5U-R-RL

Generalized model with one binding-incompetent conformation of R (for example, closed) and many binding-competent (for example, open) leading to one nal bound (closed) conformation of R

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Goals

Here I will analyze numeric solutions from "derivation.mn" document.

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Clean up

reset()

Path to previous results

ProjectName:="5U-R-RL";
CurrentPath:="/Users/kovrigin_laptop/Documents/Workspace/Global_Analysis/IDAP/Mathematical_models/Equilibrium_thermodynamic_models/U-multi-path-models/nU/5U-R-RL";

filename:=CurrentPath."/".ProjectName.".mb";
anames(User)

Assume some values for testing operation

Total_R:=1e-3:
Total_L:=10e-3:

Kb1_p1:=2:
Kb1_p2:=3:
Kb1_p3:=4:
Kb1_p4:=5:
Kb1_p5:=6:

Ka1_p1:=2:
Ka1_p2:=3:
Ka1_p3:=4:
Ka1_p4:=5:
Ka1_p5:=6:

Kb2_p1:=2:

test operation of all functions

fLeq_5U_R_RL(Total_R,   Total_L,     Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_seq_5U_R_RL(Total_R,   Total_L,   Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_1eq_5U_R_RL(Total_R,   Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_2eq_5U_R_RL(Total_R,   Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_3eq_5U_R_RL(Total_R,   Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_4eq_5U_R_RL(Total_R,   Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_5eq_5U_R_RL(Total_R,   Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_1Leq_5U_R_RL(Total_R,  Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_2Leq_5U_R_RL(Total_R,  Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_3Leq_5U_R_RL(Total_R,  Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_4Leq_5U_R_RL(Total_R,  Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_p_5Leq_5U_R_RL(Total_R,  Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);
fR_sLeq_5U_R_RL(Total_R,    Total_L, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1);

=> operative

Make wrapper functions for plotting using L/R as X axis

fLeq:=LRratio ->        fLeq_5U_R_RL(Total_R,       LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_seq:=LRratio ->         fR_seq_5U_R_RL(Total_R,   LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_1eq:=LRratio ->    fR_p_1eq_5U_R_RL(Total_R,   LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_2eq:=LRratio ->    fR_p_2eq_5U_R_RL(Total_R,   LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_3eq:=LRratio ->    fR_p_3eq_5U_R_RL(Total_R,   LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_4eq:=LRratio ->    fR_p_4eq_5U_R_RL(Total_R,   LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_5eq:=LRratio ->    fR_p_5eq_5U_R_RL(Total_R,   LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_1Leq:=LRratio ->   fR_p_1Leq_5U_R_RL(Total_R,  LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_2Leq:=LRratio ->   fR_p_2Leq_5U_R_RL(Total_R,  LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_3Leq:=LRratio ->   fR_p_3Leq_5U_R_RL(Total_R,  LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_4Leq:=LRratio ->   fR_p_4Leq_5U_R_RL(Total_R,  LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_p_5Leq:=LRratio ->   fR_p_5Leq_5U_R_RL(Total_R,  LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):
fR_sLeq:=LRratio ->     fR_sLeq_5U_R_RL(Total_R,    LRratio*Total_R, Kb1_p1,Kb1_p2,Kb1_p3,Kb1_p4,Kb1_p5,Ka1_p1,Ka1_p2,Ka1_p3,Ka1_p4,Ka1_p5,Kb2_p1):

Test plotting

Total_R:=1e-3:
LRratio_max:=2:

Kb1_p1:=2:
Kb1_p2:=3:
Kb1_p3:=4:
Kb1_p4:=5:
Kb1_p5:=6:

Ka1_p1:=1e5:
Ka1_p2:=1e5:
Ka1_p3:=1e5:
Ka1_p4:=1e5:
Ka1_p5:=1e5:

Kb2_p1:=2:

LineW:=1.5: //line width

// create plots

pLeq:=  plot::Function2d(
Function=(fLeq),
LegendText="[L]",
Color = RGB::Blue,
XMin=(0),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_sLeq:=  plot::Function2d(
Function=(fR_sLeq),
LegendText="[R*L]",
Color = RGB::Red,
XMin=(0),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

plot(pLeq, pR_sLeq, LegendVisible=TRUE)

=> works

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Assume some constants and evaluate titrations.

NOTE: Adjust dependent constant calculation if necessary.

To create a situation with a specific B2n' constant (example):

//wanted
Kb1_p1:=1e-6:

Kb1_p2:=2:
Ka1_p2:=1e5:
Kb2_p2:=2:

// Set
Ka1_p1:=Ka1_p2:
Kb2_p1:= Kb1_p2*Ka1_p2*Kb2_p2 /( Kb1_p1 * Ka1_p1);

Simulation_name:= "Full 5U-R-RL, different affinity":
Total_R:=1e-3:
LRratio_max:=2:

Kb1_p1:=2:
Kb1_p2:=2.1:
Kb1_p3:=2.2:
Kb1_p4:=2.3:
Kb1_p5:=2.4:

Ka1_p1:=1e5:
Ka1_p2:=2e5:
Ka1_p3:=3e5:
Ka1_p4:=4e5:
Ka1_p5:=5e5:

Kb2_p1:=3:

LRratio_max:=1.5: // plotting range

LineW:=1.5: // plot line width

pLeq:=  plot::Function2d(
Function=(fLeq),
LegendText="[L]",
Color = RGB::Gray,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_seq:=  plot::Function2d(
Function=(fR_seq),
LegendText="[R*]",
Color = RGB::Black,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

// --- Rn' -------

pR_p_1eq:=  plot::Function2d(
Function=(fR_p_1eq),
LegendText="[R']",
Color = RGB::Green,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_2eq:=  plot::Function2d(
Function=(fR_p_2eq),
LegendText="[R'']",
Color = RGB::LimeGreen,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_3eq:=  plot::Function2d(
Function=(fR_p_3eq),
LegendText="[R''']",
Color = RGB::SeaGreen,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_4eq:=  plot::Function2d(
Function=(fR_p_4eq),
LegendText="[R'''']",
Color = RGB::Lavender,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_5eq:=  plot::Function2d(
Function=(fR_p_5eq),
LegendText="[R''''']",
Color = RGB::YellowGreen,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

// --- Rn'L -------

pR_p_1Leq:=  plot::Function2d(
Function=(fR_p_1Leq),
LegendText="[R'L]",
Color = RGB::Blue,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_2Leq:=  plot::Function2d(
Function=(fR_p_2Leq),
LegendText="[R''L]",
Color = RGB::Cyan,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_3Leq:=  plot::Function2d(
Function=(fR_p_3Leq),
LegendText="[R'''L]",
Color = RGB::Aqua,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_4Leq:=  plot::Function2d(
Function=(fR_p_4Leq),
LegendText="[R''''L]",
Color = RGB::SeaGreen,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

pR_p_5Leq:=  plot::Function2d(
Function=(fR_p_5Leq),
LegendText="[R'''''L]",
Color = RGB::AlizarinCrimson,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

//--------

pR_sLeq:=  plot::Function2d(
Function=(fR_sLeq),
LegendText="[R*L]",
Color = RGB::Yellow,
XMin=(LRratio_max*1e-6),
XMax=(LRratio_max),
XName=(LRratio),
TitlePositionX=(0),
LineWidth=LineW):

// Text report
print(Unquoted, Simulation_name);
print(Unquoted, "-------------");
print(Unquoted,"Model: ".ProjectName);
print(Unquoted,"Total_R=".Total_R);

print(Unquoted,"Kb1'=".Kb1_p1);
print(Unquoted,"Kb1''=".Kb1_p2);
print(Unquoted,"Kb1'''=".Kb1_p3);
print(Unquoted,"Kb1''''=".Kb1_p4);
print(Unquoted,"Kb1'''''=".Kb1_p5);

print(Unquoted,"Ka'=".Ka1_p1);
print(Unquoted,"Ka''=".Ka1_p2);
print(Unquoted,"Ka'''=".Ka1_p3);
print(Unquoted,"Ka''''=".Ka1_p4);
print(Unquoted,"Ka'''''=".Ka1_p5);

Kb2_p2:= Kb1_p1*Ka1_p1*Kb2_p1 / ( Kb1_p2 * Ka1_p2):
Kb2_p3:= Kb1_p1*Ka1_p1*Kb2_p1 / ( Kb1_p3 * Ka1_p3):
Kb2_p4:= Kb1_p1*Ka1_p1*Kb2_p1 / ( Kb1_p4 * Ka1_p4):
Kb2_p5:= Kb1_p1*Ka1_p1*Kb2_p1 / ( Kb1_p5 * Ka1_p5):

print(Unquoted,"Kb2'=".Kb2_p1):

print(Unquoted,"Kb2''=".Kb2_p2." (dep)");
print(Unquoted,"Kb2'''=".Kb2_p3." (dep)");
print(Unquoted,"Kb2''''=".Kb2_p4." (dep)");
print(Unquoted,"Kb2'''''=".Kb2_p5." (dep)");

// plot all together
plot(pLeq, pR_seq,  pR_p_1eq,  pR_p_2eq,  pR_p_3eq,  pR_p_4eq,  pR_p_5eq,
pR_p_1Leq,  pR_p_2Leq,  pR_p_3Leq,  pR_p_4Leq,  pR_p_5Leq,
pR_sLeq,
Height=160, Width=100,TicksLabelFont=["Helvetica",12,[0,0,0],Left],
AxesTitleFont=["Helvetica",14,[0,0,0],Left],
XGridVisible=TRUE, YGridVisible=TRUE,
LegendVisible=TRUE, LegendFont=["Helvetica",14,[0,0,0],Left],
ViewingBoxYMax=Total_R);

Full 5U-R-RL, different affinity
-------------
Model: 5U-R-RL
Total_R=0.001
Kb1'=2
Kb1''=2.1
Kb1'''=2.2
Kb1''''=2.3
Kb1'''''=2.4
Ka'=100000.0
Ka''=200000.0
Ka'''=300000.0
Ka''''=400000.0
Ka'''''=500000.0
Kb2'=3
Kb2''=1.428571429 (dep)
Kb2'''=0.9090909091 (dep)
Kb2''''=0.652173913 (dep)
Kb2'''''=0.5 (dep)

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Test of the model: titration of  R with L

 Reduce to U (use U')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=1000000.0Kb1''=0Kb1'''=0Kb1''''=0Kb1'''''=0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=0 Reduce to U (use U'')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0Kb1''=1000000.0Kb1'''=0Kb1''''=0Kb1'''''=0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=0 Reduce to U (use U''')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0Kb1''=0Kb1'''=1000000.0Kb1''''=0Kb1'''''=0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=0 Reduce to U (use U'''')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0Kb1''=0Kb1'''=0Kb1''''=1000000.0Kb1'''''=0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=0 Reduce to U (use U''''')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0Kb1''=0Kb1'''=0Kb1''''=0Kb1'''''=1000000.0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=0 Reduce to U-5R-------------Model: 5U-R-RLTotal_R=0.001Kb1'=1000000.0Kb1''=2000000.0Kb1'''=3000000.0Kb1''''=4000000.0Kb1'''''=5000000.0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=0 Reduce to U-R-RL (use ')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=2Kb1''=0Kb1'''=0Kb1''''=0Kb1'''''=0Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=2 Reduce to U-R-RL (use '')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0.000001Kb1''=2Kb1'''=0.000001Kb1''''=0.000001Kb1'''''=0.000001Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=4000000.0Kb2''=2.0 (dep)Kb2'''=4000000.0 (dep)Kb2''''=4000000.0 (dep)Kb2'''''=4000000.0 (dep) Reduce to U-R-RL (use ''')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0.000001Kb1''=0.000001Kb1'''=2Kb1''''=0.000001Kb1'''''=0.000001Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=4000000.0Kb2''=4000000.0 (dep)Kb2'''=2.0 (dep)Kb2''''=4000000.0 (dep)Kb2'''''=4000000.0 (dep) Reduce to U-R-RL (use '''')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0.000001Kb1''=0.000001Kb1'''=0.000001Kb1''''=2Kb1'''''=0.000001Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=4000000.0Kb2''=4000000.0 (dep)Kb2'''=4000000.0 (dep)Kb2''''=2.0 (dep)Kb2'''''=4000000.0 (dep) Reduce to U-R-RL (use ''''')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=0.000001Kb1''=0.000001Kb1'''=0.000001Kb1''''=0.000001Kb1'''''=2Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=4000000.0Kb2''=4000000.0 (dep)Kb2'''=4000000.0 (dep)Kb2''''=4000000.0 (dep)Kb2'''''=2.0 (dep) Reduce to 2U-R-RL (use ' and '')-------------Model: 5U-R-RLTotal_R=0.001Kb1'=2Kb1''=3Kb1'''=0.000001Kb1''''=0.000001Kb1'''''=0.000001Ka'=100000.0Ka''=100000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=3Kb2''=2.0 (dep)Kb2'''=6000000.0 (dep)Kb2''''=6000000.0 (dep)Kb2'''''=6000000.0 (dep) Reduce to 2U-R-RL (use ' and ''), different affinity-------------Model: 5U-R-RLTotal_R=0.001Kb1'=2Kb1''=2.1Kb1'''=0.000001Kb1''''=0.000001Kb1'''''=0.000001Ka'=100000.0Ka''=1000000.0Ka'''=100000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=3Kb2''=0.2857142857 (dep)Kb2'''=6000000.0 (dep)Kb2''''=6000000.0 (dep)Kb2'''''=6000000.0 (dep) Reduce to 3U-R-RL, different affinity-------------Model: 5U-R-RLTotal_R=0.001Kb1'=2Kb1''=2.1Kb1'''=2.2Kb1''''=0.000001Kb1'''''=0.000001Ka'=100000.0Ka''=200000.0Ka'''=300000.0Ka''''=100000.0Ka'''''=100000.0Kb2'=3Kb2''=1.428571429 (dep)Kb2'''=0.9090909091 (dep)Kb2''''=6000000.0 (dep)Kb2'''''=6000000.0 (dep)

 Reduce to 4U-R-RL, different affinity-------------Model: 5U-R-RLTotal_R=0.001Kb1'=2Kb1''=2.1Kb1'''=2.2Kb1''''=2.3Kb1'''''=0.000001Ka'=100000.0Ka''=200000.0Ka'''=300000.0Ka''''=400000.0Ka'''''=100000.0Kb2'=3Kb2''=1.428571429 (dep)Kb2'''=0.9090909091 (dep)Kb2''''=0.652173913 (dep)Kb2'''''=6000000.0 (dep) Full 5U-R-RL, different affinity-------------Model: 5U-R-RLTotal_R=0.001Kb1'=2Kb1''=2.1Kb1'''=2.2Kb1''''=2.3Kb1'''''=2.4Ka'=100000.0Ka''=200000.0Ka'''=300000.0Ka''''=400000.0Ka'''''=500000.0Kb2'=3Kb2''=1.428571429 (dep)Kb2'''=0.9090909091 (dep)Kb2''''=0.652173913 (dep)Kb2'''''=0.5 (dep)

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Conclusion:

The model works as expected

NOTE: To turn on one path, you need to find out how to set B2' constant. See example  how to set up Kb1' and Kb2'