An implicit boundary integral method for computing electric potential of macromolecules in solvent

Zhong, Yimin; Ren, Kui; Tsai, Richard

doi:10.1016/j.jcp.2018.01.021

Cited by 20 publications

(8 citation statements)

References 92 publications

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“…The method evaluates the limit of a family of surface integrals utilizing extrapolative averaging kernels. An IBIM is applied to compute electrostatic potential from large molecules submerged in a solvent in [30]. That paper also demonstrates that IBIM, coupled with an "off-the-shelf" Fast Multipole Method, can easily be applied to solve the equations for very large molecules.…”

Section: Introductionmentioning

confidence: 90%

Corrected trapezoidal rules for singular implicit boundary integrals

Izzo,

Runborg,

Tsai

2021

Preprint

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We present new higher-order quadratures for a family of boundary integral operators re-derived using the approach introduced in [Kublik, Tanushev, and Tsai. J. Comp. Phys. 247: 279-311, 2013]. In this formulation, a boundary integral over a smooth, closed hypersurface is transformed into an equivalent volume integral defined in a sufficiently thin tubular neighborhood of the surface. The volumetric formulation makes it possible to use the simple trapezoidal rule on uniform Cartesian grids and relieves the need to use parameterization for developing quadrature. Consequently, typical point singularities in a layer potential extend along the surface's normal lines. We propose new higher-order corrections to the trapezoidal rule on the grid nodes around the singularities. This correction is based on local decompositions of the singularity and is dependent on the angle of approach to the singularity relative to the surface's principal curvature directions. The proposed decomposition, combined with the volumetric formulation, leads to a special quadrature error cancellation.

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Section: Introductionmentioning

confidence: 90%

Corrected trapezoidal rules for singular implicit boundary integrals

Izzo,

Runborg,

Tsai

2021

Preprint

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“…Starting from different initial guesses, such as a tight wrap or a loose wrap, the level-set relaxation for VISM can lead to different molecular surfaces, corresponding to multiple solvation states of biomolecules [54,55]. We consider the solvation of protein molecules in a binary monovalent ionic solution with PBD ID: 1A63 and 2AID, which have been studied with a linearized PB theory without steric effects [1,20,50]. For the protein 1A63, we apply the Newton iteration method with truncation to solve both the steric PB theory and classical PB theory on a mesh of grid size 200 3 .…”

Section: Testsmentioning

confidence: 99%

“…We also consider the solvation of the protein 2AID, which is a non-peptide inhibitor complexed with the HIV-1 protease [50]. The VISM calculations predict two solvation states with different initial guesses [52,55].…”

Section: Biomolecular Solvationmentioning

confidence: 99%

Fast Newton Iterative Method for Local Steric Poisson--Boltzmann Theories in Biomolecular Solvation

Chen

Dou

Zhou

2021

Preprint

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This work proposes a fast iterative method for local steric Poisson-Boltzmann (PB) theories, in which the electrostatic potential is governed by the Poisson's equation and ionic concentrations satisfy equilibrium conditions. To present the method, we focus on a local steric PB theory derived from a lattice-gas model, as an example. The advantages of the proposed method in efficiency lies on a key idea that ionic concentrations as scalar implicit functions of the electrostatic potential, i.e, generalized Boltzmann distributions, are numerically available. The existence, uniqueness, boundness, and smoothness of such distributions are rigorously established. A Newton iteration method with truncation is proposed to solve a nonlinear system discretized from the generalized PB equations. The existence and uniqueness of the solution to the discretized nonlinear system are established by showing that it is a unique minimizer of a constructed convex energy. Thanks to the boundness of ionic concentrations, truncation bounds for the potential are obtained by using the extremum principle. The truncation step in iterations is shown to be energy, residual, and error decreasing. To further speed-up computations, we propose a novel precomputing-interpolation strategy, which is applicable to other local steric PB theories and makes the proposed methods for solving steric PB theories as efficient as for solving the classical PB theory. Analysis on the Newton iteration method with truncation shows local quadratic convergence for the proposed numerical methods. Applications to realistic biomolecular solvation systems reveal that counterions with steric hindrance stratify in an order prescribed by the parameter of ionic valence-to-volume ratio. Finally, we remark that the proposed iterative methods for local steric PB theories can be readily incorporated in well-known classical PB solvers.

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“…An alternative approach is to reformulate the PB equation as a boundary integral equation and use the boundary elements to discretize the molecular surface, e.g. [25][26][27][28][29][30][31][32][33]. Besides the reduction from three dimensional space to the two dimensional molecular boundary, this approach has the advantage that singular charges, interface conditions, and far-field condition are incorporated analytically in the formulation, and hence do not impose additional approximation errors.…”

Section: Introductionmentioning

confidence: 99%

A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

Chen¹,

Tausch²,

Geng³

2021

Preprint

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The Poisson-Boltzmann model is an effective and popular approach for modeling solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we report our recent work in developing a Galerkin boundary integral method for solving the Poisson-Boltzmann (PB) equation. The solver has combined advantages in accuracy, efficiency, and memory usage as it applies a well-posed boundary integral formulation to circumvent many numerical difficulties associated with the PB equation and uses an O(N ) Cartesian Fast Multipole Method (FMM) to accelerate the GMRES iteration. In addition, special numerical treatments such as adaptive FMM order, block diagonal preconditioners, Galerkin discretization, and Duffy's transformation are combined to improve the performance of the solver, which is validated on benchmark Kirkwood's sphere and a series of testing proteins.

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An implicit boundary integral method for computing electric potential of macromolecules in solvent

Cited by 20 publications

References 92 publications

Corrected trapezoidal rules for singular implicit boundary integrals

Corrected trapezoidal rules for singular implicit boundary integrals

Fast Newton Iterative Method for Local Steric Poisson--Boltzmann Theories in Biomolecular Solvation

A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

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