Finite-element estimation of protein-ligand association rates with post-encounter effects: Applications to calcium binding in troponin C and SERCA

We introduce a computational pipeline and suite of software tools for the approximation of diffusion-limited binding based on a recently developed theoretical framework. Our approach handles molecular geometries generated from high-resolution structural data and can account for active sites buried within the protein or behind gating mechanisms. Using tools from the FEniCS library and the APBS solver, we implement a numerical code for our method and study two Ca²⁺-binding proteins: troponin C and the sarcoplasmic reticulum Ca²⁺ ATPase. We find that a combination of diffusional encounter and internal 'buried channel' descriptions provides superior descriptions of association rates, improving estimates by orders of magnitude.