No abstract

Poisson-Boltzmann electrostatics is a well established model in biophysics; however, its application to large-scale biomolecular processes such as protein-protein encounter is still limited by the efficiency and memory constraints of existing numerical techniques. In this article, we present an efficient and accurate scheme that incorporates recently developed numerical techniques to enhance our computational ability. In particular, a boundary integral equation approach is applied to discretize the linearized Poisson-Boltzmann equation; the resulting integral formulas are well conditioned and are extended to systems with arbitrary numbers of biomolecules. The solution process is accelerated by Krylov subspace methods and a new version of the fast multipole method. In addition to the electrostatic energy, fast calculations of the forces and torques are made possible by using an interpolation procedure. Numerical experiments show that the implemented algorithm is asymptotically optimal O(N) in both CPU time and required memory, and application to the acetylcholinesterasefasciculin complex is illustrated. In recent years, because of the rapid advances in biotechnology, both the temporal and spatial scales of biomolecular studies have been increased significantly: from single molecules to interacting molecular networks in a cell, and from the static molecular structures at different resolutions to the dynamical interactions in biophysical processes. In these studies, the electrostatics modeled by the well established Poisson-Boltzmann (PB) equation has been shown to play an important role under physiological solution conditions. Therefore, its accurate and efficient numerical treatment becomes extremely important, especially in the study of large-scale dynamical processes such as protein-protein association and dissociation in which the PB equation has to be solved repetitively during a simulation.Traditional numerical schemes for PB electrostatics include the finite difference methods, where difference approximations are used on structured grids, and finite element methods in which arbitrarily shaped biomolecules are discretized by using elements and the associated basis functions. The resulting algebraic systems for both are commonly solved by using multigrid or domain decomposition accelerations for optimal efficiency. However, as the grid number (and thus the storage, number of operations, and condition number of the system) increases proportionally to the volume size, finite difference and finite element methods become less efficient and accurate for systems with large spatial sizes, e.g., as encountered in protein association and dissociation. Alternative methods include the boundary element method (BEM) and the boundary integral equation (BIE) method. In these methods, only the surfaces of the molecules are discretized; hence, the number of unknowns is greatly reduced. Unfortunately, in earlier versions of BEM, the matrix is stored explicitly and the resulting dense linear system is solved by using Gauss eli...

No abstract

No abstract