PROJECT SUMMARY Cells shape and reshape themselves as they accomplish diverse functions in vivo. These cell shape changes result from physical and chemical feedback loops at multiple scales. At the biochemical scale, spatiotemporally varying signaling cascades control cytoskeletal polymerization that pushes on the plasma membrane from the inside, inducing cell morphology change at the scale of micrometers. Cell morphology in turn feedbacks to alter intracellular signaling, via mechanisms such as surface curvature-sensing proteins in the plasma membrane. Understanding these feedbacks across scales is particularly critical since they are a target for pharmaceutical intervention. Scientists have developed a wealth of techniques for interrogating the biochemical and genetic basis of cell function. However, disentangling the many feedback loops coupling cell morphology, intracellular organization, and spatiotemporally varying biochemical pathways, such as intracellular signaling, remains ex- perimentally challenging. Live-cell fluorescence microscopy can visualize these feedbacks in action, but imaging across scales produces enormous and detailed datasets that are impossible to make sense of without dedicated computational pipelines. We will develop algorithms for cell biology rooted in computational geometry. Using computational geometry approaches will allow us to draw from decades of math and computer science research to work in biologically relevant geometries, increasing accuracy and easing interpretation. We propose to develop essential algorithms to reconstruct plasma membrane organization from 3D microscopy images and track its movements across time. We will also measure the organizational rules that couple plasma membrane shape and dynamics to spatiotemporally varying biochemical pathways on the cell surface. Finally, we will focus on understanding feedbacks related to intracellular organization throughout the cell, not just on the plasma mem- brane, by broadening the computational approaches we developed for the plasma membrane to other geome- tries. The computational methods that we are proposing to develop will aid in further opening up to scientific investigation the many feedback loops and physical interactions of the meso-scale world of subcellular organi- zation.