Stochastic phase model with drifting frequencies and intercellular phase coupling

Copyright information:

Taken from "Dynamical signatures of cellular fluctuations and oscillator stability in peripheral circadian clocks"

Molecular Systems Biology 2007;3():93-93.

Published online 13 Mar 2007

PMCID:PMC1847945.

Copyright © 2007, EMBO and Nature Publishing Group

() An extended Kuramoto model for the oscillator phases φ() and frequencies () describes coupled circadian phase oscillators. The total luminescence signal () is the sum of a population of initially oscillators each contributing a cosine signal centered around a constant with relative amplitude . Cell death follows a Poisson process with time constant τ reflected by the indicator variable θ() taking value 1 before (and 0 after) cell has died. The time-dependent frequencies and phases of the individual oscillators are subject to a stochastic differential equation (cf. Materials and methods and ). () Sample frequency trajectory; γ and σ are free constants representing the inverse memory of the frequency trajectories and the frequency dispersion, respectively. () Parameter listing. describes the intercellular coupling between the phases and is taken as all-to-all. More realistic coupling geometries are considered in .