title: Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics.
abstract: BACKGROUND
  The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors.
  
  
  METHODS
  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. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with "imperfect" reaction rates.
  
  
  RESULTS
  The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. 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.
authors.affiliation: Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, MSID K7-90, 99352, Richland, PO Box 999 WA USA.
authors.forename: Wenxiao
authors.initials: W
authors.lastname: Pan
authors.affiliation: Chemical Physics and Analysis Division, Mathematics and Data Division, Pacific Northwest National Laboratory, MSID K1-83, 99352, Richland, PO Box 999 WA USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Daily
authors.affiliation: Computational and Statistical Analytics Division, Pacific Northwest National Laboratory, MSID K7-20, 99352, Richland, PO Box 999 WA USA.
authors.forename: Nathan A
authors.initials: NA
authors.lastname: Baker
keywords: Acetylcholinesterase; Binding rates; Diffusion; Protein-ligand interactions; Smoluchowski equation; Smoothed particle hydrodynamics