  Background. The calculation of diffusion-controlled ligand binding rates is
important for understanding enzyme mechanisms as well as designing enzyme
inhibitors. We demonstrate the accuracy and effectiveness of a Lagrangian
particle-based method, smoothed particle hydrodynamics (SPH), to study
diffusion in biomolecular systems by numerically solving the time-dependent
Smoluchowski equation for continuum diffusion.
  Results. The numerical method is first verified in simple systems and then
applied to the calculation of ligand binding to an acetylcholinesterase
monomer. Unlike previous studies, a reactive Robin boundary condition (BC),
rather than the absolute absorbing (Dirichlet) boundary condition, is
considered on the reactive boundaries. This new boundary condition treatment
allows for the analysis of enzymes with "imperfect" reaction rates. Rates for
inhibitor binding to mAChE are calculated at various ionic strengths and
compared with experiment and other numerical methods. We find that imposition
of the Robin BC improves agreement between calculated and experimental reaction
rates.
  Conclusions. Although this initial application focuses on a single monomer
system, our new method provides a framework to explore broader applications of
SPH in larger-scale biomolecular complexes by taking advantage of its
Lagrangian particle-based nature.
