Monte Carlo-based linear Poisson-Boltzmann approach makes accurate salt-dependent solvation free energy predictions possible

Simonov, Nikolai A.; Mascagni, Michael; Fenley, Márcia O.

doi:10.1063/1.2803189

Cited by 23 publications

(23 citation statements)

References 37 publications

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“…The Monte Carlo approximation of u(x) and the associated discretization scheme of X t that we describe here have been originally proposed by Mascagni and Simonov in [23] to approximate the solution of PoissonBoltzmann's equation [34]. In this algorithm, after having hit Γ, the process jumps randomly and symmetrically with respect to Γ (see below).…”

Section: The Monte Carlo Methods Proposed By Mascagni and Simonov And mentioning

confidence: 99%

Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Bossy¹,

Champagnat²,

Maire³

et al. 2010

ESAIM: M2AN

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Abstract.Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of R d . This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal generator belongs to this family, as the solution of a SDE including a non standard local time term related to the interface of discontinuity. We then prove an extended Feynman-Kac formula for the Poisson-Boltzmann equation. This formula allows us to justify various probabilistic numerical methods to approximate the free energy of a molecule. We analyse the convergence rate of these simulation procedures and numerically compare them on idealized molecules models.Mathematics Subject Classification. 35Q60, 92C40, 60J60, 65C05, 65C20, 68U20.

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Section: The Monte Carlo Methods Proposed By Mascagni and Simonov And mentioning

confidence: 99%

Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Bossy¹,

Champagnat²,

Maire³

et al. 2010

ESAIM: M2AN

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“…35,36,36–52 By replacing discrete water models with a continuum medium using the average dielectric properties of water, implicit solvents provide significant decrease in the computational cost of simulations. Within the implicit solvent framework, the Generalized Born (GB) model 43,53–75 provides a relatively simple, efficient and robust estimate to calculate the long-range electrostatic interactions in molecular simulations.…”

Section: Introductionmentioning

confidence: 99%

Protein–Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation

Izadi

Aguilar

Onufriev

2015

J. Chem. Theory Comput.

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Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613–3639), in estimating the electrostatic solvation free energies (ΔGpol) and binding free energies (ΔΔGpol) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw and OPC). The two main findings are as follows. First, the deviation (RMSD=7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs. TIP3P (RMSD=5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above “error margin” – differences between ΔΔGpol estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔGpol) between GBNSR6 and two out of the three explicit water models, and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔGpol values can be up to ~50% in relative error, or ~9 kcal/mol in absolute error, which is significantly larger than “chemical accuracy” goal of ~1 kcal/mol. The absolute ΔGpol calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear “gold standard” among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

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“…, [6–8]). Dilute ionic solutions are also commonly studied using Poisson–Boltzmann (PB) theory [9–22], with reasonable agreement for the energetics between PB theory and primitive-model Monte-Carlo simulations, for sufficiently low concentrations of monovalent salts [23–26]. …”

Section: Introductionmentioning

confidence: 99%

Discretization of the induced-charge boundary integral equation

2009

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Boundary-element methods (BEM) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few Angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein/solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch, Wang, and White (IEEE. Trans. Comput.-Aided Des. 20:1398, 2001) to compute the BEM matrix elements is always more accurate than the traditional centroid collocation method. Qualocation is no more expensive to implement than collocation and can save significant computional time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

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Monte Carlo-based linear Poisson-Boltzmann approach makes accurate salt-dependent solvation free energy predictions possible

Cited by 23 publications

References 37 publications

Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Protein–Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation

Discretization of the induced-charge boundary integral equation

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