First, commonly used solvent-solute interfaces, i.e., the van der Walls (vdW) surface, solvent accessible surface (SAS), and the solvent excluded surface (SES) 19, 20 admit geometric singularities, such as sharp tips, cusps and self-intersecting surfaces, 21 which make the rigorous enforcement of interface jump conditions a formidable task in PB solvers. Numerically, there are three major obstacles in constructing accurate and reliable PB solvers. The MIBPB package is a second-order convergence PB solver for dealing with the SESs of biomolecules. #POISSON RELATIONS THERMODYNAMICS CALCULATOR FREE#In the current work, we employ the our MIBPB package 4, 18 to predict the electrostatic solvation free energy. We therefore believe that when it is used properly, the PB methodology is able to deliver accurate and reliable electrostatic binding analysis. In fact, a grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in ΔΔ G el calculation. 18 Here the L ∞ norm means the maximum absolute error measure and “second order accurate” means that the error reduces four times when the grid spacing is halved. The MIBPB solver is by far the only existing method that is second-order accurate in L ∞ norm for solving the Poisson-Boltzmann equation with discontinuous dielectric constants, singular charge sources, and geometric singularities from the solvent excluded surfaces (SESs) of biomolecules. In this work, we investigate the grid dependence of our PB solver (MIBPB) 4, 18 in estimating both electrostatic solvation free energies and electrostatic binding free energies. 16, 17 However, no confirmation for the reliable use of grid spacing of 0.5 Å in ΔΔ G el has been given. In the past few years, there have been many attempts to develop highly accurate PB solvers using advance techniques for interface treatments. The emblematic solvers in this category are Amber PBSA, 11, 12 Delphi, 13, 14 APBS 15 and CHARMM PBEQ. 9, 10 Among them, the FDM is prevalently used in the field due to its simplicity in implementation. Mathematically, most PB solvers reported in the literature are based on three major approaches, namely, the finite difference method (FDM), 6 the finite element method (FEM), 7, 8 and the boundary element method (BEM). 1– 5 In past decades, the development of a robust PB solver catches much attention in computational biophysics and biochemistry. Technically, the accuracy and reliability of electrostatic binding energy prediction depend essentially on the quality of electrostatic solvation (Δ G el) estimation, which can be achieved by solving the Poisson-Boltzmann (PB) equation in the implicit solvent model. Additionally, many pharmaceutical applications, specially in the final stage of the drug design, rely on the accurate and reliable calculation of binding free energy. The prediction of ΔΔ G el plays a vital role in the study of many cellular processes, such as signal transduction, gene expression, and protein synthesis. Accurate and reliable prediction of electrostatic binding free energy, ΔΔ G el, is crucial to biophysical modeling and computation. Also, it takes energy for an air parcel to move from potential surface to another potential energy surface.Electrostatics is ubiquitous in biomolecular and cellular systems and of paramount importance to biological processes. An air parcel needs no energy to move along an adiabatic surface. We can plot adiabatic (isentropic) surfaces in the atmosphere. We can find the temperature in State College due only to adiabatic changes by the following equation:
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