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. We show that variations in F-actin assembly dynamics can be inferred directly from experimental data by combining a mathematical model with a neural network trained to associate parameter sets with data. Our neural approach differentiates data sets more precisely than traditional summary statistics, and yields a complete and robust likelihood function for each data set. Utilizing the trained network, we demonstrate how RhoGAP tunes RhoA waves via interaction with F-actin. After showing that the known functions of RhoGAP are insufficient to explain experimentally-observed dynamics, we use neural methods to infer that RhoGAP must, at a minimum, also 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.