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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.

The gating motion of the human nicotinic acetylcholine receptor (nAChR) alpha 7 was investigated with normal mode analysis (NMA) of two homology models. The first model, referred to as model 1, was built from both the Lymnaea stagnalis acetylcholine binding protein (AChBP) and the transmembrane (TM) domain of the Torpedo marmorata nAChR. The second model, referred to as model C, was based solely on the recent electron microscopy structure of the T. marmorata nAChR. Despite structural differences, both models exhibit nearly identical patterns of flexibility and correlated motions. In addition, both models show a similar global twisting motion that may represent channel gating. The similar results obtained for the two models indicate that NMA is most sensitive to the contact topology of the structure rather than its finer detail. The major difference between the low-frequency motions sampled for the two models is that a symmetrical pore-breathing motion, favoring channel opening, is present as the second most dominant motion in model 1, whilst largely absent from model C. The absence of this mode in model C can be attributed to its less symmetrical architecture. Finally, as a further goal of the present study, an approximate open channel model, consistent with many experimental findings, has been produced. (c) 2005 Elsevier Ltd. All rights reserved.

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM. (c) 2005 American Institute of Physics.