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. Zhao, Rundong; Wang, Menglun; Chen, Jiahui; Tong, Yiying; Wei, Guo-Wei: The de Rham-Hodge analysis and modeling of biomolecules (2020)
  2. Chen, Duan; Cai, Wei: An (O(N \logN)) hierarchical random compression method for kernel matrices by sampling partial matrix entries (2019)
  3. Krasny, Robert; Wang, Lei: A treecode based on barycentric Hermite interpolation for electrostatic particle interactions (2019)
  4. Chen, Jiahui; Geng, Weihua: On preconditioning the treecode-accelerated boundary integral (TABI) Poisson-Boltzmann solver (2018)
  5. Deng, Weishan; Xu, Jin; Zhao, Shan: On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics (2018)
  6. Zhong, Yimin; Ren, Kui; Tsai, Richard: An implicit boundary integral method for computing electric potential of macromolecules in solvent (2018)
  7. Cheng, Yingda; Christlieb, Andrew J.; Guo, Wei; Ong, Benjamin: An asymptotic preserving Maxwell solver resulting in the Darwin limit of electrodynamics (2017)
  8. Geng, Weihua; Zhao, Shan: A two-component matched interface and boundary (MIB) regularization for charge singularity in implicit solvation (2017)
  9. Cooper, Christopher D.; Barba, Lorena A.: Poisson-Boltzmann model for protein-surface electrostatic interactions and grid-convergence study using the \textscPyGBecode (2016)
  10. Geng, Weihua: A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations (2015)
  11. Jiang, Yi; Xie, Yang; Ying, Jinyong; Xie, Dexuan; Yu, Zeyun: SDPBS web server for calculation of electrostatics of ionic solvated biomolecules (2015)
  12. Li, Jiao; Xie, Dexuan: A new linear Poisson-Boltzmann equation and finite element solver by solution decomposition approach (2015)
  13. Zhang, Bo; Peng, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai; Lu, Benzhuo: Parallel AFMPB solver with automatic surface meshing for calculation of molecular solvation free energy (2015)
  14. Chen, Duan: Modeling and computation of heterogeneous implicit solvent and its applications for biomolecules (2014)
  15. Chen, Duan: Modeling and computation of heterogeneous implicit solvent and its applications for biomolecules (2014)
  16. Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A.: A biomolecular electrostatics solver using python, GPUs and boundary elements that can handle solvent-filled cavities and stern layers (2014)
  17. Gan, Zecheng; Xu, Zhenli: Efficient implementation of the Barnes-Hut octree algorithm for Monte Carlo simulations of charged systems (2014)
  18. Xie, Dexuan: New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics (2014)
  19. Geng, Weihua; Jacob, Ferosh: A GPU-accelerated direct-sum boundary integral Poisson-Boltzmann solver (2013)
  20. Geng, Weihua; Krasny, Robert: A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules (2013)

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