Two-moment characterisation of subcellular biochemical networks: when noise matters

Noise can significantly influence the behaviour of biochemical reaction networks. While ordinary differential equation (ODE) models remain the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insights into the influence of noise on cell function. Towards this end, the recently developed two-moment approximation (2MA) is a promising approach, accounting for the coupling between the means and (co)variances. It is this influence of (co)variance on the mean behaviour, which cannot be represented by conventional ODE models. We extend the derivation of the 2MA by establishing two advances to previous efforts: a) relative concentrations and b) non-elementary reactions. Both aspects are important in systems biology where one is often forced to aggregate elementary reactions into single step reactions, and some models use relative concentrations (as a ratio of two concentrations or copy numbers). Previous derivations assume elementary reactions and rely on concentrations defined as copy numbers per unit volume. We demonstrate this 2MA approach with an application to the well established fission yeast cell cycle model. The simulations of the 2MA model show oscillatory behaviour near the M/G checkpoint. The behaviour around this bifurcation point is significantly different from that predicted by the ODE model. What this suggests is that the 2MA approach can reveal hidden dynamics near critical points.