Atomistic determination of bending rigidity in the HPV-16 capsid

The assembly of viral capsids emerges from local interactions between protein building blocks that collectively generate highly ordered shells with defined geometry and robust mechanical properties. However, a quantitative link between atomistic interactions and the macroscopic elastic parameters that determine capsid shape and rigidity has remained elusive. Here, we present an atomistic framework that bridges molecular interactions and continuum-scale mechanics in human papillomavirus type 16 (HPV-16). Using all-atom molecular dynamics simulations with umbrella sampling, we evaluate the potential of mean force governing angular deviations between neighboring L1 pentamers and extract both the preferred interaction angle and the associated bending modulus. We find a clear decoupling between spontaneous curvature of the capsid and bending rigidity. While the optimal interaction angle remains almost invariant across changes in pH and ionic strength, the bending modulus, which is an order of magnitude larger than any previous estimates, is strongly modulated by the electrostatic environment: protonation enhances angular stiffness at low ionic strength, whereas electrostatic screening suppresses this effect at higher salt concentrations. Our results identify inter-capsomer rigidity as a key determinant of capsid size and shape and provide a quantitative framework for linking specific protein-protein interactions to the emergent mechanical properties of self-assembled viral capsids.