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. 2009 Jun 9;5(6):1692-1699.
doi: 10.1021/ct900083k. Epub 2009 May 21.

An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics

Benzhuo Lu  1 , Xiaolin Cheng, Jingfang Huang, J Andrew McCammon
Affiliations

An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics

Benzhuo Lu et al. J Chem Theory Comput. .

Abstract

The numerical solution of the Poisson-Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.

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Figures

Figure 1
Figure 1
A “node patch” around the ith corner enclosed by the dashed lines is constructed on a triangular mesh. O and n are the centroid and normal vector of an element respectively, and C is the middle point of an edge.
Figure 2
Figure 2
A schematic 2D adaptive tree structure.
Figure 3
Figure 3
Accuracy of energy and potential calculations with the conventional and adaptive solvers. The relative errors of surface potentials are averaged over all node points.
Figure 4
Figure 4
Electrostatic potential surface of the acetylcholinestase.
Figure 5
Figure 5
Electrostatic potential surface of the 30S ribosome subunit.
See this image and copyright information in PMC

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