Imperial College/Courses/2010/Synthetic Biology/Computer Modelling Practicals/Practical 1

   Practical 1

Foreword: "All models are wrong, but some of them are useful, George Box"


 * Possible Way to understand this: Modelling = Catching the Trend and Explaining it
 * Analysis of a problem identifies the most important process shaping the problem
 * The effect of each process is described with some equations (or any tools borrowed from mathematics) - their combination is then simulated.
 * Successful Modelling:
 * Predictive Power: the outcome to simulation is very close to the outcome in real life
 * Reusability: the model can be reused in another, similar case
 * Another Possible Explanation:
 * when data deviate from predictions, something interesting may be happening
 * New effect at work?
 * Models are therefore wrong but sometimes useful!

 Part I: Getting to know CellDesigner


 * Thanks to Dr V rouilly for the Cell Designer Tutorial!!!
 * Read through the tutorial example, and get familiar with CellDesigner features. Official CellDesigner Tutorial
 * Please Note: the link redirects you to the 2008 tutorials. Make sure that when you are done you come back to this page!!!


 * Open a sample file: File -> Open -> Samples/...
 * Select items, move them around, delete, undo...

 Part II: Your First Model: A --> B --> C 


 * Now is the time to build your first model from scratch with CellDesigner, and to run a simulation.
 * The model explored describe a system where a compound 'A' is transformed into a compound 'B', which is consequently transformed into a compound 'C'.
 * To start, launch the CellDesigner Application: Double Click on the Icon found on your Desktop.
 * Then follow the instructions below to build the model.

You are now ready to analyse the behaviour of the biochemical network A --> B --> C.

 Questions

The following qustions are to be addressed in Section A of your coursework.


 * Question 1:  Description of the Dynamics
 * Q1.1: Plot and Describe the evolution with time of the concentrations of A, B and C, using these default parameters?
 * Q1.2: Now swap the values of k1 and k2 (k1=10 and k2=1)under the parameters tab
 * How does this alter the formation of C?
 * How does B change?
 * Explain these results


 * Question 2:  Now, let us place ourselves in the position of an experimentalist.
 * Q2.1: If you had real life data showing the accumulation of C for an A-B-C reaction you could fit the data using this model and two rate constants would be returned. Could you assign these rate constants to k1 or k2 (yes or no)?
 * Q2.2: What additional data would you need to assign k1 and k2? (Explain how you would extract k1 and k2)



Part III: Simulating an Enzymatic Reaction


 * An enzyme converts a substrate into a product, this is usually an irreversible reaction.
 * 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.
 * A convenient approaximation, called the Michaelis-Menten approaximation is often used -sometimes wrongly!

 Recommended Simulations

Now that you have a network representation and a system of ODEs, you can run simulations and try to understand the dynamics of enzymatic reactions.


 * Typical Simulation: let us consider the following realistic values:
 * $$ k_{1}=10^8 M^{-1} s^{-1}$$ ; $$ k_{2}= 100 s^{-1} $$ ; $$ k_{3}= 10^{-1} s^{-1}$$
 * Initial Conditions: $$ [E]_{t=0}= 10^{-7} M$$ ; $$ [S]_{t=0}=10^{-5} M $$ ; $$ [P]_{t=0}=0$$
 * Open the Simulation Panel, set Time=2000, NbPoints=10000. NB: values have been changed - they should be correct now
 * Run the simulation - Get the feel for the behaviour of the system
 * Pay special attention to the formation and decay of the [ES] complex.
 * Note that this is a full simulation of the reaction scheme and does not rely on any assumption.

A critical input of the system is the initial concentration of substrate $$ [S]_{t=0}$$.
 * To investigate the influence of $$ [S]_{t=0}$$, we will make it vary between $$ 10^{-9} M$$  and 10^{-4} M  . The remaining parameters are kept as:
 * $$ k_{1}=10^8 M^{-1} s^{-1}$$ ; $$ k_{2}= 100 s^{-1} $$ ; $$ k_{3}= 10^{-1} s^{-1}$$
 * Initial Conditions : $$ [E]_{t=0}= 10^{-7} M$$ ; $$ [P]_{t=0}=0$$
 * Run the simulation
 * Again pay special attention to the formation and decay of the [ES] complex.
 * This time pay also attention to the profile of [P], especially at the start of the simulation (time close to 0)

 Questions

The following questions must be addressed in your coursework (Section B).


 * Question 1: Apply the law of mass action and derive the system of ODE
 * Question 2: Describe and explain the evolution with time of the species involved in the enzymatic reaction
 * Use the first (typical) simulation - You can comment directly on the graph(s) if you want
 * Do not forget that the evolution of the species is linked
 * Question 3: Describe and explain (in qulalitative terms) the impact of the initial concentration of substrate  on the dynamics of the enzymatic reaction
 * Question 4: The Michaelis-Menten MM) Approximation. MM assumes that the enzyme complex ES is in a dynamic steady state ( $$ \frac{d[ES]}{dt} =0 $$ ) over the course of the reaction (that is while there is some substrate to turn into product).
 * Q4.1: Show that if this is verified then the product is created at a constant rate and that substrate disappears at the same rate.
 * Q4.2: Show that this rate is proportional to a fraction $$ \frac{[S]_{t=0}}{[S]_{t=0}+K_{m}} $$
 * What is the enzymatic constant $$ K_{m} $$ ?
 * How does the rate of production of P depend on the initial concentration of enzyme $$ [E]_{t=0} $$ ? What does this mean in practice?
 * Q4.3: Sketch the evolution with time of the compounds
 * Q4.4: Given the simulations you have run, when do you think MM is justified? (Bonus points if you can show this analytically)


 * Question 5: The gradient at the origin $$ \frac{d[P]}{dt}_{t=0} $$ is very useful to estimate the enzymatic constant $$ K_{m} $$ from data
 * Q5.1: How do you measure d[P]/dt from a simulation graph or experimental data?
 * Q5.2: Now imagine that you have conducted a set of enzymatic experiments where the initial concentration of enzyme was kept constant and the amount of substrate was made to vary over a large range of concentrations. Often you can not directly record the evolution with time of the product P: P(t), but let us say you have been able to convert the experimental data into a reliable estimate of P(t). How would you estimate $$ K_{m} $$ from these data?

 Part IV: Additional Resources


 * Law of Mass Action
 * Law of Mass Action (Wolfram's site)
 * Law of Mass Action in Chemistry (Wikipedia site)
 * Rate Law (from Wikipedia)


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