Team:Technion-Israel/Modeling

From 2014.igem.org

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<p>When modelling our system, we began with the simplest method known – deterministic rate equations. Moreover, from the design it was clear that the most important benchmark for the signal within the system would be the concentration of AHL as a function of time, so we began by modelling this part of our system. It took only a simple derivation (see [1]) to obtain these equations which characterize this part of the system:</p>
<p>When modelling our system, we began with the simplest method known – deterministic rate equations. Moreover, from the design it was clear that the most important benchmark for the signal within the system would be the concentration of AHL as a function of time, so we began by modelling this part of our system. It took only a simple derivation (see [1]) to obtain these equations which characterize this part of the system:</p>
<div class="formula">
<div class="formula">
-
(1) <span class="fraction"><span class="ignored">(</span><span class="numerator"><i>d</i><span class="symbol">[</span><i>mRNA</i><sub><i>LuxI</i></sub><span class="symbol">]</span></span><span class="ignored">)/(</span><span class="denominator"><i>dt</i></span><span class="ignored">)</span></span> = <span class="fraction"><span class="ignored">(</span><span class="numerator"><i>v</i><sub><i>B</i></sub> + <i>v</i><sub><i>A</i></sub><i>k</i><sub><i>A</i></sub><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span><sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">1 + <i>k</i><sub><i>A</i></sub><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span><sup>2</sup></span><span class="ignored">)</span></span> − <i>γ</i><sub><i>mRNA</i><sub><i>LuxI</i></sub></sub><span class="symbol">[</span><i>mRNA</i><sub><i>LuxI</i></sub><span class="symbol">]</span> + <i>GateI</i>
+
<span class="fraction"><span class="ignored">(</span><span class="numerator"><i>d</i><span class="symbol">[</span><i>mRNA</i><sub><i>LuxI</i></sub><span class="symbol">]</span></span><span class="ignored">)/(</span><span class="denominator"><i>dt</i></span><span class="ignored">)</span></span> = <span class="fraction"><span class="ignored">(</span><span class="numerator"><i>v</i><sub><i>B</i></sub> + <i>v</i><sub><i>A</i></sub><i>k</i><sub><i>A</i></sub><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span><sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">1 + <i>k</i><sub><i>A</i></sub><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span><sup>2</sup></span><span class="ignored">)</span></span> − <i>γ</i><sub><i>mRNA</i><sub><i>LuxI</i></sub></sub><span class="symbol">[</span><i>mRNA</i><sub><i>LuxI</i></sub><span class="symbol">]</span> + <i>GateI</i>
 +
</div>
 +
<div class="formula">
 +
<span class="fraction"><span class="ignored">(</span><span class="numerator"><i>d</i><span class="symbol">[</span><i>LuxI</i><span class="symbol">]</span></span><span class="ignored">)/(</span><span class="denominator"><i>dt</i></span><span class="ignored">)</span></span> = <i>α</i><sub><i>LuxI</i></sub><span class="symbol">[</span><i>mRNA</i><sub><i>LuxI</i></sub><span class="symbol">]</span> − <i>γ</i><sub><i>LuxI</i></sub><span class="symbol">[</span><i>LuxI</i><span class="symbol">]</span>
 +
</div>
 +
<div class="formula">
 +
<span class="fraction"><span class="ignored">(</span><span class="numerator"><i>d</i><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span></span><span class="ignored">)/(</span><span class="denominator"><i>dt</i></span><span class="ignored">)</span></span> = <i>α</i><sub><i>AHL</i></sub><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span> − <i>γ</i><sub><i>AHL</i></sub><span class="symbol">[</span><i>AHL</i><span class="symbol">]</span>
</div>
</div>

Revision as of 08:09, 13 October 2014


Safie by Technion-Israel

Why Should it Work

Why Alpha System Should Work – a deterministic model of alpha system

When modelling our system, we began with the simplest method known – deterministic rate equations. Moreover, from the design it was clear that the most important benchmark for the signal within the system would be the concentration of AHL as a function of time, so we began by modelling this part of our system. It took only a simple derivation (see [1]) to obtain these equations which characterize this part of the system:

(d[mRNALuxI])/(dt) = (vB + vAkA[AHL]2)/(1 + kA[AHL]2) − γmRNALuxI[mRNALuxI] + GateI
(d[LuxI])/(dt) = αLuxI[mRNALuxI] − γLuxI[LuxI]
(d[AHL])/(dt) = αAHL[AHL] − γAHL[AHL]
Why Should it Fail
Synthetic Biofilm Formation

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