# 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.

Model CellDesigner Instructions
$E + S \begin{matrix} k_1 \\ \longrightarrow \\ \longleftarrow \\ k_{2} \end{matrix} ES \begin{matrix} k_3 \\ \longrightarrow\\ \end{matrix} E + P$
• 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:

\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}

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