Solving the finite-difference, nonlinear, Poisson–Boltzmann equation under a linear approach

✍ Scribed by Xiang Zhexin; Shi Yunyu; Xu Yinwu

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 499 KB
• Volume: 16
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/jcc.540160207

✦ Synopsis

Electrostatic interactions are among the key factors in determining the structure and function of biomolecules. Simulating such interactions involves solving the Poisson equation and the Poisson-Boltzmann (P-B) equation in the molecular interior and exterior region, respectively. The P-B equation is a nonlinear partial differential equation. The central processing unit (CPU) time for solving the full nonlinear P-B equation has been severalfold greater than the equivalent linear case. Here a simple method is proposed to solve the full nonlinear P-B equation under a linear approach, which has been tested both on a spherical case and on small molecules. Results show that our method converges rapidly even under highly charged cases. With this method, the CPU time for solving the full nonlinear P-B equation is somewhat less than the equivalent linear case in our calculations. 0 1995 by John Wiley & Sons, Inc.

exterior region, respectively. The finite-difference method provides a fast and accurate approach to solving such equations iterati~ely.~-~ Because the P-B equation is a nonlinear partial differential equation, most applications of the finite-difference method have been restricted to solving its linear form. ~i ~~~~i ~i ~ the p-g equation is equivalent to assuming that the molecule is relatively weakly charged and/or the mobile salt concentration is high." These assumptions are not valid for some *Author to whom all correspondence should be addressed.