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

Journal Article · · BMC Biophysics, 8:Article No. 7
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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. 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. 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.

Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC05-76RL01830
OSTI ID:
1208757
Report Number(s):
PNNL-SA-107569; KJ0401000
Journal Information:
BMC Biophysics, 8:Article No. 7, Journal Name: BMC Biophysics, 8:Article No. 7
Country of Publication:
United States
Language:
English

References (41)

Multiple time step diffusive Langevin dynamics for proteins journal February 1998
Continuum Diffusion Reaction Rate Calculations of Wild-Type and Mutant Mouse Acetylcholinesterase: Adaptive Finite Element Analysis journal September 2004
Non-Boltzmann Rate Distributions in Stochastically Gated Reactions journal January 1999
Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian dynamics program journal March 1991
Smoothed particle hydrodynamics continuous boundary force method for Navier–Stokes equations subject to a Robin boundary condition journal February 2014
Finite concentration effects on diffusion-controlled reactions journal January 2004
Smoothed Particle Hydrodynamics and Its Diverse Applications journal January 2012
Self-consistent generalized Langevin equation for colloid dynamics journal November 2001
A new smoothed particle hydrodynamics non-Newtonian model for friction stir welding: Process modeling and simulation of microstructure evolution in a magnesium alloy journal September 2013
Finite Element Solution of the Steady-State Smoluchowski Equation for Rate Constant Calculations journal April 2004
Very fast empirical prediction and rationalization of protein pKa values journal October 2005
Poisson–Nernst–Planck equations for simulating biomolecular diffusion–reaction processes I: Finite element solutions journal September 2010
Diffusion Control in Biochemical Reactions book January 1974
Finite Element Analysis of the Time-Dependent Smoluchowski Equation for Acetylcholinesterase Reaction Rate Calculations journal May 2007
A commentary on gating of the active site of triose phosphate isomerase: Brownian dynamics simulations of flexible peptide loops in the enzyme, by R. C. Wade, M. E. Davis, B. A. Luty, J. D. Madura, and J. A. McCammon journal January 1993
Kinetics of diffusion-controlled enzymatic reactions with charged substrates journal January 2010
Gating of the active site of triose phosphate isomerase: Brownian dynamics simulations of flexible peptide loops in the enzyme journal January 1993
[22] Diffusion-controlled enzymatic reactions book January 1991
PDB2PQR: an automated pipeline for the setup of Poisson-Boltzmann electrostatics calculations journal July 2004
Fractional diffusion-limited component of reactions catalyzed by acetylcholinesterase journal January 1986
Effective charge on acetylcholinesterase active sites determined from the ionic strength dependence of association rate constants with cationic ligands journal August 1980
A Monte Carlo simulation study of the influence of internal motions on the molecular conformation deduced from two-dimensional nmr experiments journal November 1989
Improving implicit solvent simulations: a Poisson-centric view journal April 2005
A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics journal December 2010
PDB2PQR: expanding and upgrading automated preparation of biomolecular structures for molecular simulations journal May 2007
Hydrolysis of low concentrations of the acetylthiocholine analogs acetyl(homo)thiocholine and acetyl(nor)thiocholine by acetylcholinesterase may be limited by selective gating at the enzyme peripheral site journal March 2013
Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces journal January 2008
Lateral diffusion and aggregation. A Monte Carlo study journal January 1992
Stochastic Simulation of Chemical Kinetics journal May 2007
Electrostatic Influence on the Kinetics of Ligand Binding to Acetylcholinesterase journal September 1997
Acetylcholinesterase: electrostatic steering increases the rate of ligand binding journal January 1993
Rapid binding of a cationic active site inhibitor to wild type and mutant mouse acetylcholinesterase: Brownian dynamics simulation including diffusion in the active site gorge journal December 1998
Brownian dynamics of cytochrome c and cytochrome c peroxidase association journal July 1988
A Lattice Relaxation Algorithm for Three-Dimensional Poisson-Nernst-Planck Theory with Application to Ion Transport through the Gramicidin A Channel journal February 1999
Analysis of Synaptic Transmission in the Neuromuscular Junction Using a Continuum Finite Element Model journal October 1998
Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics journal June 2013
Conformation gating as a mechanism for enzyme specificity journal August 1998
On the calculation of diffusive reaction rates using Brownian dynamics simulations journal March 1990
Divergent Structure–Activity Relationships of Structurally Similar Acetylcholinesterase Inhibitors journal September 2013
Electrostatics of nanosystems: Application to microtubules and the ribosome journal August 2001
Potential theory, path integrals and the Laplacian of the indicator journal November 2012

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