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• W1991951822 abstract "An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities - obtained with both linear and nonlinear Poisson-Boltzmann equation - for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers." @default.
• W1991951822 created "2016-06-24" @default.
• W1991951822 creator A5005951988 @default.
• W1991951822 creator A5067145582 @default.
• W1991951822 date "2011-04-15" @default.
• W1991951822 modified "2023-10-01" @default.
• W1991951822 title "A Fast and Robust Poisson–Boltzmann Solver Based on Adaptive Cartesian Grids" @default.
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• W1991951822 doi "https://doi.org/10.1021/ct1006983" @default.
• W1991951822 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/3188438" @default.
• W1991951822 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/21984876" @default.
• W1991951822 hasPublicationYear "2011" @default.
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