(a) A synthetic toggle switch is built from two mutually repressing genes with Hill…

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Biophysics & Medical Physics · Genetic circuits, regulation and biological information

Forces, Machines and Signals, Ch Genetic circuits and biological pattern

Problem

(a) A synthetic toggle switch is built from two mutually repressing genes with Hill coefficient nH=2n_H=2 and scaled parameter α=4\alpha=4, so that in the standard scaled units u˙=α/(1+v2)−u\dot u = \alpha/(1+v^2)-u, v˙=α/(1+u2)−v\dot v = \alpha/(1+u^2)-v. Using the stability criterion for the symmetric fixed point given for the toggle switch, find the symmetric fixed point u=vu=v and decide whether the circuit is bistable. (b) Two identical copies of a reporter gene (one tagged CFP, one tagged YFP) are expressed from the same promoter in one bacterium and report the same regulatory input. Their fluorescence means are ⟨x1⟩=⟨x2⟩=800\langle x_1\rangle=\langle x_2\rangle=800 (arbitrary units), the mean squared difference between the two colours is ⟨(x1−x2)2⟩=3.2×104\langle (x_1-x_2)^2\rangle = 3.2\times10^4, and their covariance is cov(x1,x2)=6.4×104\mathrm{cov}(x_1,x_2)=6.4\times10^4. Compute the intrinsic noise ηint2\eta_{\rm int}^2 and the extrinsic noise ηext2\eta_{\rm ext}^2.

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