A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules. We present a treecode-accelerated boundary integral (TABI) solver for electrostatics of solvated biomolecules described by the linear Poisson-Boltzmann equation. The method employs a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES iteration and the matrix-vector product is carried out by a Cartesian treecode which reduces the cost from $O(N^2)$ to $O(Nlog N)$, where $N$ is the number of faces in the triangulation. The TABI solver is applied to compute the electrostatic solvation energy in two cases, the Kirkwood sphere and a solvated protein. We present the error, CPU time, and memory usage, and compare results for the Poisson-Boltzmann and Poisson equations. We show that the treecode approximation error can be made smaller than the discretization error, and we compare two versions of the treecode, one with uniform clusters and one with non-uniform clusters adapted to the molecular surface. For the protein test case, we compare TABI results with those obtained using the grid-based APBS code, and we also present parallel TABI simulations using up to eight processors. We find that the TABI solver exhibits good serial and parallel performance combined with relatively simple implementation, efficient memory usage, and geometric adaptability.

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  1. Bramas, Bérenger; Hassan, Muhammad; Stamm, Benjamin: An integral equation formulation of the (N)-body dielectric spheres problem. II: Complexity analysis (2021)
  2. Fu, Jing; Gan, Zecheng: Harmonic surface mapping algorithm for electrostatic potentials in an atomistic/continuum hybrid model for electrolyte solutions (2021)
  3. Lee, Arum; Geng, Weihua; Zhao, Shan: Regularization methods for the Poisson-Boltzmann equation: comparison and accuracy recovery (2021)
  4. Wang, Lei: A kernel-independent treecode for general Rotne-Prager-Yamakawa tensor (2021)
  5. Borleske, George; Zhou, Y. C.: Enriched gradient recovery for interface solutions of the Poisson-Boltzmann equation (2020)
  6. Wang, Lei; Krasny, Robert; Tlupova, Svetlana: A kernel-independent treecode based on barycentric Lagrange interpolation (2020)
  7. Zhao, Rundong; Wang, Menglun; Chen, Jiahui; Tong, Yiying; Wei, Guo-Wei: The de Rham-Hodge analysis and modeling of biomolecules (2020)
  8. Zhou, Y. C.; Argudo, David; Marcoline, Frank V.; Grabe, Michael: A computational model of protein induced membrane morphology with geodesic curvature driven protein-membrane interface (2020)
  9. Chen, Duan; Cai, Wei: An (O(N \logN)) hierarchical random compression method for kernel matrices by sampling partial matrix entries (2019)
  10. Krasny, Robert; Wang, Lei: A treecode based on barycentric Hermite interpolation for electrostatic particle interactions (2019)
  11. Wang, Lei; Tlupova, Svetlana; Krasny, Robert: A treecode algorithm for 3D stokeslets and stresslets (2019)
  12. Zhang, Bo; Debuhr, Jackson; Niedzielski, Drake; Mayolo, Silvio; Lu, Benzhuo; Sterling, Thomas: DASHMM accelerated adaptive fast multipole Poisson-Boltzmann solver on distributed memory architecture (2019)
  13. Chen, Jiahui; Geng, Weihua: On preconditioning the treecode-accelerated boundary integral (TABI) Poisson-Boltzmann solver (2018)
  14. Deng, Weishan; Xu, Jin; Zhao, Shan: On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics (2018)
  15. Hu, Jingzhen; Zhao, Shan; Geng, Weihua: Accurate p(K_a) computation using matched interface and boundary (MIB) method based Poisson-Boltzmann solver (2018)
  16. Zhong, Yimin; Ren, Kui; Tsai, Richard: An implicit boundary integral method for computing electric potential of macromolecules in solvent (2018)
  17. Cheng, Yingda; Christlieb, Andrew J.; Guo, Wei; Ong, Benjamin: An asymptotic preserving Maxwell solver resulting in the Darwin limit of electrodynamics (2017)
  18. Geng, Weihua; Zhao, Shan: A two-component matched interface and boundary (MIB) regularization for charge singularity in implicit solvation (2017)
  19. Cooper, Christopher D.; Barba, Lorena A.: Poisson-Boltzmann model for protein-surface electrostatic interactions and grid-convergence study using the \textscPyGBecode (2016)
  20. Geng, Weihua: A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations (2015)

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