We address the intricate dynamics of self-organized pattern-forming systems that span multiple spatial and temporal scales, and demonstrate an approach that enables us to reconstruct and forecast the dynamics at small scales from a reduced dynamics at large length and time scales. Our work provides a new route to deal with complex multiscale dynamics that emerge in a broad range of physical systems. Spatiotemporal patterns are vital for the organization of many biological processes such as cell division, collective cell migration, and morphogenesis. Although commonly assumed in theoretical approaches on pattern-forming systems, patterns generally do not emerge from homogeneity, but rather transition from one pattern to another over time and across different spatial regions – a key scientific challenge, as Turing pointed out in his seminal paper on pattern formation. Coarse-graining methods allow the dynamics of such multiscale systems to be reduced to the essential degrees of freedom at large scales. However, a drawback of traditional coarse-graining approaches is that information about the patterns at small scales, that are integrated out, are lost and cannot be reconstructed from the dynamics at large scales. more

Proteins control many vital functions in living cells, such as cell growth and cell division. Reliable coordination of these functions requires spatial and temporal organizaton of proteins inside cells, which encodes information about the cell geometry and the current state in the cell cycle. Here, we review how protein patterns are guided by the cell size and shape, by other protein patterns that act as template, and by the mechanical properties of the cell. We posit that understanding the controlled formation of protein patterns in cells will be an essential part of understanding information processing in living systems. more