Feedback simulation with linear stability analysis
F(R) = dR/dt = n kpP kIa - kdegR
f(R* + h) ~= f(R*) + h f'(R*) ... (Taylor approximation)
R* = steady-state level of repressor, i.e. when f(R) = 0
P = RNA polymerase concentration,
kp and kr = binding constants of polymerase & repressor,
kI = promoter isomerization rate to initiate,
a = ratio of mRNA and protein concentrations,
kdeg = degradation rate of , n = gene copy number.