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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.

SUBMITTER: Pan W

PROVIDER: S-EPMC4438506 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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

Pan Wenxiao W Daily Michael M Baker Nathan A NA

BMC biophysics 20150507

<h4>Background</h4>The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors.<h4>Methods</h4>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 ...[more]

PMID: 25995835

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Project description:This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works. ELECTRONIC SUPPLEMENTARY MATERIAL:Supplementary material is available for this article at 10.12942/lrr-2008-7.

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

Publications

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

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