Mechanics and dynamics of filaments on curved membranes

Protein filaments that bind to curved membranes exhibit rich behavior, as shown in previous studies of bacterial morphogenesis. Here we model the direct binding of protein filaments to membranes and show that it is typically energetically favorable for filaments to orient along the direction of largest curvature. We then model the dynamics of an ensemble of filaments, each translocating along the direction of largest curvature and subject to noise. We show that their macroscopic properties, such as localization, can vary significantly depending on membrane geometry. Finally, we discuss the implications of our study to bacterial morphogenesis and regulation of bacterial rod shape. Our work shows, from a physical perspective, how cellular-scale dynamics which dictates growth may arise from nanometer-scale properties.