Directed and Spiral Wave Propagation in Communities with Correlated Heterogeneity

Directed signal propagation in cellular communities is an important and ubiquitous phenomenon. However, heterogeneity in these communities may pose a challenge to directed propagation. Additionally, spatial correlations in the heterogeneity may alter the dynamic behavior. In general, the relationship between correlated heterogeneity and wave propagation is poorly understood. Here we use a FitHugh Nagumo-type model to investigate wave propagation in a two-dimensional heterogeneous community. Our model predicts three dynamic regimes in which waves either propagate directly, die out, or spiral indefinitely. In some parameter regimes, correlations in the heterogeneity enhance directionality and suppress spiraling, as expected. In contrast, in other regimes, correlations promote spiraling, a surprising feature that we explain by demonstrating that these spirals form by a second, distinct mechanism. Finally, we characterize the dependence of the spiral period on the degree of heterogeneity and connect our results to percolation theory. Our work reveals that the spatial structure of cell-to-cell heterogeneity can have important consequences for directed signal propagation in cellular communities, and provides predictions that can be tested in experiments.