2_p_2_4 - k_1_C_2_p_2_5 - k_2_C_2_p_1_2, 0, k_2_C_2_p_2_3, 0, k_2_C_2_p_2_4, 0, k_2_C_2_p_2_5], [k_1_B_1_p_3, 0, k_1_C_1_p_1_3, 0, k_1_C_1_p_2_3, 0, - k_2_B_1_p_3 - k_1_C_1_p_3_4 - k_1_C_1_p_3_5 - k_2_C_1_p_1_3 - k_2_C_1_p_2_3 - Leq*k_1_A_p_3, k_2_A_p_3, k_2_C_1_p_3_4, 0, k_2_C_1_p_3_5, 0], [0, k_2_B_2_p_3, 0, k_1_C_2_p_1_3, 0, k_1_C_2_p_2_3, Leq*k_1_A_p_3, - k_2_A_p_3 - k_1_B_2_p_3 - k_1_C_2_p_3_4 - k_1_C_2_p_3_5 - k_2_C_2_p_1_3 - k_2_C_2_p_2_3, 0, k_2_C_2_p_3_4, 0, k_2_C_2_p_3_5], [k_1_B_1_p_4, 0, k_1_C_1_p_1_4, 0, k_1_C_1_p_2_4, 0, k_1_C_1_p_3_4, 0, - k_2_B_1_p_4 - k_1_C_1_p_4_5 - k_2_C_1_p_1_4 - k_2_C_1_p_2_4 - k_2_C_1_p_3_4 - Leq*k_1_A_p_4, k_2_A_p_4, k_2_C_1_p_4_5, 0], [0, k_2_B_2_p_4, 0, k_1_C_2_p_1_4, 0, k_1_C_2_p_2_4, 0, k_1_C_2_p_3_4, Leq*k_1_A_p_4, - k_2_A_p_4 - k_1_B_2_p_4 - k_1_C_2_p_4_5 - k_2_C_2_p_1_4 - k_2_C_2_p_2_4 - k_2_C_2_p_3_4, 0, k_2_C_2_p_4_5], [k_1_B_1_p_5, 0, k_1_C_1_p_1_5, 0, k_1_C_1_p_2_5, 0, k_1_C_1_p_3_5, 0, k_1_C_1_p_4_5, 0, - k_2_B_1_p_5 - k_2_C_1_p_1_5 - k_2_C_1_p_2_5 - k_2_C_1_p_3_5 - k_2_C_1_p_4_5 - Leq*k_1_A_p_5, k_2_A_p_5], [0, k_2_B_2_p_5, 0, k_1_C_2_p_1_5, 0, k_1_C_2_p_2_5, 0, k_1_C_2_p_3_5, 0, k_1_C_2_p_4_5, Leq*k_1_A_p_5, - k_2_A_p_5 - k_1_B_2_p_5 - k_2_C_2_p_1_5 - k_2_C_2_p_2_5 - k_2_C_2_p_3_5 - k_2_C_2_p_4_5]])

 

 

 

 

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Conclusions

 

K matrices for nU-R-RL models were successfully developed.

NOTE: 1U-R-RL is not the same as U-R-RL but identical to U-1R-RL!

 

 

 

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