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 stepreactions, 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 .
 While ordinary differential equations (ODEs) form 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 insight into the influence of noise . Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and ( co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing a) non-elementary reactions and b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use relative concentrations . We investigate the applicability of the 2MA approach to the well established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of MPF, caused by the coupling between mean and (co)variance, near the G2 / M transition .
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non-elementary reactions. Both aspects are important in systems biology where one is often forced to aggregate elementary reactions into single stepreactions, and some models
relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the
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(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
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with an application
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Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of MPF, caused by the coupling between mean and (co)variance, near the G2
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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
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