IGEM:IMPERIAL/2008/New/Genetic Circuit
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Genetic CircuitWhy model 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 reuse of the part and modification of integration into novel genetic circuits. Modelling Constitutive Gene ExpressionA simple synthesisdegradation model is assumed for the modelling of the expression of a protein under the control of a constitutive promoter, with the same model assumed for all four promoterRBS constructs. The synthesisdegradation model assumes a steady state level of mRNA.
In this case, [protein] represents the concentration of GFP, k_{1} represents the rate of sythesis and d_{1} represents the degradation rate.
We can easily simulate this synthesisdegradation model using matlab: We can also solve this ODE analytically. Consider the steadystate behaviour of [protein].
Modelling Inducible Gene ExpressionThe 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
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