Team:Imperial College London/Modelling/Signalling

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{| style="width:900px;background:#f5f5f5;text-align:justify;font-family: helvetica, arial, sans-serif;color:#555555;margin-top:25px;" cellspacing="20"
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|style="font-family: helvetica, arial, sans-serif;font-size:2em;color:#ea8828;"|Signaling Model
|style="font-family: helvetica, arial, sans-serif;font-size:2em;color:#ea8828;"|Signaling Model

Revision as of 18:52, 25 October 2010

Modelling Overview | Detection Model | Signaling Model | Fast Response Model | Interactions
A major part of the project consisted of modelling each module. This enabled us to decide which ideas we should implement. Look at the Fast Response page for a great example of how modelling has made a major impact on our design!
Objectives | Description | Results | Constants | MATLAB Code
Signaling Model

Objectives

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.

Detailed description

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.
IC Signalling Diagram.JPG
Overview of the signalling module
Equation 1: AIP binds to ComD receptor to form a complex (AIP-ComD)
AIP + ComD ↔ AIP-ComD
Equation 2: Phosphate binds to the AIP-ComD complex to form another complex (AIP-ComD*)
AIP-ComD + Phosphate ↔ AIP-ComD*
Equation 3: ComE binds to the AIP-ComD* recepetor to form another complex (AIP-ComD*-ComE)
AIP-ComD* + ComE ↔ AIP-ComD*-ComE
Equation 4: Phosphate group on ComD binds to ComE and forms two products: phosphorylated ComE (ComE*) and AIP-ComD
AIP-ComD*-ComE ↔ AIP-ComD + ComE*
Using the Law of Mass Action, we can rewrite these 4 equations:
IC Signalling Equations.png

Parameters & Constants

We can neglect the production and degradation rates. Therefore, the only constants in this model are the forward and backward reaction constants: k1,2,3,4 and k-1,-2,-3,-4. In this model, we will assume that k1,2,3,4=107 and k-1,-2,-3,-4=103.

Results

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]0 or [ComE]0, then the final concentration of ComE* will always tend towards 5×10-11M. [ComE*]final will always tend towards this value, unless the initial concentrations of Phosphate and ComE are changed. However, if we increase both [AIP]0 and [ComE]0 at the same time, then [ComE*]final will be reached much faster (i.e. slope increases).

IC Signalling Results1.png
Graph showing how [ComE]final eventually reaches the value 5×10-11M.


IC Signalling Results2.png IC Signalling Results3.png IC Signalling Results4.png
1. Graph showing the production of Pr-ComD complex. 2. Graph showing the production of phosphorylated Pr-ComD* complex. 3. Graph showing the production of Pr-ComD*-ComE complex. Notice the steep increase of concentration for each of these graphs, which could be due to the high k1,2,3,4 values.

Download Matlab files