Imperial College/Courses/2010/Synthetic Biology/Computer Modelling Practicals/Practical 1: Difference between revisions
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** '''Q4.2:''' Show that this rate is proportional to a fraction <math> \frac{[S]_{t=0}}{[S]_{t=0}+K_{m}} </math> | ** '''Q4.2:''' Show that this rate is proportional to a fraction <math> \frac{[S]_{t=0}}{[S]_{t=0}+K_{m}} </math> | ||
*** What is the enzymatic constant <math> K_{m} </math> ? | *** What is the enzymatic constant <math> K_{m} </math> ? | ||
*** How does | *** How does the rate of production of P depend on the initial concentration of enzyme <math> [E]_{t=0} </math> ? What does this mean in practice? | ||
** '''Q4.3:''' '''Sketch''' the evolution with time of the compounds | ** '''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) | ** '''Q4.4:''' Given the simulations you have run, when do you think MM is justified? (Bonus points if you can show this analytically) |
Revision as of 07:04, 20 January 2010
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: |
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Simulate the dynamical behaviour |
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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!
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 products 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 compounds 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 ( [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