Team:Aberdeen Scotland/Modeling/GFP

From 2014.igem.org

(Difference between revisions)
Line 78: Line 78:
$$\frac{d[AHL-LuxR]}{dt} = k_{+}[AHL][LuxR]-k_{-}[AHL-LuxR]$$
$$\frac{d[AHL-LuxR]}{dt} = k_{+}[AHL][LuxR]-k_{-}[AHL-LuxR]$$
$$\frac{d[GFP]}{dt} = \frac{[AHL-LuxR]^n}{[AHL-LuxR]^n + a^n}V_{max} - \gamma{}[GFP] $$
$$\frac{d[GFP]}{dt} = \frac{[AHL-LuxR]^n}{[AHL-LuxR]^n + a^n}V_{max} - \gamma{}[GFP] $$
 +
<ul>
 +
<li>where
 +
<ul>
 +
<li>[AHL]      - AHL concentration</li>
 +
<li>[LuxR]    - LuxR concentration</li>
 +
<li>[AHL-LuxR] - AHL+LuxR complex concentration</li>
 +
<li>[GFP]      - GFP concentration</li>
 +
<li>V<sub>max</sub>      - maximum GFP production</li>
 +
<li>a          - dissociation constant</li>
 +
<li>n          - Hill coefficient</li>
 +
<li>γ          - GFP degradation constant</li>
 +
</ul>
 +
</li>
 +
</ul>
</div> <br class="clear"> <!-- END OF PAGE CONTENT -->
</div> <br class="clear"> <!-- END OF PAGE CONTENT -->

Revision as of 18:56, 17 October 2014

Team:Aberdeen Scotland/Modelling - 2014.ogem.org



GFP Response Model


The idea behind this model was to ensure our Receiver->Sender design is viable and Quorum Sensing will trigger GFP production. It is a simple model that explores the production of GFP protein in the Receiver cell due to AHL-activated LuxR.

Since the Receivers do not produce AHL, the surrounding AHL concentration is not affected by the Receiver itself. Thus self-stimulation is out of the picture and we can assume the amount of AHL is solely due to the "background".

We use the following equation to model how GFP production is triggered:

$$\frac{d[AHL-LuxR]}{dt} = k_{+}[AHL][LuxR]-k_{-}[AHL-LuxR]$$ $$\frac{d[GFP]}{dt} = \frac{[AHL-LuxR]^n}{[AHL-LuxR]^n + a^n}V_{max} - \gamma{}[GFP] $$
  • where
    • [AHL] - AHL concentration
    • [LuxR] - LuxR concentration
    • [AHL-LuxR] - AHL+LuxR complex concentration
    • [GFP] - GFP concentration
    • Vmax - maximum GFP production
    • a - dissociation constant
    • n - Hill coefficient
    • γ - GFP degradation constant