Mechanochemical Principles of Spatial and Temporal Patterns in Cells and Tissues

Patterns are ubiquitous in living systems and underlie the dynamic organization of cells, tissues, and embryos. Mathematical frameworks have been devised to account for the self-organization of biological patterns, most famously the Turing framework. Patterns can be defined in space, for example, to form stripes; in time, such as during oscillations; or both, to form traveling waves. The formation of these patterns can have different origins: purely chemical, purely mechanical, or a combination of the two. Beyond the variety ofmolecular implementations of such patterns, we emphasize the unitary principles associated with them, across scales in space and time, within a general mechanochemical framework. We illustrate where such mechanisms of pattern formation arise in biological systems from cellular to tissue scales, with an emphasis on morphogenesis. Our goal is to convey a picture of pattern formation that draws attention to the principles rather than solely to specific molecular mechanisms.