Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

摘要

Background. The calculation of diffusion-controlled ligand binding rates isimportant for understanding enzyme mechanisms as well as designing enzymeinhibitors. We demonstrate the accuracy and effectiveness of a Lagrangianparticle-based method, smoothed particle hydrodynamics (SPH), to studydiffusion in biomolecular systems by numerically solving the time-dependentSmoluchowski equation for continuum diffusion. Results. The numerical method is first verified in simple systems and thenapplied to the calculation of ligand binding to an acetylcholinesterasemonomer. Unlike previous studies, a reactive Robin boundary condition (BC),rather than the absolute absorbing (Dirichlet) boundary condition, isconsidered on the reactive boundaries. This new boundary condition treatmentallows for the analysis of enzymes with "imperfect" reaction rates. Rates forinhibitor binding to mAChE are calculated at various ionic strengths andcompared with experiment and other numerical methods. We find that impositionof the Robin BC improves agreement between calculated and experimental reactionrates. Conclusions. Although this initial application focuses on a single monomersystem, our new method provides a framework to explore broader applications ofSPH in larger-scale biomolecular complexes by taking advantage of itsLagrangian particle-based nature.