Information-geometric optimization of transient dynamics in gene regulatory networks

The dynamics of gene regulatory networks (GRNs) is governed by the interaction between deterministic biochemical reactions and molecular noise. To understand how GRNs process information during cell state transitions, we study stochastic dynamics derived from a Boolean network model via its representation on the parameter space of Gaussian distributions, equipped with the Fisher information metric. Restricting our analysis to transitions towards a single attractor, this reformulation reveals that dynamics along the gradient flows of the Kullback-Leibler (KL) divergence requires isotropic decay rates across all nodes, and that the noise intensity quantitatively determines the potential differentiation between the initial and final states. Furthermore, we show that the Fisher geodesics, previously identified with minimal biological cost, would require the suppression of noise and lead to deterministic dynamics that lacks biological relevance. This suggests that some departure from minimal cost is necessary for cell differentiation. Our approach frames noise and decay rates as fundamental control parameters, providing a geometric principle for the analysis and design of synthetic networks.