We propose a robust and efficient numerical discretization scheme for the infinitesimal generator of a diffusion process based on a finite volume approximation. The resulting discrete-space operator can be interpreted as a jump process on the mesh whose invariant measure is precisely the cell approximation of the Boltzmann distribution of the original process. Moreover the resulting jump process preserves the detailed balance property of the original stochastic process.
Protein-ligand interactions are essential for nearly all biological processes, and yet the bio-
physical mechanism that enables potential binding partners to associate before specific binding
occurs remains poorly understood. Fundamental questions include which factors influence the
formation of protein-ligand encounter complexes, and whether designated association path-
ways exist. In this article we introduce a computational approach to systematically analyze
the complete ensemble of association pathways and to thus investigate these questions. This
approach is employed here to study the binding of a phosphate ion to the Escherichia coli
Phosphate Binding Protein. Various mutants of the protein are considered and their effects
on binding free energy profiles, association rates and association pathway distributions are
quantified. The results reveal the existence of two anion attractors, i.e. regions that initially
attract negatively charged particles and allow them to be efficiently screened for phosphate
which is specifically bound subsequently. Point mutations that affect the charge on these
attractors modulate their attraction strength and speed up association to a factor of 10 of
the diffusion limit and thus change the association pathways of the phosphate ligand. It is
demonstrated that a phosphate that pre-binds to such an attractor neutralizes its attraction
effect to the environment, making the simultaneous association of a second phosphate ion
unlikely. Our study suggests ways how structural properties can be used to tune molecular
association kinetics so as to optimize the efficiency of binding, and highlights the importance
of kinetic properties.