Team:Imperial College/Genetic Circuit

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 Parameter scan on <math>k_1</math> Parameter scan on <math>d_1</math>

{{Imperial/Box1|Modelling Inducible Gene Expression|

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

<math>\frac{d[R]}{dt} = k_{1} - d_{1}[R]</math>

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

<math> R + I \Leftrightarrow RI </math>

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

<math> Transcription = \frac{\beta.{[R]}^n}{{K_m}^n+[R]^n}</math>

And overall protein expression can be described as

<math>\frac{d[protein]}{dt} = Transcription - d_2[protein]</math>

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

<biblio>

1. 1 pmid=18612302

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