Model reduction, coherence, and information transfer in stochastic biochemical systems

Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such models have also found widespread application in the quantification of how information is transmitted in reaction networks via the mutual information (MI) rate. A common assumption is that under timescale separation, estimates for the coherence and MI rate obtained from simplified (reduced) models closely approximate those in the underlying full models. Here, we challenge that assumption by showing that while reduced models can faithfully reproduce low-order statistics of molecular counts, they frequently incur substantial discrepancies in the coherence spectrum, especially at intermediate and high frequencies. These errors, in turn, lead to significant inaccuracies in the resulting estimates for the MI rates. We show that the observed discrepancies are due to the interplay between the structure of the underlying reaction networks, the specific model reduction method that is applied, and the asymptotic limits relating the full and reduced models. We illustrate our results in canonical models of enzyme catalysis and gene expression, highlighting practical implications for quantifying information flow in cells.