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* [[Image:File | Presentation Slides]]: "All models are wrong, but some of them are useful", George Box.
* "All models are wrong, but some of them are useful", George Box.


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Revision as of 13:39, 14 January 2008

Synthetic Biology (Spring2008): Computer Modelling Practicals

Home        CellDesigner Tutorial        Practical 1        Practical 2        Practical 3        Schedule        Back to Synthetic Biology Course       

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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 ( see structure)
  • 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

  • "All models are wrong, but some of them are useful", George Box.

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] -k_{2}*[B] \\ \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:(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.

Part IV: Synthesis-Degradation Model


In this section, we investigate a very common motif in biochemistry. It models the continuous and constant 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]

CellDesigner Synthesis-Degradation Model

  • 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.
From the law of mass action, we can write:
  • [math]\displaystyle{ \frac{d[A]}{dt} = k_{1} - k_{2}*[A] }[/math]

Define the kinetics 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, with 1000 points.
  • Press Execute, and check results.
  • Questions:(see report structure)
    • Run a simulation over t=1000s, nb points=1000. 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.

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
[math]\displaystyle{ E + S \begin{matrix} k_1 \\ \longrightarrow \\ \longleftarrow \\ k_{2} \end{matrix} ES \begin{matrix} k_3 \\ \longrightarrow\\ \longleftarrow \\ k_{4} \end{matrix} E + P }[/math]
  • Download this File on your desktop.
  • Open the file with CellDesigner.
  • 1 reaction network topology is described in this file, no kinetics information is yet defined.
Following law of mass action, we can write:

[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] - k_{3}[ES] + k_{4}[E][P]\\ \frac{d[P]}{dt} & = k_{3}[ES] - k_{4}[E][P] \end{alignat} }[/math]

Simple Enzymatic Reaction

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} }[/math],[math]\displaystyle{ K_{2}= 1000 s^{-1} }[/math],[math]\displaystyle{ K_{3}= 10^{-1} }[/math],[math]\displaystyle{ K_{4}= 2 M^{-1} s^{-1} }[/math],[math]\displaystyle{ [E]_{t=0}= 0.01 M }[/math],[math]\displaystyle{ [S]_{t=0}=0.01M }[/math],[math]\displaystyle{ [P]_{t=0}=0 }[/math]
  • Open the Simulation Panel, set Time=100, 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
[math]\displaystyle{ S \xrightarrow{E0} P }[/math]

Simple Enzymatic Reaction

  • We want now to investigate the Michaelis-Menten approximation. Show that under the assumption that the complex [ES] is at steady-state ([math]\displaystyle{ \frac{d[ES]}{dt}=0 }[/math]), and K_4=0, 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 in CellDesigner(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.
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