Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1: Difference between revisions

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* To explore the properties of simple biochemical reactions.
* To explore the properties of simple biochemical reactions.
** A --> B --> C model
** A --> B --> C model
** Synthesis-Degradation model
** Michaelis-Menten model
** Michaelis-Menten model


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</div>
</div>


* A report is expected by ... (Word or PDF format, sent to XXX@XXX)
* A brief report is expected ([[Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/Practical_1/Report | see structure]]). Report due '''Monday 18th February 2008'''.
* 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.
* 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:'''[[User:Vincent Rouilly| Vincent Rouilly]], Geoff Baldwin.
* '''Instructors:'''[[User:Vincent Rouilly| Vincent Rouilly]], Geoff Baldwin.
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</div>


* [[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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'''Part II: Getting to know CellDesigner'''
'''Part II: Getting to know CellDesigner'''
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* '''Define the topology of the reaction network''':
* '''Define the topology of the reaction network''':
** Open a NEW document: File -> New.
** Open a NEW document: File -> New.
** Create 3 compounds A, B, and C [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Compounds | (help)]].
** Create 3 compounds A, B, and C [[Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/CellDesigner_Tutorial/Compounds | (help)]].
** Create Reaction_1 linking 'A' to 'B' [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Reactions | (help)]].
** Create Reaction_1 linking 'A' to 'B' [[Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/CellDesigner_Tutorial/Reactions | (help)]].
** Create Reaction_2 linking 'B' to 'C'
** Create Reaction_2 linking 'B' to 'C'
* Save your model
* Save your model
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<center><math>
<center><math>
\begin{alignat}{2}
\begin{alignat}{2}
\frac{d[A]}{dt} = - k_{1}*[A] \\
\frac{d[A]}{dt} & = - k_{1}*[A] \\
\frac{d[B]}{dt} =  k_{1}*[A] \\
\frac{d[B]}{dt} & =  k_{1}*[A] -k_{2}*[B] \\
\frac{d[C]}{dt} =  k_{2}*[B]  
\frac{d[C]}{dt} & =  k_{2}*[B]  
\end{alignat}
\end{alignat}
</math></center>
</math></center>
|  
|  
* Edit Reaction_1, Create a NEW local parameter called k1, value equals 1.0 [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Kinetic Simulation | (help)]].
* Edit Reaction_1, Create a NEW local parameter called k1, value equals 1.0 [[Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/CellDesigner_Tutorial/Kinetic Simulation | (help)]].
* Create a kinetic law for Reaction_1, according to the dynamical system [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Kinetic Simulation | (help)]].
* Create a kinetic law for Reaction_1, according to the dynamical system [[Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/CellDesigner_Tutorial/Kinetic Simulation | (help)]].
* Edit Reaction_2, Create a NEW local parameter called k2, value equals 10.0
* 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.
* Create a kinetic law for Reaction_2, according to the dynamical system.
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| Simulate the dynamical behaviour
| Simulate the dynamical behaviour
|  
|  
* Open Simulation Panel [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Simulation_Panel | (help)]]
* Open Simulation Panel [[Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/CellDesigner_Tutorial/Simulation_Panel | (help)]]
* Set time for the simulation to be 10 seconds
* In the top left panel set the End Time as 10 seconds
* Set the number of points as 1000 (gives a nice smooth curve)
* The panel below will be on the species tab, set Initial quantity of A as 10
* Press Execute, and check results.
* Press Execute, and check results.
|}
|}


* '''Questions:'''([[Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1/Report|see report structure]])
* '''Questions:'''([[Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1/Report|see report structure]])
** Describe the time evolution of A, B and C, taking into account the default parameters.
** How do A, B and C, change with time using these default parameters?
** Using the 'Parameter Scan' function, investigate how parameters 'k1' and 'k2' influence the production of 'C'.
** Now swap the values of k1 and k2 (k1=10 and k2=1)under the parameters tab
** 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.
*** How does this alter the formation of C?
*** How does B change?
**** Explain these results
** 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)?
** What additional data would you need to assign k1 and k2?


* '''Additional Resources:'''
* '''Additional Resources:'''
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** [http://en.wikipedia.org/wiki/Rate_law Rate Law (from Wikipedia)]
** [http://en.wikipedia.org/wiki/Rate_law Rate Law (from Wikipedia)]


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<font face="trebuchet ms" style="color:#2171B7" size="3">
'''Part IV: Synthesis-Degradation Model
</font><br>
</div>
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.
{| border="1" cellpadding="10" cellspacing="2" style="width:700px"
!Model
!CellDesigner Instructions
|-
| <center><math>
0 \xrightarrow{k_{1}} A \xrightarrow{k_{2}} 0
</math></center>
|
* 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>\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''':([[Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1/Report|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> \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>[A]_{t=0}=A_{0} > 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:'''
** [http://en.wikipedia.org/wiki/Exponential_decay Exponential decay formula (from Wikipedia)]
** [http://en.wikipedia.org/wiki/Linear_differential_equation Linear differential equation]


<div style="padding: 0px; width: 710px; color: #2171B7; background-color: #B3CD4E">
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<font face="trebuchet ms" style="color:#2171B7" size="3">


'''Part V: Michaelis-Menten Model'''
'''Part IV: Michaelis-Menten Model'''
</font><br>
</font><br>
</div>
</div>




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.
An '''enzyme''' converts a '''substrate''' into a '''product''', this is usually an irreversible reaction and is treated as such in the Michaelis-Menten model. 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.
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.
Here, we will focus on comparing the Michaelis-Menten approximation to the full enzymatic reaction network.
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     k_3 \\
     k_3 \\
     \longrightarrow\\
     \longrightarrow\\
    \longleftarrow  \\
   
    k_{4}
   \end{matrix}
   \end{matrix}
  E + P
  E + P
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</center>
</center>
|  
|  
* Download this [[Media:Enzymatic Reaction Network No Kinetics.xml | File]] on your desktop.
* Download this [[Media:Enzymatic_Reaction_Network_No_Kinetics_2.xml | File]] on your desktop.
* Open the file with CellDesigner.
* Open the file with CellDesigner.
* 1 reaction network topology is described in this file, no kinetics information.
* 1 reaction network topology is described in this file, no kinetics information is yet defined.
|-
|-
| Following Law of Mass action, we can write: <math> a </math>
| Following law of mass action, we can write:
<center><math>
<math>
\begin{alignat}{2}
\begin{alignat}{2}
\frac{d[E]}{dt} = k_{2}[ES] - k_{1}[E][S] \\
\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[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[ES]}{dt} & = k_{1}[E][S] - k_{2}[ES] - k_{3}[ES] \\
\frac{d[P]}{dt} = k_{3}[ES] - k_{4}[E][P]
\frac{d[P]}{dt} & = k_{3}[ES]  
\end{alignat}
\end{alignat}
</math></center>
</math>
|
|
[[Image:CellDesigner_EnzymaticReaction_Network1.png|300px|Simple Enzymatic Reaction]]
[[Image:Enzymatic_Reaction_Network_No_Kinetics_2.png|300px|Simple Enzymatic Reaction]]
|}
|}


'''Questions''':([[Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1/Report|see report structure]])
'''Questions''':([[Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/Practical 1/Report|see report structure]])
* From the ODE system description, create all the necessary kinetics reactions in the network provided. We will be considering <math> 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>
* From the ODE system description, create all the necessary kinetics reactions in the network provided. We will be considering <math> k_{1}=10^5 M^{-1} s^{-1}</math>,<math> k_{2}= 1000 s^{-1} </math>,<math> k_{3}= 10^{-1} s^{-1}</math>,<math> [E]_{t=0}= 0.01 M</math>,<math> [S]_{t=0}=0.1M </math>,<math> [P]_{t=0}=0</math>
* Open the Simulation Panel, set Time=20, NbPoints=1000.
* Open the Simulation Panel, set Time=150, 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.
* Run a simulation, and comment on the different phases during the product formation. Pay special attention to the formation and decay of the [ES] complex. Note that this is a full simulation of the reaction scheme and so does not rely on any assumptions.


{| border="1" cellpadding="10" cellspacing="2" style="width:700px"
{| border="1" cellpadding="10" cellspacing="2" style="width:700px"
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<center><math> S \xrightarrow{E0} P </math> </center>
<center><math> S \xrightarrow{E0} P </math> </center>
|  
|  
[[Image:CellDesigner_EnzymaticReaction_Network.png|300px|Simple Enzymatic Reaction]]
[[Image:Enzymatic_Reaction_Network_No_Kinetics_3.png|300px|Simple Enzymatic Reaction]]
|}
|}


* We want now to investigate the Michaelis-Menten expression. Show that under the assumption that the complex [ES] is at steady-state (<math>\frac{d[ES]}{dt}=0</math>), we can write: <math> \frac{d[P]}{dt}= \frac{Vmax*[S]}{Km+[S]} </math>. (Note that <math> [E]_{t=0}=[E]_{t}+[ES]_{t} </math>)
* We want now to investigate the Michaelis-Menten approximation. Show that under the assumption that the complex [ES] is at steady-state (<math>\frac{d[ES]}{dt}=0</math>), we can write: <math> \frac{d[P]}{dt}= \frac{Vmax[S]}{Km+[S]} </math>. (Note that <math> [E]_{t=0}=[E]_{t}+[ES]_{t} </math>). Also, make sure that the concentration of the substrate is at least 10 fold greater than the concentration of the enzyme.
* Express (Km and Vmax) with regards to K_1, K_2, K_3 and <math>[E]_{0}</math>
* Express (Km and Vmax) with regards to k_1, k_2, k_3 and <math>[E]_{0}</math>; see the links below on how the Michaelis-Menten equation is derived if you are not sure.
* From the expressions found above, create a new reaction (as shown above). Make sure that both models are equivalent with regards to their parameters.
* Now create a new reaction in CellDesigner(as shown above)with an Enzyme that acts on the reaction. Define the maths for this reaction based on the above form of the Michaelis Menten equation. 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.
* Run simulations, and comment on the differences observed between the full model, and the Michaelis-Menten approximation.


* '''Additional Resources:'''
* '''Additional Resources:'''

Latest revision as of 02:47, 19 February 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
    • Michaelis-Menten model

Deliverables

  • A brief report is expected ( see structure). Report due Monday 18th February 2008.
  • 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)
  • In the top left panel set the End Time as 10 seconds
  • Set the number of points as 1000 (gives a nice smooth curve)
  • The panel below will be on the species tab, set Initial quantity of A as 10
  • Press Execute, and check results.
  • Questions:(see report structure)
    • How do A, B and C, change with time using these default parameters?
    • 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
    • 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)?
    • What additional data would you need to assign k1 and k2?


Part IV: Michaelis-Menten Model


An enzyme converts a substrate into a product, this is usually an irreversible reaction and is treated as such in the Michaelis-Menten model. 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\\ \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] + 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]

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} s^{-1} }[/math],[math]\displaystyle{ [E]_{t=0}= 0.01 M }[/math],[math]\displaystyle{ [S]_{t=0}=0.1M }[/math],[math]\displaystyle{ [P]_{t=0}=0 }[/math]
  • Open the Simulation Panel, set Time=150, NbPoints=1000.
  • Run a simulation, and comment on the different phases during the product formation. Pay special attention to the formation and decay of the [ES] complex. Note that this is a full simulation of the reaction scheme and so does not rely on any assumptions.
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]), 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]). Also, make sure that the concentration of the substrate is at least 10 fold greater than the concentration of the enzyme.
  • Express (Km and Vmax) with regards to k_1, k_2, k_3 and [math]\displaystyle{ [E]_{0} }[/math]; see the links below on how the Michaelis-Menten equation is derived if you are not sure.
  • Now create a new reaction in CellDesigner(as shown above)with an Enzyme that acts on the reaction. Define the maths for this reaction based on the above form of the Michaelis Menten equation. Make sure that both models are equivalent with regards to their parameters.
  • Run simulations, and comment on the differences observed between the full model, and the Michaelis-Menten approximation.
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