http://2007.igem.org/wiki/index.php?title=Special:Contributions/Charkness&feed=atom&limit=50&target=Charkness&year=&month=2007.igem.org - User contributions [en]2024-03-28T19:13:12ZFrom 2007.igem.orgMediaWiki 1.16.5http://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:12:24Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure 1. The reasons for using these modified equations are discussed below. <br />
<br />
<center>[[Image:screenshot1.jpg]]</center><br />
<br />
''Discussion''<br />
<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
<center>[[Image:screenshot2.jpg]]</center><br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured physically in the laboratory. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
<center>[[Image:screenshot3.jpg]]</center><br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
<center>[[Image:screenshot4.jpg]]</center><br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown in Equation 1.<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown in Equation 2. <br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.<br />
<br />
<br />
<center>[[Image:Simplemodel.jpg|500px]]</center><br />
<center>Figure 1</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:10:13Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure 1. The reasons for using these modified equations are discussed below. <br />
<br />
<center>[[Image:screenshot1.jpg]]</center><br />
<br />
''Discussion''<br />
<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
<center>[[Image:screenshot2.jpg]]</center><br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
<center>[[Image:screenshot3.jpg]]</center><br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
<center>[[Image:screenshot4.jpg]]</center><br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown in Equation 1.<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown in Equation 2. <br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.<br />
<br />
<br />
<center>[[Image:Simplemodel.jpg|500px]]</center><br />
<center>Figure 1</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:10:01Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure 1. The reasons for using these modified equations are discussed below. <br />
<br />
<center>[[Image:screenshot1.jpg]]</center><br />
<br />
''Discussion''<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
<center>[[Image:screenshot2.jpg]]</center><br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
<center>[[Image:screenshot3.jpg]]</center><br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
<center>[[Image:screenshot4.jpg]]</center><br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown in Equation 1.<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown in Equation 2. <br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.<br />
<br />
<br />
<center>[[Image:Simplemodel.jpg|500px]]</center><br />
<center>Figure 1</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:09:24Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure 1 The reasons for using these modified equations are discussed below. <br />
<br />
<center>[[Image:screenshot1.jpg]]</center><br />
<br />
''Discussion''<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
<center>[[Image:screenshot2.jpg]]</center><br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
<center>[[Image:screenshot3.jpg]]</center><br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
<center>[[Image:screenshot4.jpg]]</center><br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown in Equation 1.<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown in Equation 2. <br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.<br />
<br />
<br />
<center>[[Image:Simplemodel.jpg|500px]]</center><br />
<center>Figure 1</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:08:58Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure 1 The reasons for using these modified equations are discussed below. <br />
<br />
<center>[[Image:screenshot1.jpg]]</center><br />
<br />
''Discussion''<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
<center>[[Image:screenshot2.jpg]]</center><br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
<center>[[Image:screenshot3.jpg]]</center><br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
<center>[[Image:screenshot4.jpg]]</center><br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown in Equation 1.<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown in Equation 2. <br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.<br />
<br />
<br />
<center>[[Image:Simplemodel.jpg|400px]]</center><br />
<center>Figure 1</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:05:51Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure 1 The reasons for using these modified equations are discussed below. <br />
<br />
<center>[[Image:screenshot1.jpg]]</center><br />
<center>[[Image:Simplemodel.jpg|400px]]</center><br />
<center>Figure 1</center><br />
<br />
''Discussion''<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
<center>[[Image:screenshot2.jpg]]</center><br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
<center>[[Image:screenshot3.jpg]]</center><br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
<center>[[Image:screenshot4.jpg]]</center><br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown.<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown. <br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:02:41Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure?? The reasons for using these modified equations are discussed below. <br />
<br />
[[Image:screenshot1.jpg]]<br />
<br />
''Discussion''<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
[[Image:screenshot2.jpg]]<br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
[[Image:screenshot3.jpg]]<br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
[[Image:screenshot4.jpg]]<br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown.<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown. <br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.<br />
<br />
<center>[[Image:Simplemodel.jpg|400px]]</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T09:00:20Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
[[Image:Simplemodel.jpg|400px]]<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure?? The reasons for using these modified equations are discussed below. <br />
<br />
[[Image:screenshot1.jpg]]<br />
<br />
<br />
Discussion<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
[[Image:screenshot2.jpg]]<br />
<br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
[[Image:screenshot3.jpg]]<br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
[[Image:screenshot4.jpg]]<br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown.<br />
<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown. <br />
<br />
<br />
<br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T08:59:22Z<p>Charkness: /* Trial model for the promoter DmpR */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===<br />
[[Image:Simplemodel.jpg]]<br />
<br />
The current model that will be used for modeling purposes will use the three following equations to model the simple system as shown in Figure?? The reasons for using these modified equations are discussed below. <br />
<br />
[[Image:screenshot1.jpg]]<br />
<br />
<br />
Discussion<br />
The equation for the change of DntR|S within the system could be modelled by Equation 4<br />
<br />
[[Image:screenshot2.jpg]]<br />
<br />
<br />
At the beginning of the reaction DntR will have an unknown constant value as it cannot be measured. As the DntR will have a constant value the DntR and kb can be replaced by another constant kb’ as shown <br />
<br />
[[Image:screenshot3.jpg]]<br />
<br />
By substituting Equation 5 into Equation 4 gives<br />
<br />
[[Image:screenshot4.jpg]]<br />
<br />
However it is clear from Equation 6 that as the signal increases the DntR|S will increase without ever reaching a saturation limit. It was decided that the equation should be changed to utilize Michaelis-Menten. This means that a saturation limit will now be possible as shown.<br />
<br />
<br />
<br />
Next it is important to note that the signal equation includes a term for the degradation of the signal as this is possible in the physical model. This equation also includes a term for the binding and a term for the unbinding as shown. <br />
<br />
<br />
<br />
<br />
<br />
Also it should be noted that in this model XGAL is ignored, this is because the level of blue that is measured is proportional to the LacZ produced. By ignoring XGAL it will simplify the system equations.<br />
<br />
Another point to note is that in this model of the system the transcription and the translation steps have been ‘lumped’ together by using Michaelis-Menten rather than modeling these biological steps separately.</div>Charknesshttp://2007.igem.org/wiki/index.php/File:Screenshot4.jpgFile:Screenshot4.jpg2007-07-25T08:58:33Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Screenshot3.jpgFile:Screenshot3.jpg2007-07-25T08:56:43Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Screenshot2.jpgFile:Screenshot2.jpg2007-07-25T08:54:59Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Screenshot1.jpgFile:Screenshot1.jpg2007-07-25T08:52:42Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Simplemodel.jpgFile:Simplemodel.jpg2007-07-25T08:52:09Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T08:43:46Z<p>Charkness: /* Modelling */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Modelling ==<br />
=== Trial model for the promoter DmpR ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/ModelingGlasgow/Modeling2007-07-25T08:42:28Z<p>Charkness: </p>
<hr />
<div>== Modelling ==<br />
=== Trial model for the promoter DmpR ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:35:52Z<p>Charkness: /* 18/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
We were given a brief introduction to Bionessie and SBML. Also we be begun to get to grips with Global Sensitivity analysis.<br />
<br />
=== 18/07 ===<br />
A brief overview of SimBiology was given to the drylab by Gary. Martina and Rachel continued with learning about Stochastic modelling while the rest of the team were working on Sensitivity Analysis.<br />
<br />
=== 19/07 ===<br />
A presentation was given to both the wetlab and the drylab about the Full Text Fetcher programme which will help to search and retrive research articles.<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:35:37Z<p>Charkness: /* 17/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
We were given a brief introduction to Bionessie and SBML. Also we be begun to get to grips with Global Sensitivity analysis.<br />
<br />
=== 18/07 ===<br />
A brief overview of SimBiology was given to the drylab by Gary. Martina and Rachel continued with learning about Stochastic modelling while the rest of the team were working on Multi Parameter Sensitivity Analysis.<br />
<br />
=== 19/07 ===<br />
A presentation was given to both the wetlab and the drylab about the Full Text Fetcher programme which will help to search and retrive research articles.<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:34:36Z<p>Charkness: /* 19/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
We were given a brief introduction to Bionessie and SBML. Also we be begun to get to grips with Multi Parameter Sensitivity analysis.<br />
<br />
=== 18/07 ===<br />
A brief overview of SimBiology was given to the drylab by Gary. Martina and Rachel continued with learning about Stochastic modelling while the rest of the team were working on Multi Parameter Sensitivity Analysis.<br />
<br />
=== 19/07 ===<br />
A presentation was given to both the wetlab and the drylab about the Full Text Fetcher programme which will help to search and retrive research articles.<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:34:04Z<p>Charkness: /* 18/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
We were given a brief introduction to Bionessie and SBML. Also we be begun to get to grips with Multi Parameter Sensitivity analysis.<br />
<br />
=== 18/07 ===<br />
A brief overview of SimBiology was given to the drylab by Gary. Martina and Rachel continued with learning about Stochastic modelling while the rest of the team were working on Multi Parameter Sensitivity Analysis.<br />
<br />
=== 19/07 ===<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:32:09Z<p>Charkness: /* 17/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
We were given a brief introduction to Bionessie and SBML. Also we be begun to get to grips with Multi Parameter Sensitivity analysis.<br />
<br />
=== 18/07 ===<br />
<br />
=== 19/07 ===<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:31:23Z<p>Charkness: /* 17/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
We were given an introduction to Bionessie and SBML. Also we be begun to get to grips with Multi Parameter Sensitivity analysis.<br />
<br />
=== 18/07 ===<br />
<br />
=== 19/07 ===<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:29:43Z<p>Charkness: /* 16/07 */</p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
Glasgow Bank Holiday.<br />
<br />
=== 17/07 ===<br />
<br />
=== 18/07 ===<br />
<br />
=== 19/07 ===<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:29:00Z<p>Charkness: </p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 16/07 ===<br />
<br />
=== 17/07 ===<br />
<br />
=== 18/07 ===<br />
<br />
=== 19/07 ===<br />
<br />
=== 20/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Glasgow/DrylabGlasgow/Drylab2007-07-20T09:27:38Z<p>Charkness: </p>
<hr />
<div><u>[[Glasgow|Glasgow Main Page]]</u><br />
<br />
== Week 1 ==<br />
=== 02/07 ===<br />
After a brief re-introduction to the Laboratory and our project proposal, we outlined a 6-PHASE approach to guide our practice over the summer.<br />
<br />
From here the Modellers began working on basic Matlab modelling tutorials, designed by Xu Gu, to allow all modellers to reach a satisfactory ability. By the end of the day we had completed a number of Mass-action programs using the ode45 funtion and grasped the translation from basic notaion into Substrate, Enzyme and S/E-complex notation.<br />
<br />
=== 03/07 ===<br />
We developed our modelling techniques by programming responses to basic metabolic and signalling pathways. We then learnt more precise techniques of modelling, e.g. accuracy and tolerace variance and noting parameters. We then covered Loop and Switch functions.<br />
<br />
=== 04/07 ===<br />
We are were introduced to the Nested function to allow for simpler programming, and the basic ideas behind Sensitivity of output due to a range of possible values of varying constants.<br />
<br />
In the afternoon, all modellers were shown some Wetlab techniques for the sake of a more thorough understanding of the processes involved.<br />
<br />
Our experiment was to extract plasmids from a number of different bacterial cultures.<br />
<br />
=== 05/07 ===<br />
blank<br />
<br />
=== 06/07 ===<br />
Raya Khanin introduced us to the Michaelis-Menton equation and its use in biochemical process modelling. We then discussed the methods of modelling different promoters's 'Acceptablility', i.e. 'And', 'Or' and 'Sum'.<br />
<br />
== Week 2 ==<br />
=== 09/07 ===<br />
Our first step towards modelling a possible method for PHASE 1.<br />
<br />
=== 10/07 ===<br />
We planned and gave a lecture to those in Wetlab explaining the methods we employ as modellers to represent various biochemical reactions. We also received a complementary lecture from those in Wetlab explaining the processes they employ to carry out and observe experimentation.<br />
[[User:Toby|Toby]] 11:27, 11 July 2007 (EDT)<br />
<br />
=== 11/07 ===<br />
We have finally agreed on model we are going to simulate, but wet lab updated us, that first experiment went wrong and we have to remodel. First few minutes after such news were shocking. It took me an hour to finalize all the details. And now I have to go again.<br><br />
Lucky for us modelers, computers dot care much about bacteria used in experiment so as long as we follow the same path we only need to rename variables. Bless! <br />
<br />
=== 12/07 ===<br />
A day dedicated to manual math as Rachel and Kristin does some analytical derivations for our models optimization. To be honest, we were very optimistic about the outcome, and though the formula derived were fine, and simulations went on as smoothly as ever, the optimization part shoved that 9 dimensional space is though nut to crack even for MatLAB. <br><br />
<br />
--[[User:0602359k|Karolis]] 04:53, 13 July 2007 (EDT)<br />
=== 13/07 ===<br />
Some introduction to Stochastic Modelling intrinsicaly contained in gene transcription. We took some decisions about the design of the wiki. More optimization done it by Maciej.<br><br />
<br />
== Week 3 ==<br />
=== 17/07 ===</div>Charknesshttp://2007.igem.org/wiki/index.php/User:CharknessUser:Charkness2007-07-20T08:56:52Z<p>Charkness: </p>
<hr />
<div>Hello! <br />
My name is Christine and I am originally from Northern Ireland. I’ve just finished my degree in Mechanical Engineering at Glasgow Uni. Later this year im planning to work on an Engineers without Borders project in Cambodia. I like getting emails... charkness987@hotmail.com</div>Charknesshttp://2007.igem.org/wiki/index.php/User:CharknessUser:Charkness2007-07-20T08:50:07Z<p>Charkness: </p>
<hr />
<div>Hello! <br />
Ive just finished my degree in Mechanical Engineering at Glasgow Uni. Later this year im planning to work on an Engineers without Borders project in Cambodia.</div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:48:35Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases.<br />
<br />
[[Image:simpledecayequation.jpg|400px]]<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversibleequation.jpg|400px]]<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. Three differential equations are formed to model this reaction.<br />
<br />
[[Image:additionequation.jpg|400px]]<br />
[[Image:addition.jpg|400px]]<br />
<br />
An enzyme reaction can be modeled as shown below. The enzyme complex is modeled by using both the addition reaction and the reversible reaction. <br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Additionequation.jpgFile:Additionequation.jpg2007-07-12T13:44:30Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:44:19Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases.<br />
<br />
[[Image:simpledecayequation.jpg|400px]]<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversibleequation.jpg|400px]]<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
<br />
[[Image:additionequation.jpg|400px]]<br />
[[Image:addition.jpg|400px]]<br />
<br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Reversibleequation.jpgFile:Reversibleequation.jpg2007-07-12T13:43:03Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:42:28Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases.<br />
<br />
[[Image:simpledecayequation.jpg|400px]]<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversibleequation.jpg|400px]]<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
[[Image:addition.jpg|400px]]<br />
<br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:40:42Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases.<br />
<br />
[[Image:simpledecayequation.jpg|400px]]<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
[[Image:addition.jpg|400px]]<br />
<br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Simpledecayequation.jpgFile:Simpledecayequation.jpg2007-07-12T13:40:20Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:40:10Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases.<br />
<br />
[[Image:simpledecayequation.jpg|400px]]<br />
<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
[[Image:addition.jpg|400px]]<br />
<br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:39:48Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases.<br />
<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
[[Image:addition.jpg|400px]]<br />
<br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Enzymeequation.jpgFile:Enzymeequation.jpg2007-07-12T13:38:04Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:37:54Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases. <br />
<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
[[Image:addition.jpg|400px]]<br />
<br />
<br />
[[Image:enzymeequation.jpg|400px]]<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-12T13:36:01Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
There are many advantages of modeling a biological system in differential equations. Predictions can be made for experiments before they are carried out in the wetlab which can prove to be very useful.<br />
<br />
The simplest reaction which is shown is simple decay where substance A decays to substance B. This can be modeled by two differential equations. The quantities which must be known to model these equations are the initial concentrations of both A and B and also the rate constant k1. By using Matlab a graph can be produced which shows that as A is used up B increases. <br />
<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
<br />
The decay reaction can also take the form of becoming a reversible reaction where A turns into B via a rate constant of k1 while at the same time B turns into A via a rate constant of k2. This again is modeled by two differential equations<br />
<br />
[[Image:reversible.jpg|400px]]<br />
<br />
<br />
Another type of reaction which can be shown is an addition reaction where both A and B must be present to react to form C via a rate constant. <br />
[[Image:addition.jpg|400px]]<br />
<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menten ===<br />
''This was taken from 'Biochemistry' by 'Stryer'''<br><br />
Anybody who has done any sort of biological study will know Michaelis-Menten what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need. In this case all k values are rate constants and [] means concentration and E is enzyme, S is substrate and [E]t is total enzyme concentration. <br><br />
The Michaelis-Menten equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is (i will add it in when i have figured out how to)<br><br />
what we want is an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps.<br><br />
Our starting point is that the catalytic rate is equal to the product of the ES complex and k3.<br />
'''Vo=K2[ES]''' ''call this '''eqn(1)''' as i will be referring to it again''<br />
Now expressing [ES]in terms of known quantities the rates of '''formation''' and '''breakdown''' of [ES] are given by:<br />
'''formation [ES] = k1*[E]*[S]'''<br />
'''breakdown [ES] = (k2+k3)*[ES]'''<br />
A steady state occurs when the rates of formation and breakdown of the ES complex are equal, this gives the formula<br />
'''k1*[E]*[S]=(k2+k3)*[ES]'''<br />
which then gives <br />
'''[E][S] / [ES]=(k2+k3) / k1''' <br> <br />
This can be simplified by defining '''Km''' called the Michaelis constant<br><br />
'''Km = (k2+k3) / k1'''<br />
from this we get<br />
'''[ES] = [E][S] / Km''' ''call this '''eqn(2)''' as i will be referring to it again'' <br><br />
Now examining the numerator of this equation: because substrate is usually present at much higher concentrations than the enzyme, the concentration of uncombined substrate [S]is very nearly equal to the total substrate concentration. The concentration of enzyme [E] is equal to '''[E]t - [ES]''' now substituting this into ''eqn(2)'' and after some simplification we get<br />
'''[ES]=([E]t*[S]) / ([S]+Km)'''<br />
by substituting this expression into ''eqn(1)'' we get<br />
'''Vo = (k2[E]t*[S]) / ([s]+Km)'''<br />
The maximised rate Vmax is obtained when the catalytic sites on the enzyme are saturated with substrate i.e '''[ES] = [E]t''' thus<br />
'''Vmax = k2*[E]t<br />
this gives the Michaelis-Menten equation <br />
'''Vo = Vmax*([S] / ([S]+km)) ''' ''call this '''eqn(3)''' as i will refer to it again'' <br />
when '''[S]=Km''' then '''Vo = Vmax / 2'''. Thus Km is equal to the substrate concentration at which the reaction rate is half its maximal value.<br><br />
<br />
<br><br><br />
<br />
<br />
=== <u> Multiple Transcription Factors </u> ===<br />
<br />
There is an extension of the formulas from Michaelis-Menten, for '''multiple transcription factors'''. <br />
<br />
''Regulation of gene expression is controlled by the binding of transcription factors to specific DNA sequences in gene promoter regions. Multiple transcription factor binding events are involved in the regulation of cellular processes.'' <br />
<br />
<br />
When we have more than one '''transcription factor''' (TF) involved we can find two situations:<br><br />
(In this page we will study the scenario with only 2 transcription factors involved) <br />
<br />
- SUM Gate.<br><br />
- ADD Gate.<br />
<br />
<br />
<u>'''SUM Gate'''</u>: As the word refers in this situation the effect from multiple TFs is additive. That means that the transcription could be induced for one '''OR''' other factor (or both together). But we have to note in this point that it’s not necessary the presence of both of them.<br />
<br />
<u>'''ADD Gate'''</u>: Implies the situation where the effect from multiple TFs is multiplicative. That means that the transcription will be induced for one '''AND''' the other factor at the same time (both actuate together). Nottice that if one of them is not active the transcription will not be done.<br />
<br />
<center>[[Image:formulas.jpg|400px]]</center></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-11T14:11:12Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
<br />
[[Image:simpledecay.jpg|400px]]<br />
<br />
[[Image:reversible.jpg|400px]]<br />
<br />
[[Image:addition.jpg|400px]]<br />
<br />
[[Image:enzyme.jpg|400px]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG | 700px]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in [[Mass-Action Reaction Modelling]] and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response.jpg | 800px]]<br />
<br />
=== Michaelis-Menton ===<br />
Anybody who has done any sort of biological study will know michaelis menton what i am trying to acheive here is to take it from the basics so as to equate it to the equations we will be using to model the system and to give the biologists an idea of what values and models we need.<br />
The michaelis-Menton equation describes the kinetic properties of many enzymes. Consider the simple system A -> P<br />
The rate of V is the quantity of A that disappears over a specified unit of time which is equal to the rate of appearance of P. For this system V=k[A] where k is the rate constant. <br />
The simplest model that accounts for the kinetic properties of many enzymes is<br />
<br />
=== Sum & And Promoters ===<br />
<br />
=== Application ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-11T13:54:05Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
<br />
[[Image:simpledecay.jpg]]<br />
<br />
[[Image:reversible.jpg]]<br />
<br />
[[Image:addition.jpg]]<br />
<br />
[[Image:enzyme.jpg]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''<br><br />
<br />
One method of exposing the variation of a model is to program a loop exposing a modelled reaction to increasing values of a chosen constant. This process was followed with the metabolic pathway showing in..... and ploted on a graph showing the response of all 4 species for a set range of varying K2 values from 1 to 10 where 10 is highlighted red.<br><br />
[[Image: metabolic sensetivity response]]<br />
<br />
=== Michaelis-Menton ===<br />
<br />
=== Sum & And Promoters ===<br />
<br />
=== Application ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-11T13:51:46Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
[[Image:simpledecay.jpg]]<br />
<br />
[[Image:reversible.jpg]]<br />
<br />
[[Image:addition.jpg]]<br />
<br />
[[Image:enzyme.jpg]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''- <br />
=== Michaelis-Menton ===<br />
<br />
=== Sum & And Promoters ===<br />
<br />
=== Application ===</div>Charknesshttp://2007.igem.org/wiki/index.php/File:Simpledecay.jpgFile:Simpledecay.jpg2007-07-11T13:50:44Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Reversible.jpgFile:Reversible.jpg2007-07-11T13:50:27Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Enzyme.jpgFile:Enzyme.jpg2007-07-11T13:50:00Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/File:Addition.jpgFile:Addition.jpg2007-07-11T13:49:37Z<p>Charkness: </p>
<hr />
<div></div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-11T13:49:14Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
[[Image:addition.jpg]]<br />
[[Image:enzyme.jpg]]<br />
[[Image:reversible.jpg]]<br />
[[Image:simpledecay.jpg]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''- <br />
=== Michaelis-Menton ===<br />
<br />
=== Sum & And Promoters ===<br />
<br />
=== Application ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-11T13:46:35Z<p>Charkness: /* Mass-Action Reaction Modelling */</p>
<hr />
<div>=== Mass-Action Reaction Modelling ===<br />
[[addition.jpg]]<br />
[[enzyme.jpg]]<br />
[[reversible.jpg]]<br />
[[simpledecay.jpg]]<br />
<br />
=== RKIP network ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Sensitivity ===<br />
''An insight into a system's sensitivity will show how the variation of a model can be apportioned qualitatively or quantitatively to different sources of variation''- <br />
=== Michaelis-Menton ===<br />
<br />
=== Sum & And Promoters ===<br />
<br />
=== Application ===</div>Charknesshttp://2007.igem.org/wiki/index.php/Dry_to_WetDry to Wet2007-07-11T13:38:01Z<p>Charkness: /* Christine's Bit */</p>
<hr />
<div>=== Christine's Bit ===<br />
[[Image:aname.jpg]]<br />
<br />
=== Toby's Bit ===<br />
After gaining a thorough understanding of methods involved with modeling simple mass-action reactions, we can move on to more complex systems such as the RKIP network.<br><br />
[[Image:RKIP network.JPG]]<br><br />
In the above diagram, substrates, enzymes and substrate/enzyme complexes are represented by numbered circles, rate constants are represented by numbered squares. By isolating individual species and their direct peripheral species (those being formed from or forming the isolated species) we are able to treat the group as a simple mass-action reaction. A differential equation is then found for each species based on the rate constants and code can be written and a graph plotted showing the trend of all the species’ concentration over time giving the following graph:<br><br />
[[Image:RKIP network graph.jpg]]<br><br />
<br />
=== Karolis' Bit ===<br />
<br />
=== Rachael's Bit ===<br />
<br />
=== Martina's Bit ===<br />
<br />
=== Maciej's Bit ===</div>Charknesshttp://2007.igem.org/wiki/index.php/User:CharknessUser:Charkness2007-07-11T13:30:44Z<p>Charkness: </p>
<hr />
<div>Hello!</div>Charkness