Multicellularity and collective cell behavior exemplify the emergence of complex patterns and structures across scales in living systems. When cells interact they can generate higher order patterns of gene expression or patterns of mechanical stresses and strains. There are a wide range of phenomena in which a key element to a developmental process is the appearance of a traveling wave of chemical concentration, mechanical deformation, electrical or other type of signal. Thus, studying traveling waves is relevant to our understanding of fundamental mechanisms underlying pattern formation. We have developed a study of the coupling between a synthetic genetic oscillator and constraints on cell growth in colonies via protein dilution. Our theory predicts that these mechanical constraints generate characteristic patterns of growth rate inhomogeneity in growing cell colonies, inducing the emergence of traveling waves of gene expression. The dynamics of these traveling waves are determined by two parameters feasible to control experimentally: protein degradation rate and maximal protein synthesis rate. This work demonstrates that mechanical constraints give rise to higher order gene expression patterns in cell colonies, and provide a simple system for their design and analysis. The understanding of complex multicellular behaviors at multiple scales in order to control how these patterns are generated and maintained will enable applications in natural phenomena such as embryonic development, tumor formation, wound healing and tissue engineering. Supporting our predictions, we have preliminary experimental evidence that colonies of bacterial cells carrying the synthetic oscillatory circuit do indeed form traveling waves.
