Order N algorithm for computation of electrostatic interactions in biomolecular systems

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 acetylcholinesterase–fasciculin complex is illustrated