Hybrid Dynamical Simulation Reveals Apparent Stiffening of Flexible Protein Lattices Driving Membrane Bending

Membrane-deforming protein lattices play a central role in essential and pathogenic remodeling processes, including clathrin-mediated endocytosis and viral budding. Simulating these systems at biologically relevant length and time scales requires mesoscale approaches that preserve structural detail while avoiding the computational cost of atomistic resolution. Here, we present a hybrid simulation framework that couples a particle-based flexible protein lattice to a continuum membrane model, enabling systematic investigation of how lattice geometry and rigidity influence dynamic membrane remodeling. We validate the coupled model by comparing simulation results with theoretical predictions for membranes under increasing tension. Using buckling-based deformations of pre-assembled clathrin lattices, we quantify the lattice flexural rigidity and establish a direct relationship between the force constants in the coarse-grained energy and the emergent mechanical properties of the lattice. We then compare this flexural rigidity to an effective rigidity commonly used in continuum descriptions of sphere-forming protein assemblies. Although the flexural rigidity is set solely by the energy function, the effective rigidity depends on lattice size and connectivity, with the two measures converging only for weakly connected lattices. As a result, the effective rigidity relevant for spherical bud formation increases as the lattice grows. This size-dependent stiffening highlights the importance of structural details in interpreting lattice mechanics and cautions against assuming a single constant stiffness throughout assembly. We demonstrate the generality of the method by applying it to pre-assembled viral lattices generated with NERDSS. This work provides a validated framework for simulating how deformable, stable protein assemblies of diverse geometry couple to membrane dynamics and remodeling.