Moment-based uncertainty propagation for deterministic biochemical network models with rational reaction rates

Biochemical networks in clonal cell populations often display highly heterogeneous behavior, which needs to be adequately captured by dynamical models. When the underlying biochemical process is modelled by a system of ordinary differential equations (ODEs), slow-varying cell-tocell heterogeneity can be introduced via uncertain parameters and/or initial conditions. By considering a joint distribution over initial states and parameters, the effect of this uncertainty on population dynamics can be studied in a computationally efficient manner by tracking low-order moments of the state distribution over time. In this paper, we present a systematic approach for deriving moment equations for ODEs with rates that are ratios of polynomials, a class of systems typically encountered in models of biochemical networks. We then apply our results to a gene expression model with negative autoregulation, and evaluate the performance of normal and log-normal moment closure approximations. Our results expand the range of applicability of moment equations for deterministic systems with uncertainty, and provide a first insight into the applicability and performance of moment closure approximations for this class of systems.