MCB111: Mathematics in Biology (Fall 2019)

week 12:

Genetic Switches

A fast and robust oscillator

In class, we discussed the repressilator by Elowitz & Leibler, a synthetic network implemented in E. coli that produces oscillations. The repressilator turned out to be not very robust, as only 40% of the cells presented oscillations. In this homework, we are going to implement a different oscillator that depends on two genes with both negative and positive feedback loops: “A fast, robust and tunable synthetic gene oscillator” by J. Stricker et al.

Figure 1. Basic diagram of the Stricker oscillator.

A diagramtic representation of this oscillator is given in Figure 1. In terms of the actual parameters:

parameter Description value
lacI RNA production 2.5
araC RNA production 2.5
lacI RNA degradation 0.6
araC RNA degradation 0.8
cooperativity coefficient of LacI binding 2
cooperativity coefficient of AraC binding 4
Hill constant for LacI (-) feedback loop 2
Hill constant for AraC (+) feedback loop 0.003
lacI translation rate 0.4
araC translation rate 0.1
LacI degradation rate 0.8
AraC degradation rate 0.2
Michaelis constant for lacI RNA degradation 0.01
Michaelis constant for araC RNA degradation 0.1
Michaelis constant for LacI degradation 0.01
Michaelis constant for AraC degradation 0.1