Reconstructing spatiotemporal protein patterns in heterogeneous systems

Many cellular processes, such as cell division and cell motility, are spatially and temporally organized by protein patterns. Such self-organized patterns can be mathematically described by reaction-diffusion equations, which has greatly advanced our understanding of how spontaneous spatial patterns emerge from homogeneity. Biological systems, however, are intrinsically heterogeneous, such that patterns may involve multiple spatial and temporal scales, thus complicating their theoretical analysis. We will discuss multiscale patterns of the Min protein system, a paradigmatic model for pattern formation, in a spatially heterogeneous setup. Building up on a recently developed theoretical framework for mass-conserving reaction-diffusion systems [1], we show that the intricate dynamics is well described by the spatiotemporal evolution of the total densities, which we identify as the relevant degrees of freedom at large length and time scales. Moreover, we show that the spatiotemporal pattern-forming dynamics at small scales can be reconstructed and even predicted from the spatial distribution of the total densities in the system.

[1] Phase-space geometry of mass-conserving reaction-diffusion dynamics, F. Brauns, J. Halatek, and E. Frey., Phys. Rev. X 10, 041036 (2020)