Heterogeneous Cell Population Dynamics: Equation-Free Uncertainty Quantification Computations

We propose a computational approach to modeling the collective dynamics of populations of coupled heterogeneous biological oscillators. In contrast to Monte Carlo simulation, this approach utilizes generalized Polynomial Chaos (gPC) to represent random properties of the population, thus reducing the dynamics of ensembles of oscillators to dynamics of their (typically significantly fewer) representative gPC coefficients. Equation-Free (EF) methods are employed to efficiently evolve these gPC coefficients in time and compute their coarse-grained stationary state and/or limit cycle solutions, circumventing the derivation of explicit, closed-form evolution equations. Ensemble realizations of the oscillators and their statistics can be readily reconstructed from these gPC coefficients. We apply this methodology to the synchronization of yeast ∗To whom correspondence should be addressed: [email protected]; +1-609-258-2818