Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai; McCammon, J. Andrew

doi:10.4208/cicp.210711.111111s

Cited by 14 publications

(6 citation statements)

References 54 publications

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“…Equation (30) translates the moment of c to the local expansion coefficients of the cluster c, and it is therefore called MtL translation. Since f h is a linear combination of basis functions, we obtain from linearity that…”

Section: Cartesian Fast Multipole Methods (Fmm)mentioning

confidence: 99%

“…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%

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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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Section: Cartesian Fast Multipole Methods (Fmm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chen¹,

Tausch²,

Geng³

2021

Preprint

View full text Add to dashboard Cite

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“…[25,[29][30][31][32][33][34][35], and (2) boundary integral methods that discretize the molecular surface, e.g. [36][37][38][39][40][41][42][43]. The reader may see [44,45] for comprehensive review for numerical methods in solving PB equations.…”

Section: Numerical Methods For Solving Pb Equationmentioning

confidence: 99%

Accurate p$K_a$ Computation Using Matched Interface and Boundary (MIB) Method Based Poisson-Boltzmann Solver

Hu¹,

Zhao²,

Geng³

2018

CICP

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The pK a values are important quantities characterizing the ability of protein active sites to give up protons. pK a can be measured using NMR by tracing chemicalshifts of some special atoms, which is however expensive and time-consuming. Alternatively, pK a can be calculated numerically by electrostatic free energy changes subject to the protonation and deprotonation of titration sites. To this end, the Poisson-Boltzmann (PB) model is an effective approach for the electrostatics. However, numerically solving PB equation is challenging due to the jump conditions across the dielectric interfaces, irregular geometry of the molecular surface, and charge singularities. Our recently developed matched interface and boundary (MIB) method treats these challenges rigorously, resulting in a solid second order MIBPB solver. Since the MIBPB solver uses Green's function based regularization of charge singularities by decomposing the solution into a singular component and a regularized component, it is particularly efficient in treating the accuracy-sensitive, numerous, and complicated charge distributions from the pK a calculation. Our numerical results demonstrate that accurate free energies and pK a values are achieved at coarse grid rapidly. In addition, the resulting software, which pipelines the entire pK a calculation procedure, is available to all potential users from the greater bioscience community.

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“…Taking all these facts together, indeed modeling of electrostatics is must for understanding the effects in molecular biophysics [14, 15, 87, 97, 164, 173, 184] . A collection of relevant papers can be found in the special issues of the journal Communications in Computational Physics [118, 121, 127, 148, 156, 183] , where various methods for modeling electrostatics and their applications in molecular biology are presented.…”

Section: Introductionmentioning

confidence: 99%

Progress in developing Poisson-Boltzmann equation solvers

Li¹,

Li²,

Petukh³

et al. 2013

Computational and Mathematical Biophysics

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This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

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Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

Cited by 14 publications

References 54 publications

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

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

Accurate p$K_a$ Computation Using Matched Interface and Boundary (MIB) Method Based Poisson-Boltzmann Solver

Progress in developing Poisson-Boltzmann equation solvers

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