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.
Model  CellDesigner Instructions 

Following the Law of Mass action, the dynamic of the system is described as: 

Simulate the dynamical behaviour 

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 ABC 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 steadystates and their stability properties.
 A convenient approaximation, called the MichaelisMenten approaximation is often used sometimes wrongly!
Model  CellDesigner Instructions 

 
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] 
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:
 [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 Conditions: [math]\displaystyle{ [E]_{t=0}= 10^{7} M }[/math] ; [math]\displaystyle{ [S]_{t=0}=10^{5} M }[/math] ; [math]\displaystyle{ [P]_{t=0}=0 }[/math]
 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 [math]\displaystyle{ [S]_{t=0} }[/math].
 To investigate the influence of [math]\displaystyle{ [S]_{t=0} }[/math], we will make it vary between [math]\displaystyle{ 10^{9} M }[/math] and 10^{4} M</math> . The remaining parameters are kept as:
 [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 Conditions : [math]\displaystyle{ [E]_{t=0}= 10^{7} M }[/math] ; [math]\displaystyle{ [P]_{t=0}=0 }[/math]
 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 MichaelisMenten MM) Approximation. MM assumes that the enzyme complex ES is in a dynamic steady state ( [math]\displaystyle{ \frac{d[ES]}{dt} =0 }[/math] ) 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 [math]\displaystyle{ \frac{[S]_{t=0}}{[S]_{t=0}+K_{m}} }[/math]
 What is the enzymatic constant [math]\displaystyle{ K_{m} }[/math] ?
 How does the rate of production of P depend on the initial concentration of enzyme [math]\displaystyle{ [E]_{t=0} }[/math] ? 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 [math]\displaystyle{ \frac{d[P]}{dt}_{t=0} }[/math] is very useful to estimate the enzymatic constant [math]\displaystyle{ K_{m} }[/math] 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 [math]\displaystyle{ K_{m} }[/math] from these data?
Part IV: Additional Resources
 Law of Mass Action
 Enzyme Kynetics