scholarly journals Modeling and computation of heterogeneous implicit solvent and its applications for biomolecules

2014 ◽  
Vol 2 (1) ◽  
pp. 107-127 ◽  
Author(s):  
Duan Chen
Keyword(s):  
Free Energy ◽  
Jacobian Matrix ◽  
Discontinuous Coefficients ◽  
Energy Functional ◽  
Implicit Solvent ◽  
Newton's Iteration ◽  
Solvent Model ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Dna Strand

Abstract Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the form of total free energy functional and a quasi-linear Poisson-Boltzmann equation (QPBE) is derived. Classical Newton’s iteration can be used to solve the QPBE numerically but the corresponding Jacobian matrix is complicated due to the quasi-linear term. In the current work, a systematic formulation of the Jacobian matrix is derived. As an alternative option, an algorithm mixing the Newton’s iteration and the fixed point method is proposed to avoid the complicated Jacobian matrix, and it is a more general algorithm for equation with discontinuous coefficients. Computational efficiency and accuracy for these two methods are investigated based on a set of equation parameters. At last, the QPBE with singular charge source and piece-wisely defined dielectric functions has been applied to analyze electrostatics of macro biomolecules in a complicated solvent. A set of computational algorithms such as interface method, singular charge removal technique and the Newtonfixed- point iteration are employed to solve the QPBE. Biological applications of the proposed model and algorithms are provided, including calculation of electrostatic solvation free energy of proteins, investigation of physical properties of channel pore of an ion channel, and electrostatics analysis for the segment of a DNA strand.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

Solvation Free Energies and Adsorption Energies at the Metal/Water Interface from Hybrid QM-MM Simulations

2020 ◽  
Author(s):  
Paul Clabaut ◽  
Benjamin Schweitzer ◽  
Andreas Goetz ◽  
Carine Michel ◽  
Stephan Steinmann
Keyword(s):  
Free Energy ◽  
Adsorption Energy ◽  
Metallic Surface ◽  
Implicit Solvent ◽  
Water Interface ◽  
Free Energies ◽  
Hybrid Scheme ◽  
Aromatic Molecules ◽  
Solvent Model ◽  
Metal Water

Modeling adsorption at the metal/water interfaces is a corner-stone towards an improved understanding in a variety of fields from heterogeneous catalysis to corrosion. We propose and validate a hybrid scheme that combines the adsorption free energies obtained in gas phase at the DFT level with the variation in solvation from the bulk phase to the interface evaluated using a molecular mechanics based alchemical transformation, denoted MMsolv. Using the GAL17 force field for the platinum/water interaction, we retrieve a qualitatively correct interaction energy of the water solvent at the interface. This interaction is of near chemisorption character and thus challenging, both for the alchemical transformation, but also for the fixed point-charge electrostatics. Our scheme passes through a state characterized by a well-behaved physisorption potential for the Pt(111)/H<sub>2</sub>O interaction to converge the free energy difference. The workflow is implemented in the freely available SolvHybrid package. We first assess the adsorption of a water molecule at the Pt/water interface, which turns out to be a stringent test. The intrinsic error of our QM-MM hybrid scheme is limited to 6 kcal/mol through the introduction of a correction term to attenuate the electrostatic interaction between near-chemisorbed water molecules and the underlying Pt atoms. Next, we show that the MMsolv solvation free energy of Pt (-0.46 J/m<sup>2</sup>) is in good agreement with the experimental estimate (-0.32 J/m<sup>2</sup>). Furthermore, we show that the entropy contribution at room temperature is roughly of equal magnitude as the free energy, but with opposite sign. Finally, we compute the adsorption energy of benzene and phenol at the Pt(111)/water interface, one of the rare systems for which experimental data are available. In qualitative agreement with experiment, but in stark contrast with a standard implicit solvent model, the adsorption of these aromatic molecules is strongly reduced (i.e., less exothermic by ~30 and 40 kcal/mol for our QM/MM hybrid scheme and experiment, respectively, but ~0 with the implicit solvent) at the solid/liquid compared to the solid/gas interface. This reduction is mainly due to the competition between the organic adsorbate and the solvent for adsorption on the metallic surface. The semi-quantitative agreement with experimental estimates for the adsorption energy of aromatic molecules thus validates the soundness of our hybrid QM-MM scheme.

scholarly journals Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 632
Author(s):  
Tzyy-Leng Horng
Keyword(s):  
Free Energy ◽  
Lattice Gas ◽  
Steric Effect ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Experimental Conditions ◽  
Ion Concentrations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Ion Size

The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.

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