LRIM_U

Analysis of U-L model

A: R + L <=> RL

B: L <=> L*

Contents

Goals

1. Definitions

2. Derivation of working equation

3. Express concentrations of equilibrium species in terms of a found solution

4. Define functions for equilibrium concentrations

5. Test if solution is meaningful

6. Check whether the solution satisfies all initial equation and conditions

7. Save results on disk for future use

8. 2D plotting

9. ITC curve simulation

Conclusions

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Goals

In this notebook I will write out equations for equilibrium concentrations and either solve them or generate expressions for numeric solutions for a number of models derived in /Users/kovrigin/Documents/Workspace/Data/Data.XV/EKM16.Analysis_of_multistep_kinetic_mechanisms/LRIM/Specific_models/Models.pdf

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1. Definitions

clean up workspace

reset()

Set path to save results into:

ProjectName:="LRIM_U_L";

CurrentPath:="/Users/kovrigin/Documents/Workspace/Data/Data.XV/EKM16.Analysis_of_multistep_kinetic_mechanisms/Equilibria/";

Binding constants:

All binding constants I am using are formation constants so I denote them all as Ka and add a label for the transition.

K_a_A - monomer-ligand interaction

K_a_A;

assume(K_a_A >= 0):

assumeAlso(K_a_A, R_):

K_a_B - Ligand isomerization constant

K_a_B;

assumeAlso(K_a_B>=0):

assumeAlso(K_a_B,R_):

Total concentrations

Rtot - total concentration of the receptor

Rtot;

assumeAlso(Rtot>=0):

assumeAlso(Rtot,R_):

Ltot - total concentration of a ligand

Ltot;

assumeAlso(Ltot>=0):

assumeAlso(Ltot,R_):

Common equilibrium concentrations

Req - equilibrium concentration of a receptor monomer

Req;

assumeAlso(Req>=0):

assumeAlso(Req<=Rtot):

assumeAlso(Req,R_):

Leq - equilibrium concentration of a receptor monomer

Leq;

assumeAlso(Leq>=0):

assumeAlso(Leq<=Ltot):

assumeAlso(Leq,R_):

RLeq - equilibrium concentration of a receptor monomer

RLeq;

assumeAlso(RLeq>=0):

assumeAlso(RLeq<=Rtot):

assumeAlso(RLeq,R_):

Other species will be defined in the sections of specific models.

anames(All,User);

anames(Properties,User);

math

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2. Derivation of working equation

U-L is a model with a ligand isomerization such that only one of the isomers binds a receptor.

Working equation: I will try to express analytical [L] from equation for a total concentration of a receptor or use it for numeric solution if analytical is not possible

[L*] - equilibrium concentration of a non-binding L-isomer

Lstareq;

assumeAlso(Lstareq>=0):

assumeAlso(Lstareq<=Ltot):

assumeAlso(Lstareq,R_):