Ten coupled genetic oscillators. The parameter values in (1), (2), and (3) are set as follows: αa = αb = αc = 216, αS = 20, μ = 1.2, μS = 1, n = 2, γS = 1, ηS = 2, βS = 0.1, βA = βB = βC = 1, γm = 6.9315, γp = 1.1552 and Qe = 0.09 . Suppose the nonlinear stochastic coupled synthetic oscillators suffer from stochastic parameter fluctuations as shown in (8) with Δαa = Δαb = Δαc = 2.16, ΔαS = 0.2, ΔβA = ΔβB = ΔβC = 0.01, ΔβS = 0.001, ΔηS = 0.02, Δγm = 0.06, Δγp = 0.01, and ΔγS = 0.01. For the convenience of simulation, we assume that the extrinsic molecular noise v1~v10 is independent Gaussian white noise with a mean of zero and standard deviation of 0.02. It can be seen that coupled synthetic oscillators cannot achieve synchronization under these intrinsic kinetic parameter fluctuations and extrinsic molecular noise.
Chen and Hsu BMC Systems Biology 2012 6:136 doi:10.1186/1752-0509-6-136