# 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 |
---|---|

- 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] \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] |

**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] k_{1}=10^8 M^{-1} s^{-1}[/math]
- [math] k_{2}= 100 s^{-1} [/math]
- [math] k_{3}= 10^{-1} s^{-1}[/math]
- Initial Condition: [math] [E]_{t=0}= 10^{-7} M[/math]
- Initial Condition: [math] [S]_{t=0}=10^{-5} M [/math]
- Initial Condition: [math] [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] k_{1}=10^8 M^{-1} s^{-1}[/math]
- [math] k_{2}= 100 s^{-1} [/math]
- [math] k_{3}= 10^{-1} s^{-1}[/math]
- Initial Condition: [math] [E]_{t=0}= 10^{-7} M[/math]
- Initial Condition: [math] [P]_{t=0}=0[/math]
- Simulation parameters Time=150, NbPoints=1000.

- A critical input of the system is the initial concentration of substrate [math] [S]_{t=0}[/math]. To investigate the influence of [math] [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 **

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