Revision as of 13:21, 11 September 2008


Home	Biofabricator Subtilis Project Specifications Why B. subtilis? B. subtilis: Benefits vs Challenges	Wet Lab Wet Lab Hub Cloning Strategy Experiments & Protocols Experimental Results BioBricks & Characterisation	Dry Lab Dry Lab Hub Growth Curves Genetic Circuits Motility Analysis Appendices - Code etc.	Notebook	Our Team

Genetic Circuit

Why 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 re-use of the part and modification of integration into novel genetic circuits.

Modelling Constitutive Gene Expression

A simple synthesis-degradation 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 promoter-RBS constructs. The synthesis-degradation model assumes a steady state level of mRNA.

$\frac{d[protein]}{dt} = k_{1} - d_{1}[protein]$

In this case, $[p r o t e i n]$ represents the concentration of GFP, $k 1$ represents the rate of sythesis and $d 1$ represents the degradation rate. We can easily simulate this synthesis-degradation model using matlab:
ODE
Simulation File

Parameter scan on $k 1$

Parameter scan on $d 1$

We can also solve this ODE analytically.
At $\frac{d[protein]}{dt}=0$ , $[protein]=\frac{k_1}{d_1}$ and you can see this relationship in the parameter scan graphs.
From the wetlab experiments it is likely that we will obtain steady-state data for each of the four promoter-RBS constructs. If we assume the same rate of degradation of GFP in each case, we can have some measure of the relative rate of transcription through each promoter which will help us with the selection of the most appropriate promoter to use for Phase 2. In order to obtain an absolute measure of transcription (as opposed to a relative measure of transcriptional strength) we require constitutive expression in terms of molecules per cell (as opposed to fluorescene in arbitrary units).
Note from the parameter scan graphs: