Modeling collective dynamics of biological systems in curved space

Many interesting biological phenomena occur in curved environments, from epithelial jamming within lung bronchioles, to biofilm colonization of rough sewer walls, to animal herds migrating together over hilly landscapes. Much of our understanding of these collective behaviors comes either from extensive work in flat spaces or theoretical and computational studies that make use of tractable curved spaces with particularly simple geometries, such as models confined to spherical or cylindrical surfaces. Recently, numerical approaches have been developed that solve differential equations for the evolution of continuum fields on arbitrarily curved surfaces; these have been used to study familiar phenomena such as flocking or epithelial relaxation dynamics. Complementing such continuum approaches, we present a molecular dynamics-like framework for performing agent-based simulations on surfaces of arbitrary curvature. We will discuss the basics of this simulation framework and share preliminary results for flocking dynamics on some sample surfaces of varying Gaussian curvature.