Abstract
Biological systems can display diverse patterns of self-organization, even when built on conserved networks of interaction between molecular species. In these cases, reaction-diffusion equations provide a valuable tool to learn how new dynamics could emerge from quantitative tuning of parameters. Bringing these models into quantitative correspondence with biological data remains an outstanding challenge, especially when the data manifest heterogeneities that are difficult to account for mathematically. One particular example occurs in cell biology, where the membrane-bound regulatory protein RhoA interacts with the filamentous actin cortex in an activator-inhibitor loop. Though this core biochemical circuit is conserved across multiple cell types in different organisms, it produces different patterns of RhoA activity in different contexts, from traveling waves in starfish to transient pulses in Caenorhabditis elegans. To understand how this variation emerges, we develop an activator-inhibitor model that accounts explicitly for actin assembly and heterogeneity. By fitting the model to summary statistics of experimental data, subject to known parameter constraints, we show that F-actin assembly dynamics tune the spatiotemporal patterns of RhoA activity. A minimal representation of these dynamics reveals how directional transport (via polymerization) combines with stochasticity in F-actin number and orientation to produce the observed patterns. This work sheds light on how phenotypic diversity arises from heterogeneity and anisotropy, with important implications for the next generation of activator-inhibitor models.