The repressilator was described and implemented in E. coli in [1]. A simplified version of Elowitz and Leibler's mathematical model is implemented here; we omit consideration of mRNA and focus exclusively on the protein (repressor) concentrations. The parameters of this implementation are: the ratio
of the repressor production rate at a concentration of 1 to the repressor degradation rate, and the Hill function exponent
, which specifies the cooperativity of the repressor activity. It is possible to show that sustained oscillations occur for values of
approximately greater than
. This implies that sustained oscillations can be achieved at small values of
for large values of
, but only at large values of
for smaller values of
. Interestingly, it is not possible to achieve sustained oscillations at all for
, irrespective of the values of
, which is borne out in the Demonstration.
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