Imperial College/Courses/2009/Synthetic Biology/Computer Modelling Practicals/Practical 2
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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 MichaelisMenten 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 steadystates and their stability properties.
Model  CellDesigner Instructions 



Following law of mass action, we can write:

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} = 100s^{ − 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 wellchosen 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 MichaelisMenten.
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} = 100s^{ − 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 steadystate approximation. What do you think bout it?
 Question 5: Why does d[P]/dt vary with [S]?
Part III: Additional Resources
 MichaelisMenten_kinetics
 MichaelisMenten Formula Derivation
 Steady State Approximation (from Wikipedia)