BPS2026 – Mathematical modelling of load adaptation during frustrated endocytosis

Actin networks assemble at endocytic sites to drive cargo-bearing membrane into the cell. These sites contain branched actin nucleators on the membrane surface and actin-membrane anchoring proteins on the pit. Under elevated membrane tension, actin networks reorganize to produce additional force in a process known as load adaptation. Load adaptation has been observed in cells and in vitro systems, but underlying mechanisms remain elusive. We hypothesized that the spatial arrangement of endocytic proteins mediates actin growth response to local geometric and physical changes. This question has been investigated in silico with agent-based simulations and continuum models, but their interpretability remains limited without numerical solutions and stochastic description. An approach balancing dynamics with numerical interpretability is necessary to determine how endocytic geometry shapes load adaptation in actin networks. To investigate mechanisms of load adaptation, we formulated a model of the actin network as an ensemble of confined, diffusive monomers following a dynamic vesicle, governed by differential equations for monomer motion, polymerization, and spatially localized branch nucleation. We quantified load adaptation by network growth in response to vesicle internalization velocity and trajectory. Numerical results from this model were validated by Monte Carlo and agent-based simulation. All approaches demonstrated that reduced internalization velocity increased actin accumulation via enhanced branch nucleation. Additionally, transient stalling abated the decrease in growth rate, with the extent of response limited by stall distance and duration. These results provide evidence that endocytic geometry is sufficient to account for key features of load adaptation, even in the absence of molecular-scale mechanisms. This motivates experiments to quantify actin levels under elevated membrane tension and to develop refined methods to stall endocytosis in cells. Broadly, our findings illustrate the wide state space available to self-assembling systems of minimal components.