SoftBio Theory Seminar: Emergent space-filling and hyperuniform tiling in growing tissues

Efficient space-filling is a fundamental design principle in living tissues, where branched architectures such as neurons and vascular networks must optimize spatial coverage for proper function. Yet the physical rules driving this self-organized coverage remain poorly understood. In this talk, I will first address this problem at the level of individual branching structures. I will present a theoretical framework that combines local feedback with global guidance to explain the diverse morphologies and coverage patterns observed across different length scales, from single neurons to vascular networks. In most tissues, however, these structures do not grow in isolation but collectively, raising a key question: How do cells partition a shared territory without gaps or redundant overlap? I will argue that such collective tiling can arise from a simple local rule based on neighbor repulsion. An extended model incorporating this rule not only yields non-redundant tiling but also predicts a hyperuniform-like state, in which large-scale density fluctuations are progressively suppressed during growth. Consistent with these predictions, glial cells in the developing retina exhibit both efficient tiling and reduced fluctuations, supporting this mechanism as a driver of retinal patterning. Together, these findings reveal how simple local interactions can give rise to efficient tiling and long-range order, suggesting a general principle for tissue-scale organization.