Commit 93059bd6 authored by FAGES Francois's avatar FAGES Francois
Browse files

TD12

parent 796d2e8b
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# TD2: Enzyme kinetics
* Michaelis-Menten enzymatic reaction network
* conservation laws
* time scales
* Michaelis-Menten kinetics
* with quasi-steady state approximation (QSSA)
* with quasi-equilibrium (QE) approximation
* Cooperative allosteric enzymatic reaction network
* Hill kinetics
F. Fages, 18 Jan 2019
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## Michaelis-Menten enzymatic reaction CRN
* CRN of 3 reactions with mass action law kinetics
* Real parameter values for the hydrolysis of benzoyl-L-arginine ethyl ester by trypsin (protein of 247 amino acids)
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```
present(E,z). parameter(z=1e-8).
present(S,s). parameter(s=1e-5).
absent(C).
absent(P).
```
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```
parameter(k1=4e6, k2=25, k3=15).
```
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```
k1*E*S for E+S => C.
k2*C for C => E+S.
k3*C for C => E+P.
```
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```
list_model.
```
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```
draw_influences.
```
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```
draw_reactions.
```
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```
search_conservations.
```
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```
list_ode.
```
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```
option(time:500).
```
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```
numerical_simulation. plot.
```
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```
numerical_simulation(time:0.1). plot(show:{E,C,P}).
```
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```
numerical_simulation(time:1). plot(show:{E,C}).
```
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```
plot(show: {E, C}, against: S).
```
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## Michaelis-Menten kinetics
* Michaelis-Menten reduced reaction `Vm*A/(Km+A) for A => B.` obtained by Quasi-Steady State Approximation(QSSA)
* Vm=k3*z and Km=(k2+k3)/k1
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```
present(A,s).
absent(B).
```
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```
function(Vm=k3*z).
```
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```
function(Km=(k2+k3)/k1).
```
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```
Vm*A/(Km+A) for A => B.
```
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```
draw_influences.
```
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```
list_model.
```
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```
list_ode.
```
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```
option(show:{A,B,S,P}).
```
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```
numerical_simulation. plot.
```
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```
numerical_simulation(time:0.1). plot(show:{E,C,P,B}).
```
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# Questions
1) change the values of the kinetic parameters to evaluate the robustness of that approximation on the long time scale (500 units)
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```
%slider k1 k2 k3
```
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## Quasi-Equilibrium (QE) approximation
2) Implement the Quasi-Equilibrium reduced reaction `Vm*X/(Kd+X) for X => Y.` with Kd=k2/k1
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```
```
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```
```
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```
```
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```
```
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```
```
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```
```
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3) compare the results with the QSSA approximation
4) to which kinetic parameters is the quality of the QE reduction sensitive ?
*write your answer here*
*...*
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```
%slider k1 k2 k3
```
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```
```
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