Thermodynamics of morphological transitions in growing membranes

The growth of lipid membranes at sub-micron scales plays an important role in many essential cellular processes, such as the formation and organization of vital cellular organelles. However, describing the underlying physics of this growth remains an ongoing challenge. This challenge stems from the fact that, at these scales, membrane growth reflects a delicate interplay of material exchange, bending deformation, apparent variation in material properties, and, crucially, in-plane viscous flow that often cannot be neglected. To address this challenge, we consider the nonequilibrium growth dynamics of a minimal model of fluid membranes, in which sufficiently large driving forces produce a striking morphological transition marked by out-of-plane buckling, in-plane flow, and dramatic changes in the growth rate. To understand this behavior, we first construct a continuum description of growing membranes using tools from differential geometry and linear irreversible thermodynamics. This yields expressions relating the nonequilibrium driving to the rate of growth, size fluctuations, and effective material properties. We then validate these predictions via coarse-grained simulations of fluid vesicles. Next, we demonstrate that one can derive analogous relationships using ideas from stochastic thermodynamics, including the recently derived thermodynamic uncertainty relations. These allow us to establish rigorous constraints on the parameters required for growth-driven morphological changes, which we validate in simulations. Our results suggest a multifaceted approach for understanding and constraining the effects of active driving forces on the mechanics and morphology of biological matter.