×

zbMATH — the first resource for mathematics

“New-version-fast-multipole-method” accelerated electrostatic calculations in biomolecular systems. (English) Zbl 1121.92007
Summary: We present an efficient and accurate numerical algorithm for calculating the electrostatic interactions in biomolecular systems. In our scheme, a boundary integral equation (BIE) approach is applied to discretize the linearized Poisson-Boltzmann (PB) equation. The resulting integral formulas are well conditioned for single molecule cases as well as for systems with more than one macromolecule, and are solved efficiently using Krylov subspace based iterative methods such as generalized minimal residual (GMRES) or biconjugate gradient stabilized (BiCGStab) methods. In each iteration, the convolution type matrix-vector multiplications are accelerated by a new version of the fast multipole method (FMM).
The implemented algorithm is asymptotically optimal \(O(N)\) both in CPU time and memory usage with optimized prefactors. Our approach enhances the present computational ability to treat electrostatics of large scale systems in protein-protein interactions and nano particle assembly processes. Applications including calculating the electrostatics of the nicotinic acetylcholine receptor (nAChR) and interactions between protein Sso7d and DNA are presented.

MSC:
92C05 Biophysics
65R20 Numerical methods for integral equations
92C40 Biochemistry, molecular biology
Software:
FFTSVD; PIM; APBS
PDF BibTeX Cite
Full Text: DOI
References:
[1] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1965), Dover Publications New York · Zbl 0515.33001
[2] Altman, M.; Bardhan, J.; White, J.; Tidor, B., An accurate surface formulation for biomolecule electrostatics in non-ionic solutions, Conf. proc. IEEE eng. med. biol. soc., 7, NIL, 7591-7595, (2005)
[3] Altman, M.D.; Bardhan, J.P.; Tidor, B.; White, J.K., FFTSVD: a fast multiscale boundary-element method solver suitable for bio-MEMS and biomolecule simulation, IEEE trans. comput.-aided des. integr. circuits syst., 25, 2, 274-284, (2006)
[4] Appel, A.W., An efficient program for many-body simulations, SIAM J. sci. stat. comput., 6, 85-103, (1985)
[5] Baker, N.A.; Sept, D.; Joseph, S.; Holst, M.J.; McCammon, J.A., Electrostatics of nanosystems: application to microtubules and the ribosome, Proc. natl. acad. sci. USA, 98, 18, 10037-10041, (2001)
[6] Barnes, J.; Hut, P., A hierarchical O(nlogn) force-calculation algorithm, Nature, 324, 4, 446-449, (1986)
[7] Bharadwaj, R.; Windemuth, A.; Sridharan, S.; Honig, B.; Nicholls, A., The fast multipole boundary-element method for molecular electrostatics – an optimal approach for large systems, J. comput. chem., 16, 7, 898-913, (1995)
[8] Bordner, A.J.; Huber, G.A., Boundary element solution of the linear poisson – boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution, J. comput. chem., 24, 3, 353-367, (2003)
[9] Boschitsch, A.H.; Fenley, M.O.; Olson, W.K., A fast adaptive multipole algorithm for calculating screened Coulomb (Yukawa) interactions, J. comput. phys., 151, 1, 212-241, (1999) · Zbl 1017.92500
[10] Boschitsch, A.H.; Fenley, M.O.; Zhou, H.X., Fast boundary element method for the linear poisson – boltzmann equation, J. phys. chem. B, 106, 10, 2741-2754, (2002)
[11] Capener, C.E.; Kim, H.J.; Arinaminpathy, Y.; Sansom, M.S.P., Ion channels: structural bioinformatics and modelling, Hum. mol. genet., 11, 20, 2425-2433, (2002)
[12] Cornell, W.D.; Cieplak, P.; Bayly, C.I.; Gould, I.R.; Merz, K.M.; Ferguson, D.M.; Spellmeyer, D.C.; Fox, T.; Caldwell, J.W.; Kollman, P.A., A 2nd generation force-field for the simulation of proteins, nucleic-acids, and organic-molecules, J. am. chem. soc., 117, 19, 5179-5197, (1995)
[13] Cortis, C.M.; Friesner, R.A., An automatic three-dimensional finite element mesh generation system for the poisson – boltzmann equation, J. comput. chem., 18, 13, 1570-1590, (1997)
[14] Dacunha, R.D.; Hopkins, T., The parallel iterative methods (PIM) package for the solution of systems of linear equations on parallel computers, Appl. numer. math., 19, 1-2, 33-50, (1995) · Zbl 0854.65028
[15] Darden, T.; York, D.; Pedersen, L., Particle mesh ewald: an \(n \log(n)\) method for ewald sums in large systems, J. chem. phys., 98, 12, 10089-10092, (1993)
[16] Davis, M.E.; McCammon, J.A., Electrostatics in biomolecular structure and dynamics, Chem. rev., 90, 3, 509-521, (1990)
[17] Debye, P.; Huckel, E., Zur theorie der elektrolyte, Phys. zeitschr., 24, 185-206, (1923) · JFM 49.0587.11
[18] Figueirido, F.; Levy, R.M.; Zhou, R.H.; Berne, B.J., Large scale simulation of macromolecules in solution: combining the periodic fast multipole method with multiple time step integrators, J. chem. phys., 106, 23, 9835-9849, (1997)
[19] Gilson, M.K.; Rashin, A.; Fine, R.; Honig, B., On the calculation of electrostatic interactions in proteins, J. mol. biol., 184, 3, 503-516, (1985)
[20] Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, J. comput. phys., 73, 2, 325-348, (1987) · Zbl 0629.65005
[21] Greengard, L.; Rokhlin, V., A new version of the fast multipole method for the Laplace equation in three dimensions, Acta numer., 6, 229-269, (1997) · Zbl 0889.65115
[22] Greengard, L.F.; Huang, J.F., A new version of the fast multipole method for screened Coulomb interactions in three dimensions, J. comput. phys., 180, 2, 642-658, (2002) · Zbl 1143.78372
[23] Holst, M.; Baker, N.; Wang, F., Adaptive multilevel finite element solution of the poisson – boltzmann equation i. algorithms and examples, J. comput. chem., 21, 15, 1319-1342, (2000)
[24] Juffer, A.H.; Botta, E.F.F.; Vankeulen, B.A.M.; Vanderploeg, A.; Berendsen, H.J.C., The electric-potential of a macromolecule in a solvent – a fundamental approach, J. comput. phys., 97, 1, 144-171, (1991) · Zbl 0743.65094
[25] Kapur, S.; Long, D.E., IES3: efficient electrostatic and electromagnetic simulation, IEEE comput. sci. eng., 5, 4, 60-67, (1998)
[26] Kirkwood, J.G., On the theory of strong electrolyte solutions, J. chem. phys., 2, 767-781, (1934) · Zbl 0010.14001
[27] Klapper, I.; Hagstrom, R.; Fine, R.; Sharp, K.; Honig, B., Focusing of electric fields in the active site of cu – zn superoxide dismutase: effects of ionic strength and amino-acid modification, Proteins, 1, 1, 47-59, (1986)
[28] Kuo, S.S.; Altman, M.D.; Bardhan, J.P.; Tidor, B.; White, J.K., Fast methods for simulation of biomolecule electrostatics, ()
[29] Liang, J.; Subramaniam, S., Computation of molecular electrostatics with boundary element methods, Biophys. J., 73, 4, 1830-1841, (1997)
[30] Lu, B.Z.; Cheng, X.L.; Huang, J.F.; McCammon, J.A., Order N algorithm for computation of electrostatic interactions in biomolecular systems, Proc. natl. acad. sci. USA, 103, 51, 19314-19319, (2006)
[31] Lu, B.Z.; McCammon, J.A., Improved boundary element methods for poisson – boltzmann electrostatic potential and force calculations, J. chem. theory. comput., 3, 3, 1134-1142, (2007)
[32] Lu, B.Z.; Zhang, D.Q.; McCammon, J.A., Computation of electrostatic forces between solvated molecules determined by the poisson – boltzmann equation using a boundary element method, J. chem. phys., 122, 21, 214102, (2005)
[33] Ong, E.T.; Lee, K.H.; Lim, K.M., A fast algorithm for three-dimensional electrostatics analysis: fast Fourier transform on multipoles (FFTM), Int. J. numer. meth. eng., 61, 5, 633-656, (2004) · Zbl 1116.78340
[34] Ong, E.T.; Lim, K.M.; Lee, K.H.; Lee, H.P., A fast algorithm for three-dimensional potential fields calculation: fast Fourier transform on multipoles, J. comput. phys., 192, 1, 244-261, (2003) · Zbl 1117.78334
[35] Phillips, J.R.; White, J.K., A precorrected-FFT method for electrostatic analysis of complicated 3-D structures, IEEE trans. comput.-aided des. integr. circuit syst., 16, 10, 1059-1072, (1997)
[36] Richards, F.M., Areas, volumes, packing, and protein-structure, Annu. rev. biophys. bioeng., 6, 151-176, (1977)
[37] Robinson, H.; Gao, Y.G.; Mccrary, B.S.; Edmondson, S.P.; Shriver, J.W.; Wang, A.H.J., The hyperthermophile chromosomal protein sac7d sharply kinks DNA, Nature, 392, 6672, 202-205, (1998)
[38] Rokhlin, V., Solution of acoustic scattering problems by means of second kind integral equations, Wave motion, 5, 3, 257-272, (1983) · Zbl 0522.73022
[39] Sanner, M.F.; Olson, A.J.; Spehner, J.C., Reduced surface: an efficient way to compute molecular surfaces, Biopolymers, 38, 3, 305-320, (1996)
[40] Sharp, K.A.; Honig, B., Electrostatic interactions in macromolecules – theory and applications, Annu. rev. biophys. biophys. chem., 19, 301-332, (1990)
[41] Shi, W.; Liu, J.; Kakani, N.; Yu, T., A fast hierarchical algorithm for 3D capacitance extraction, ()
[42] Tanaka, M.; Sladek, V.; Sladek, J., Regularization techniques applied to boundary element method, AMSE appl. mech. rev., 47, 457-499, (1994) · Zbl 0795.73077
[43] Tausch, J.; White, J., A multiscale method for fast capacitance extraction, ()
[44] Totrov, M.; Abagyan, R., Rapid boundary element solvation electrostatics calculations in folding simulations: successful folding of a 23-residue peptide, Biopolymers, 60, 2, 124-133, (2001)
[45] Unwin, N., Refined structure of the nicotinic acetylcholine receptor at 4 angstrom resolution, J. mol. biol., 346, 4, 967-989, (2005)
[46] Warwicker, J.; Watson, H.C., Calculation of the electric-potential in the active-site cleft due to alpha-helix dipoles, J. mol. biol., 157, 4, 671-679, (1982)
[47] Xin, W.; Juffer, A.H., A boundary element formulation of protein electrostatics with explicit ions, J. comput. phys., 223, 416-435, (2007) · Zbl 1115.92007
[48] Zauhar, R.J.; Morgan, R.S., A new method for computing the macromolecular electric-potential, J. mol. biol., 186, 4, 815-820, (1985)
[49] Zauhar, R.J.; Varnek, A., A fast and space-efficient boundary element method for computing electrostatic and hydration effects in large molecules, J. comput. chem., 17, 7, 864-877, (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.