Team:Imperial College London/Modelling/Signalling

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|style="font-family: helvetica, arial, sans-serif;font-size:2em;color:#ea8828;"|Signaling Model
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|<html><h2>Objectives</h2></html>
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|We want to model the Signalling Module to find out whether the signalling pathway works as anticipated. Modelling receptors involves a lot of detailed knowledge of how the receptors function. However, the details of how our ComD receptor works have not been studied yet, which makes it impossible for us to model our system accurately. Therefore, we will try to implement a much simpler model. However, this means that a lot of assumptions have to be made. 
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|<html><h2>Detailed description</h2></html>
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|We are assuming steady-state for AIP, Phosphate, ComD and ComE in our cell/in the solution. Hence, we can neglect production and degradation rates of ComD and ComE. 
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 |[[Image:IC_Signalling_Diagram.JPG]]
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 |Overview of the signalling module
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|'''Equation 1:''' AIP binds to ComD receptor to form a complex (AIP-ComD)
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|AIP + ComD <html>&harr;</html> AIP-ComD
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|'''Equation 2:''' Phosphate binds to the AIP-ComD complex to form another complex (AIP-ComD*)
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|AIP-ComD + Phosphate <html>&harr;</html> AIP-ComD*
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|'''Equation 3:''' ComE binds to the AIP-ComD* recepetor to form another complex (AIP-ComD*-ComE) 
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|AIP-ComD* + ComE <html>&harr;</html> AIP-ComD*-ComE
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|'''Equation 4:''' Phosphate group on ComD binds to ComE and forms two products: phosphorylated ComE (ComE*) and AIP-ComD
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|AIP-ComD*-ComE <html>&harr;</html> AIP-ComD + ComE*
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|Using the Law of Mass Action, we can rewrite these 4 equations: 
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|[[Image:IC_Signalling_Equations.png]]
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|<html><h2>Parameters & Constants</h2></html>
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|We can neglect the production and degradation rates. Therefore, the only constants in this model are the forward and backward reaction constants: <html>k<sub>1,2,3,4</sub> and k<sub>-1,-2,-3,-4</sub>. In this model, we will assume that k<sub>1,2,3,4</sub>=10<sup>7</sup> and k<sub>-1,-2,-3,-4</sub>=10<sup>3</sup>.</html>
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|<html><h2>Results</h2></html>
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|Using this model, we can show that the phosphorylated ComE* is proportional to both initial concentration of AIP and ComD. 
If the initial concentration of AIP or ComD is zero, there is no formation of ComE*. 
We are assuming an initial concentration of Phosphate and ComE of 100nM. 
If we change either [AIP]<html><sub>0</sub></html> or [ComE]<html><sub>0</sub></html>, then the final concentration of ComE* will always tend towards <html>5&times;10<sup>-11</sup>M</html>. <html>[ComE*]<sub>final</sub></html> will always tend towards this value, unless the initial concentrations of Phosphate and ComE are changed. However, if we increase both [AIP]<html><sub>0</sub></html> and [ComE]<html><sub>0</sub></html> at the same time, then [ComE*]<html><sub>final</sub></html> will be reached much faster (i.e. slope increases).

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 |[[Image:IC_Signalling_Results1.png|450px]]
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 |Graph showing how [ComE]<html><sub>final</sub> eventually reaches the value 5&times;10<sup>-11</sup>M</html>. 
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|<html><h2>Download Matlab files</h2></html>
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|<html><a href="https://static.igem.org/mediawiki/2010/8/89/IC_Signalling.txt"><img src ="https://static.igem.org/mediawiki/2010/8/8c/IC_Signalling_Button.png"></a></html>
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