Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1
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Practical 1
Objectives:
- To learn how to use a computational modelling tool for biochemical reaction simulations.
- To build biochemical networks
- To simulate the time evolution of the reactions
- To explore the properties of simple biochemical reactions.
- A --> B --> C model
- Synthesis-Degradation model
- Michaelis-Menten model
Deliverables
- A report is expected by ... (Word or PDF format, sent to XXX@XXX)
- When you find in the text (illustration needed), it means that you will have to provide an image export of your simulation results in your report.
- Instructors: Vincent Rouilly, Geoff Baldwin.
Part I: Introduction to Computer Modelling
- Presentation Slides: "All models are wrong, but some of them are useful", George Box.
Part II: Getting to know CellDesigner
- Read through the tutorial example, and get familiar with CellDesigner features. Official CellDesigner Tutorial
- Open a sample file: File -> Open -> Samples/...
- Select items, move them around, delete, undo...
Part III: Building Your First Model: A --> B --> C
In this section, you will build your first model from scratch with CellDesigner, and you will learn 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 |
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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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- Questions:(see report structure)
- Describe the time evolution of A, B and C, taking into account the default parameters.
- Using the 'Parameter Scan' function, investigate how parameters 'k1' and 'k2' influence the production of 'C'.
- Find the set of parameters (k1, k2), within a 10% range of their initial value, so that B is maximal at some point in time.
- Additional Resources:
Part IV: Synthesis-Degradation Model
In this section, we investigate a very common motif in biochemistry. It models the synthesis of a compound, and its natural degradation.
From a Mathematical point of view, the model is described as a first-order linear ordinary differential equation.
Model | CellDesigner Instructions |
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Build the topology of the reaction network
| |
From the law of mass action, we can write:
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Define the kinetics driving the reaction network
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Simulate the dynamical behaviour |
|
- Questions:(see report structure)
- Run a simulation over t=1000s, comment on the time evolution of 'A'. (illustration needed).
- Using the dynamical system definition, what is the steady state level of 'A' with regards to the parameters k1 and k2 ? (Steady state means that [math]\displaystyle{ \frac{d[A]}{dt}=0 }[/math]
- Using the 'Parameter Scan' feature, illustrate the influence of both parameters (k_1 and k_2), on the steady state level of 'A' (illustration needed).
- Bonus: Give the analytical solution of the ODE system.
- Now, consider that k_1=0, and [math]\displaystyle{ [A]_{t=0}=A_{0} \gt 0 }[/math]. Keep k_2=0.01. Illustrate the concept of half-life for the compound 'A'.
- Bonus: Derive the analytical expression of the half-life of 'A', with regards to k_1 and k_2.
- Additional Resources:
Part V: Michaelis-Menten Model
An enzyme converts a substrate into a product. 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.
This part of the tutorial deals with well-known Michaelis-Menten formula.
Here, we will focus on comparing the Michaelis-Menten approximation to the full enzymatic reaction network.
Model | CellDesigner Instructions |
---|---|
| |
Following Law of Mass action, we can write: [math]\displaystyle{ a }[/math]
|
Questions:(see report structure)
- From the ODE system description, create all the necessary kinetics reactions in the network provided. We will be considering [math]\displaystyle{ K_{1}=10^5 M^{-1} s^{-1}, K_{2}= 1000 s^{-1} , K_{3}= 10^{-1} , [E]_{t=0}= 10^{-7}M, [S]_{t=0}=0.01M , [P]_{t=0}=0 }[/math]
- Open the Simulation Panel, set Time=20, NbPoints=1000.
- Run a simulation, and comment on the different phases during the product formation. Pay special attention to the formation of the [ES] complex.
Model | CellDesigner Instructions |
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|
- We want now to investigate the Michaelis-Menten expression. Show that under the assumption that the complex [ES] is at steady-state ([math]\displaystyle{ \frac{d[ES]}{dt}=0 }[/math]), we can write: [math]\displaystyle{ \frac{d[P]}{dt}= \frac{Vmax*[S]}{Km+[S]} }[/math]. (Note that [math]\displaystyle{ [E]_{t=0}=[E]_{t}+[ES]_{t} }[/math])
- Express (Km and Vmax) with regards to K_1, K_2, K_3 and [math]\displaystyle{ [E]_{0} }[/math]
- From the expressions found above, create a new reaction (as shown above). Make sure that both models are equivalent with regards to their parameters.
- Run simulations, and comment on the differences observed between to full model and the Michaelis-Menten approximation.