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

From OpenWetWare
Jump to navigationJump to search
(New page: {{Template:ImperialCollege Spring2008 SyntheticBiologyCourse ComputerModellingPractical‎}} <div style="padding: 10px; width: 720px; border: 5px solid #B3CD4E;"> ''...under development....)
 
mNo edit summary
Line 9: Line 9:
<div style="padding: 0px; width: 680px; color: #2171B7; background-color: #B3CD4E">
<div style="padding: 0px; width: 680px; color: #2171B7; background-color: #B3CD4E">
<center><font face="trebuchet ms" style="color:#2171B7" size="5">
<center><font face="trebuchet ms" style="color:#2171B7" size="5">
'''Practical 1 (3h)'''
'''Practical 1'''
</font><br></center>
</font><br></center>
</div>
</div>
Line 17: Line 17:
</div>
</div>


* Learning how to use a computational modelling tool for biochemical reaction simulations.
* Learn how to use a computational modelling tool for biochemical reaction simulations.
** Building biochemical networks
** Building biochemical networks
** Simulating the time evolution of the reactions
** Simulating the time evolution of the reactions
* Exploring the properties of simple biochemical reactions.
* Explore the properties of simple biochemical reactions.
** A --> B --> C model
** A --> B --> C model
** Synthesis-Degradation model
** Synthesis-Degradation model
Line 41: Line 41:
</div>
</div>


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


<div style="padding: 0px; width: 710px; color: #2171B7; background-color: #B3CD4E">
<div style="padding: 0px; width: 710px; color: #2171B7; background-color: #B3CD4E">
Line 50: Line 50:
</div>
</div>


* Check tutorial
* Read through the [[Imperial College/Courses/Spring2008/Synthetic Biology/Computer Modelling Practicals/CellDesigner_Tutorial/Example| tutorial example]], and get familiar with CellDesigner features. [http://celldesigner.org/documents/StartupGuide211.html Official CellDesigner Tutorial]
* Open a sample file
* Open a sample file: File -> Open -> Samples/...
* Select items, move them around, delete, undo.
* Select items, move them around, delete, undo...




Line 62: Line 62:
</div>
</div>


{| border="1" cellpadding="10" cellspacing="2" style="width:700px"
 
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.
 
 
{| border="1" cellpadding="10" cellspacing="2" style="width:700px; border:3px green"
!Model
!Model
!CellDesigner Instructions
!CellDesigner Instructions
|-
|-
| <math> A -(k_{1})-> B -(k_{2})-> C </math>
| <center><math>
A \xrightarrow{k_{1}} B \xrightarrow{k_{2}} C
</math></center>
|  
|  
* Open a NEW document.
* '''Define the topology of the reaction network''':
* Create 3 compounds A, B, and C [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Compounds | (help)]].
** Open a NEW document: File -> New.
* Create Reaction_1 linking 'A' to 'B' [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Reactions | (help)]].
** Create 3 compounds A, B, and C [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Compounds | (help)]].
* Create Reaction_2 linking 'B' to 'C'
** Create Reaction_1 linking 'A' to 'B' [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Reactions | (help)]].
** Create Reaction_2 linking 'B' to 'C'
* Save your model
* Save your model
|-
|-
| Dynamical system, Law of Mass action:
* <math>\frac{d[A]}{dt} = - k_{1}*[A]</math>
* <math>\frac{d[B]}{dt} =  k_{1}*[A]</math>
* <math>\frac{d[C]}{dt} =  k_{2}*[B]</math>
|  
|  
* 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)]].
Following the Law of Mass action, the dynamic of the system is described as:
<center><math>
\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></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)]].
* 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 [[Synthetic_Biology/UG_Course/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.
* Save your model.
* Save your model.
Line 88: Line 104:
|  
|  
* Open Simulation Panel [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Simulation_Panel | (help)]]
* Open Simulation Panel [[Synthetic_Biology/UG_Course/Computer_Modelling_Practicals/CellDesigner_Tutorial/Simulation_Panel | (help)]]
* set time for the simulation to be 10 seconds
* Set time for the simulation to be 10 seconds
* press Execute, and check results.
* Press Execute, and check results.
|}
|}


* Questions:
* '''Questions:'''
** describe the time evolution of A, B and C, with the default parameters.
** Describe the time evolution of A, B and C, taking into account the default parameters.
** Using 'Parameter Scan' function, investigate how K1 and K2 influence the production of C
** Using the 'Parameter Scan' function, investigate how parameters 'k1' and 'k2' influence the production of 'C'.
** find the set of parameters (k1, k2), within the range, so that B is maximal
** 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.


* Resources:
* '''Additional Resources:'''
** [http://scienceworld.wolfram.com/chemistry/LawofMassAction.html Law of Mass Action (Wolfram's site)]
** [http://scienceworld.wolfram.com/chemistry/LawofMassAction.html Law of Mass Action (Wolfram's site)]
** [http://en.wikipedia.org/wiki/Law_of_mass_action Law of Mass Action in Chemistry (Wikipedia site)]
** [http://en.wikipedia.org/wiki/Law_of_mass_action Law of Mass Action in Chemistry (Wikipedia site)]
** [http://en.wikipedia.org/wiki/Rate_law Rate Law (from Wikipedia)]


<div style="padding: 0px; width: 710px; color: #2171B7; background-color: #B3CD4E">
<div style="padding: 0px; width: 710px; color: #2171B7; background-color: #B3CD4E">
Line 107: Line 124:
</font><br>
</font><br>
</div>
</div>
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.


{| border="1" cellpadding="10" cellspacing="2" style="width:700px"
{| border="1" cellpadding="10" cellspacing="2" style="width:700px"
Line 112: Line 133:
!CellDesigner Instructions
!CellDesigner Instructions
|-
|-
| <math> 0 -(k_{1})-> A -(k_{2})-> 0 </math>
| <center><math>
0 \xrightarrow{k_{1}} A \xrightarrow{k_{2}} 0
</math></center>
|  
|  
* Open a NEW document.
* Open a NEW document. Name it 'Synthesis_Degradation_Model'.
* Create a 'Source', and a 'A' compounds
'''Build the topology of the reaction network'''
* Create a Reaction_1 linking  'Source' to 'A'
* Create a 'Source' compound thanks to the 'simple molecule' icon.
* Create a Reaction_2, as a 'degradation reaction', linked to 'A'
* 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.
* Save your file.
|-
|-
| Dynamical system, Law of Mass action:  
| Dynamical system, Law of Mass action:  
* <math>\frac{d[A]}{dt} = k_{1} - k_{2}*[A]</math>
* <math>\frac{d[A]}{dt} = k_{1} - k_{2}*[A]</math>
|  
|  
* Edit Reaction_1, and create a new parameter k_1 = 1.0, and create the kinetic law according to the ODE system.
'''Define the kinetic driving the reaction network'''
* Edit Reaction_2, and create a new parameter k_2 = .01, and create the kinetic law according to the ODE system.
* 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.
* Save your model.
|-
|-
Line 131: Line 156:
|  
|  
* Open Simulation Panel
* Open Simulation Panel
* Set time for the simulation to be 10 seconds, 1000 points.
* Set time for the simulation to be 1000 seconds, 1000 points.
* Press Execute, and check results.
* Press Execute, and check results.
|}
|}


* Questions:
* '''Questions''':
** Run a simulation over t=1000s, comment on the time evolution of 'A'(illustration needed).
** Run a simulation over t=1000s, comment on the time evolution of 'A'. (illustration needed).
** Using the dynamical system, define what is the steady state level of 'A' with regards to the parameters synthesisRate and degradationRate.
** 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, illustrate the influence of both parameters on the steady state level of 'A' (illustration needed).
** 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>[A]_{t=0}=A_{0} > 0 </math>. Keep k_2=0.01. Illustrate the concept of half-life for the compound 'A'.


* Resources:
* '''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">
<div style="padding: 0px; width: 710px; color: #2171B7; background-color: #B3CD4E">
Line 154: Line 181:
!CellDesigner Instructions
!CellDesigner Instructions
|-
|-
| <math> E + S <-(k_{1}/k_{2})-> ES -(k_{3})-> P </math>
| <center><math>
E+S \xrightarrow[k_{-1}]{k_{1}} ES \xrightarrow{k_{2}} E + P
</math></center>
|  
|  
* ...
* Download this [[Media:Michaelis-Menten-Model.sbml | 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> a </math>  
| Dynamical system, Law of Mass action: <math> a </math>  
* <math>\frac{d[E]}{dt} = k_{2}*[ES] - k_{1}*[E][S]</math>
<center><math>
* <math>\frac{d[S]}{dt} = k_{2}*[ES] - k_{1}*[E][S]</math>
\begin{alignat}{2}
* <math>\frac{d[ES]}{dt} = k_{1}*[E][S] - k_{2}*[ES]</math>
\frac{d[E]}{dt} = k_{2}*[ES] - k_{1}*[E][S] \\
* <math>\frac{d[P]}{dt} = k_{3}*[E][S]</math>
\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></center>
|
|
* 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
| Simulate the dynamical behaviour
Line 172: Line 212:
|}
|}


* Questions:
* '''Questions''':
** What is the influence of each parameter on how quickly the Product is formed ?
** 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.


* Resources:
* '''Additional Resources:'''
** [http://en.wikipedia.org/wiki/Michaelis-Menten_kinetics Michaelis-Menten_kinetics]
** [http://en.wikipedia.org/wiki/Michaelis-Menten_kinetics Michaelis-Menten_kinetics]
** [http://www.lsbu.ac.uk/biology/enztech/kinetics.html Michaelis-Menten Formula Derivation]
** [http://www.lsbu.ac.uk/biology/enztech/kinetics.html Michaelis-Menten Formula Derivation]
** [http://en.wikipedia.org/wiki/Steady_state_%28chemistry%29 Steady State Approximation (from Wikipedia)]

Revision as of 05:18, 11 January 2008

Synthetic Biology (Spring2008): Computer Modelling Practicals

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

<html> <body> <!-- Start of StatCounter Code --> <script type="text/javascript"> var sc_project=3315875; var sc_invisible=0; var sc_partition=36; var sc_security="779debd0"; </script> <script type="text/javascript" src="http://www.statcounter.com/counter/counter_xhtml.js"></script><noscript><div class="statcounter"><a class="statcounter" href="http://www.statcounter.com/"><img class="statcounter" src="http://c37.statcounter.com/3315875/0/779debd0/0/" alt="web metrics" /></a></div></noscript> <!-- End of StatCounter Code --> </body> </html>

...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.
Retrieved from "https://openwetware.org/mediawiki/index.php?title=Imperial_College/Courses/Spring2008/Synthetic_Biology/Computer_Modelling_Practicals/Practical_1&oldid=177951"