Accurate solution of multi-region continuum biomolecule electrostatic problems using the linearized Poisson-Boltzmann equation with curved boundary elements

摘要: We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this is desire to create solver capable of precisely describing geometries and topologies prevalent continuum models biological molecules. This enabled by synthesis four technologies developed or implemented specifically work. First, molecular accessible surfaces used describe dielectric ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce geometries. Second, we avoided explicitly forming dense BEM matrices instead solved linear systems preconditioned iterative (GMRES), matrix compression algorithm (FFTSVD) accelerate matrix-vector multiplication. Third, robust numerical integration methods employed evaluate singular near-singular integrals over elements. Finally, general boundary-integral approach modeling an arbitrary number embedded homogeneous regions differing constants, possible salt treatment, point charges. A comparison presented standard finite-difference techniques demonstrates certain classes electrostatic calculations, such as determining absolute solvation rigid-binding free energies, improved convergence properties can have significant impact on computed energetics. also demonstrate accuracy offered curved-element important when more sophisticated techniques, non-rigid-binding models, are compute relative effects modifications. In addition, show calculations requiring multiple solves same geometry, charge optimization component analysis, be high approach, times comparable traditional methods.