Team:Imperial College/Genetic Circuit

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Modelling the Genetic Circuit

An accurate mathematical description of the genetic circuit is essential for projects involving synthetic biology. Such descriptions are an integral component of part submission to the Registry, as exemplified by the canonical characterisation of part F2620 #1. The ability to capture part behaviour as a mathematical relationship between input and output is useful for future re-use of the part and modification of integration into novel genetic circuits.

Modelling Constitutive Gene Expression

Constitutive expression of antibiotic resistance (AB) and GFP. GFP brick is part E0040, GFPmut3b. Terminator is part B0015, the double-stop.

Parameter scan on <math>k_1</math>

Parameter scan on <math>d_1</math>

Modelling Inducible Gene Expression

The repressor is constitutively expressed. Hence we can assume the constitutive expression model from the previous characterisation step.

When the inducer is added it binds reversibly to the repressor.

Repressor only binds to the promoter when it is in its unbound form, hence transcription will be a function of free repressor concentration.

And overall protein expression can be described as

The ODEs and simulation may be found in the Appendices section of the Dry Lab hub.

1 pmid=18612302

</biblio>

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 <br>
-We can also solve this ODE analytically. Consider the steady-state behaviour of <math>[protein]</math>.
+We can also solve this ODE analytically. Consider the steady-state behaviour of [protein].
 [[Image:Eq2.png]]
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 <br>
 Note from the parameter scan graphs:<br>
-*In the case where <math>k_1 {{Equals}} 0</math>, no GFP is sythesised.
+*In the case where k1 = 0, no GFP is sythesised.
-*In the case where <math>d_1 {{Equals}} 0</math>, the concentration of protein does not reach a steady state.
+*In the case where d1 = 0, the concentration of protein does not reach a steady state.
 |[[Image:Phase 1.PNG|thumb|300px|Constitutive expression of antibiotic resistance (AB) and GFP. GFP brick is part E0040, GFPmut3b. Terminator is part B0015, the double-stop.]]