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 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.


Model CellDesigner Instructions
[math]\displaystyle{ E + S \begin{matrix} k_1 \\ \longrightarrow \\ \longleftarrow \\ k_{2} \end{matrix} ES \begin{matrix} k_3 \\ \longrightarrow\\ \end{matrix} E + P }[/math]
  • Download this File on your desktop.
  • Open the file with CellDesigner.
  • 1 reaction network topology is described in this file, no kinetics information is yet defined.
Following law of mass action, we can write:

[math]\displaystyle{ \begin{alignat}{2} \frac{d[E]}{dt} & = k_{2}[ES] - k_{1}[E][S] + k_{3}[ES] \\ \frac{d[S]}{dt} & = k_{2}[ES] - k_{1}[E][S] \\ \frac{d[ES]}{dt} & = k_{1}[E][S] - k_{2}[ES] - k_{3}[ES] \\ \frac{d[P]}{dt} & = k_{3}[ES] \end{alignat} }[/math]

Simple Enzymatic Reaction

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:
    • [math]\displaystyle{ k_{1}=10^8 M^{-1} s^{-1} }[/math]
    • [math]\displaystyle{ k_{2}= 100 s^{-1} }[/math]
    • [math]\displaystyle{ k_{3}= 10^{-1} s^{-1} }[/math]
    • Initial Condition: [math]\displaystyle{ [E]_{t=0}= 10^{-7} M }[/math]
    • Initial Condition: [math]\displaystyle{ [S]_{t=0}=10^{-5} M }[/math]
    • Initial Condition: [math]\displaystyle{ [P]_{t=0}=0 }[/math]
    • 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:
    • [math]\displaystyle{ k_{1}=10^8 M^{-1} s^{-1} }[/math]
    • [math]\displaystyle{ k_{2}= 100 s^{-1} }[/math]
    • [math]\displaystyle{ k_{3}= 10^{-1} s^{-1} }[/math]
    • Initial Condition: [math]\displaystyle{ [E]_{t=0}= 10^{-7} M }[/math]
    • Initial Condition: [math]\displaystyle{ [P]_{t=0}=0 }[/math]
    • Simulation parameters Time=150, NbPoints=1000.
  • A critical input of the system is the initial concentration of substrate [math]\displaystyle{ [S]_{t=0} }[/math]. To investigate the influence of [math]\displaystyle{ [S]_{t=0} }[/math], 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


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