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| ==Generalities of the Model== | | ==Generalities of the Model== |
| * '''Introduction'''
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| We can condition the system in various manners, but for the purposes of our project, Infector Detector, we will seek a formulation which is valid for both constructs considered. Our system can thus be modellied by the following Dynamical System:
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| <br><br>
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| <math>\frac{d[LuxR]}{dt} = k_1\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) + k_3[A] - k_2[LuxR][AHL]- \delta_{LuxR}[LuxR]</math>
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| <br>
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| <math>\frac{d[AHL]}{dt} = k_3[A] - k_2[LuxR][AHL]- \delta_{AHL}[AHL]</math>
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| <math>\frac{d[A]}{dt} = -k_3[A] + k_2[LuxR][AHL]- k_4[A][P] + k_5[AP]</math>
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| <math>\frac{d[P]}{dt} = -k_4[A][P] + k_5[P]</math>
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| <math>\frac{d[AP]}{dt} = k_4[A][P] - k_5[AP]</math>
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| <math>\frac{d[GFP]}{dt} = k_6[AP]\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) - \delta_{GFP}[GFP]</math>
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| <math>\frac{d[E]}{dt} = -\alpha_{1}k_1\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) - \alpha_{2}k_6[AP]\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg)</math>
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| <br>
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| where:<br><br>
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| [A] represents the concentration of AHL-LuxR complex<br>
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| [P] represents the concentration of pLux promoters<br>
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| [AP] represents the concentration of A-Promoter complex<br>
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| k1, k2, k3, k4, k5, k6 are the rate constants associated with the relevant forward and backward reactions<br>
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| <math>\alpha_i \ </math> represents the energy consumption due to gene transcription. It is a function of gene length.<br>
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| n is the positive co-operativity coefficient (Hill-coefficient)<br>
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| <math>K_E \ </math> the half-saturation coefficient
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| <br><br>
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| The system of equations for the two constructs varies strictly with respect to the value of the parameter k1. Construct 1 possesses a non-zero k1 rate constant, whereas for construct 2, a zero value is assumed.
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| ==Simulations== | | ==Simulations== |
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| ===Sensitivity Analysis=== | | ===Sensitivity Analysis=== |
