Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1

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Synthetic Biology (Spring2008): Computer Modelling Practicals

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...under development...

Practical 1


Objectives:

  • Learn how to use a computational modelling tool for biochemical reaction simulations.
    • Building biochemical networks
    • Simulating the time evolution of the reactions
  • 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.


Part I: Introduction to Computer Modelling

Part II: Getting to know CellDesigner


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
[math]\displaystyle{ A \xrightarrow{k_{1}} B \xrightarrow{k_{2}} C }[/math]
  • Define the topology of the reaction network:
    • Open a NEW document: File -> New.
    • Create 3 compounds A, B, and C (help).
    • Create Reaction_1 linking 'A' to 'B' (help).
    • Create Reaction_2 linking 'B' to 'C'
  • Save your model

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

[math]\displaystyle{ \begin{alignat}{2} \frac{d[A]}{dt} = - k_{1}*[A] \\ \frac{d[B]}{dt} = k_{1}*[A] \\ \frac{d[C]}{dt} = k_{2}*[B] \end{alignat} }[/math]
  • Edit Reaction_1, Create a NEW local parameter called k1, value equals 1.0 (help).
  • Create a kinetic law for Reaction_1, according to the dynamical system (help).
  • Edit Reaction_2, Create a NEW local parameter called k2, value equals 10.0
  • Create a kinetic law for Reaction_2, according to the dynamical system.
  • Save your model.
Simulate the dynamical behaviour
  • Open Simulation Panel (help)
  • Set time for the simulation to be 10 seconds
  • Press Execute, and check results.
  • Questions:
    • 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.

Part IV: Synthesis-Degradation Model

In this section, we are going to 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
[math]\displaystyle{ 0 \xrightarrow{k_{1}} A \xrightarrow{k_{2}} 0 }[/math]
  • Open a NEW document. Name it 'Synthesis_Degradation_Model'.

Build the topology of the reaction network

  • Create a 'Source' compound thanks to the 'simple molecule' icon.
  • The same way, create a 'A' compound.
  • Create a reaction link between 'Source' and 'A', Reaction_1, using the 'state transition' icon.
  • Create a 'degradation reaction' linked to 'A', Reaction_2, using the 'degradation reaction' icon.
  • Save your file.
Dynamical system, Law of Mass action:
  • [math]\displaystyle{ \frac{d[A]}{dt} = k_{1} - k_{2}*[A] }[/math]

Define the kinetic driving the reaction network

  • Edit Reaction_1, and define a new parameter k_1 = 1.0, and create the kinetic law according to the ODE system.
  • Edit Reaction_2, and define a new parameter k_2 = .01, and create the kinetic law according to the ODE system.
  • Save your model.
Simulate the dynamical behaviour
  • Open Simulation Panel
  • Set time for the simulation to be 1000 seconds, 1000 points.
  • Press Execute, and check results.
  • Questions:
    • 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, on the steady state level of 'A' (illustration needed).
    • 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'.

Part V: Michaelis-Menten Model

Model CellDesigner Instructions
[math]\displaystyle{ E+S \xrightarrow[k_{-1}]{k_{1}} ES \xrightarrow{k_{2}} E + P }[/math]
  • Download this File on your desktop.
  • Open the file with CellDesigner.
  • 2 reaction network topologies are described in this file.
    • full enzymatic reaction network (topology + kinetic)
    • Michaelis-Menten approximation (only topology)
Dynamical system, Law of Mass action: [math]\displaystyle{ a }[/math]
[math]\displaystyle{ \begin{alignat}{2} \frac{d[E]}{dt} = k_{2}*[ES] - k_{1}*[E][S] \\ \frac{d[S]}{dt} = k_{2}*[ES] - k_{1}*[E][S] \\ \frac{d[ES]}{dt} = k_{1}*[E][S] - k_{2}*[ES] \\ \frac{d[P]}{dt} = k_{3}*[E][S] \end{alignat} }[/math]
  • Consider the michaelis menten assumption
  • Steady state approximation on the [ES] compound formation.
  • Derive the new formula, and update the reaction network accordingly.
Simulate the dynamical behaviour
  • Open Simulation Panel
  • set time for the simulation to be 10 seconds
  • press Execute, and check results.
  • Questions:
    • What is the influence of each parameter on how quickly the Product is formed ?
    • Consider the Michaelis-Menten assumption, and derive the simplified system.
    • Update the reaction network at the bottom so that the two reactions are equivalent.
    • Simulate the full set of reactions and comment on the difference.
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