Imperial College/Courses/2009/Synthetic Biology/Computer Modelling Practicals/Practical 2

   Practical 2

Objectives:


 * To learn about enzymatic reactions.
 * how to model them
 * their behaviour
 * the steady state approximation



Part I: Simulating an Enzymatic Reaction


 * An enzyme converts a substrate into a product, this is usually an irreversible reaction and is treated as such in the Michaelis-Menten model.
 * An enzyme reaction constitutes a dynamic process and can be studied as such.
 * One may look at the time courses of the reactants, or look at the steady-states and their stability properties.

Preliminary Simulations

Now that everything is modelled, we can run simulations.


 * From the ODE system description, create all the necessary kinetics reactions in the network provided.
 * We will be considering the following realistic values:
 * $$ k_{1}=10^8 M^{-1} s^{-1}$$
 * $$ k_{2}= 100 s^{-1} $$
 * $$ k_{3}= 10^{-1} s^{-1}$$
 * Initial Condition: $$ [E]_{t=0}= 10^{-7} M$$
 * Initial Condition: $$ [S]_{t=0}=10^{-5} M $$
 * Initial Condition: $$ [P]_{t=0}=0$$
 * Open the Simulation Panel, set Time=150, NbPoints=1000.


 * Get the feel for the behaviour of the system
 * Run the simulation (and why not a few more for similarly well-chosen values of the parameters)
 * Pay special attention to the formation and decay of the [ES] complex. Note that this is a full simulation of the reaction scheme and so does not rely on any assumptions such as a the famous Michaelis-Menten.

 Part II: Questions

Now that you have played a little bit with the system, you are ready for a deeper analysis of its properties.
 * To investigate the properties of the system, use the suggested parameters:
 * $$ k_{1}=10^8 M^{-1} s^{-1}$$
 * $$ k_{2}= 100 s^{-1} $$
 * $$ k_{3}= 10^{-1} s^{-1}$$
 * Initial Condition: $$ [E]_{t=0}= 10^{-7} M$$
 * Initial Condition: $$ [P]_{t=0}=0$$
 * Simulation parameters Time=150, NbPoints=1000.
 * A critical input of the system is the initial concentration of substrate $$ [S]_{t=0}$$. To investigate the influence of $$ [S]_{t=0}$$, it is enough to make it vary between 20nM and 1000nM

The following questions must be addressed in your coursework (and should constitute its Section B).


 * Question 1: How does product formation vary with time (Plot [P] vs t)? (does the initial concentration of substrate have an influence?)
 * Question 2: How do you measure d[P]/dt from the simulation graph?
 * Question 3: Describe how d[P]/dt varies with reagards to the initial concentration of substrate
 * Question 4: Plot [E.S] vs time. Relate this plot to the plot of [P] vs time. It is common to assume that [E.S] is constant - this is called the steady-state approximation. What do you think bout it?
 * Question 5: Why does d[P]/dt vary with [S]?



Part III: Additional Resources 


 * Michaelis-Menten_kinetics
 * Michaelis-Menten Formula Derivation
 * Steady State Approximation (from Wikipedia)

