Breaking symmetry in spatially distributed networks is a fascinating dynamical systems problem and is of fundamental interest to developmental biology. We discuss two types of local interaction that underlie formation of gene expression patterns in multi-cellular organisms: diffusion and cell-to-cell contact signaling. We first present new insights on a diffusion-driven mechanism for pattern formation and propose a synthetic gene network built upon this mechanism. We then discuss contact-mediated inhibition that is responsible for segmentation and fate-specification. We introduce a dynamical model to represent this mechanism and reveal the key properties of the model that are necessary for pattern formation. The results also yield new insights for the converse problem of maintaining spatial homogeneity, that is, synchrony. We conclude the talk with a distinct biological problem where synchronization plays an important role: the locomotion of swimming microorganisms. Examples include the bundling of flagella and coordination of cilia. With large-scale numerical simulation results for low Reynolds number flows, we argue that synchronization can result from hydrodynamic interactions alone.
