Learning activator-inhibitor dynamics at the cell cortex with neural likelihood ratio estimation

A key question in cell biology is how cell-scale organization emerges from a given set of molecular players and rules of interaction. Given its multiscale nature, addressing this question requires a combination of experimental perturbation, mathematical modeling, and parameter inference. We leverage recent advances in each of these fields, focusing in particular on neural-network methods for simulation-based inference, to study how cell-scale patterns of Rho GTPase activity are defined by molecular-scale activator-inhibitor interactions with filamentous actin. Using an existing model of this interaction, we demonstrate that an over-expressive, regularized classification neural network can approximate the likelihood of data arising from a particular parameter set. We show that variations in F-actin assembly dynamics can be inferred directly from experimental data, but only if the network is made less sensitive to model misspecification. We use our approach to interpret perturbation experiments in which increasing RhoGAP coexpression increases the frequency and coherence of Rho activity waves in frog eggs. After showing that the known functions of RhoGAP are insufficient to explain experimentally-observed dynamics, we use neural methods to suggest an alternative pathway by which RhoGAP could decrease filament nucleation rates to sustain waves. Our work yields specific, experimentally-testable predictions and illustrates how a combination of traditional forward models and modern inference tools can aid in unraveling mechanisms of self-organization.