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Abstract

Advances in mathematics and computer technology, together with advances in structural biology, are opening the way to detailed modeling of biology at the molecular and cellular levels. One objective of such studies is the development of a more complete understanding of biological systems, including the emergence of behavior at the cellular level from that at the molecular level. Another objective is the development of more sophisticated models for structure-aided discovery of new pharmaceuticals.

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References

  1. J. A. McCammon, B.R. Gelin, and M. Karplus. Dynamics of folded proteins. Nature, 267:585–590, 1977.

    Article  PubMed  CAS  Google Scholar 

  2. C.W. Gear. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs, New Jersey, 1971.

    Google Scholar 

  3. D.L. Ermak and J.A. McCammon. Brownian dynamics with hydrodynamic interactions. J. Chem. Phys., 69:1352–1360, 1978.

    Article  CAS  Google Scholar 

  4. F.B. Sheinerman, R. Norel, and B. Honig. Electrostatic aspects of protein-protein interactions. Curr. Opin. Struc. Biol., 10:153–159, 2000.

    Article  CAS  Google Scholar 

  5. M.E. Davis and McCammon J.A. Solving the finite difference linearized poisson-boltzmann equation: A comparison of relaxation and conjugate gradient methods. J. Comp. Chem., 10:386–391, 1989.

    Article  CAS  Google Scholar 

  6. E.R. Kandel, J.H. Schwartz, and T.M. Jessell. Principles of neural science. Appleton & Lange, Norwalk, Connecticut, 1991.

    Google Scholar 

  7. Stanislaw T. Wlodek, Terry W. Clark, L. Ridgway Scott, and J. Andrew McCammon. Molecular dynamics of acetylcholinesterase dimer complexed with tacrine. J. Am. Chem. Soc, 119:9513–9522, 1997.

    Article  CAS  Google Scholar 

  8. Huan-Xiang Zhou, Stanislaw T. Wlodek, and J. Andrew McCammon. Conformation gating as a mechanism for enzyme specificity. Proc. Natl. Acad. Sci. USA, 95:9280–9283, 1998.

    Article  PubMed  CAS  Google Scholar 

  9. M. K. Gilson, T. P. Straatsma, J. A. McCammon, D. R. Ripoll, C. H. Faerman, P. H. Axelsen, I. Silman, and J. L. Sussman. Open “back door” in a molecular dynamics simulation of acetylcholinesterase. Science, 263:1276–1278, 1994.

    Article  PubMed  CAS  Google Scholar 

  10. Sylvia Tara, T. P. Straatsma, and J. Andrew McCammon. Mouse acetyl-cholinesterase unliganded and in complex with huperzine A: a comparison of molecular dynamics simulations. Biopolymers, 50:35–43, 1999.

    Article  PubMed  CAS  Google Scholar 

  11. Kaihsu Tai, Tongye Shen, Ulf Börjesson, Marios Philippopoulos and J. Andrew McCammon. Analysis of a 10-ns molecular dynamics simulation of mouse acetylcholinesterase. Biophys. J., 81:715–724, 2001.

    Article  PubMed  CAS  Google Scholar 

  12. Wendy D. Cornell, Piotr Cieplak, Christopher I. Bayly, Ian R. Gould, Kenneth M. Merz Jr., David M. Ferguson, David C. Spellmeyer, Thomas Fox, James W. Caldwell, and Peter A. Kollman. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc, 117:5179–5197, 1995.

    Article  CAS  Google Scholar 

  13. T. P. Straatsma, M. Philippopoulos, and J. A. McCammon. NWChem: Exploiting parallelism in molecular simulation. Comp. Phys. Commun., 128:377–385, 2000.

    Article  CAS  Google Scholar 

  14. J.A. McCammon and S.C. Harvey. Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge, 1987.

    Book  Google Scholar 

  15. Charles L. Brooks, III, Martin Karplus, and B. Montgomery Pettitt. Proteins: a theoretical perspective of dynamics, structure, and thermodynamics, volume LXXI of Wiley Series on Advances in Chemical Physics. Wiley-Interscience, New York, 1988.

    Google Scholar 

  16. M. Karplus and J.A. McCammon. The internal dynamics of globular proteins. CRC Crit. Revs. Biochem., 9:293–349, 1981.

    Article  CAS  Google Scholar 

  17. Y. Bourne, P. Taylor, and P. Marchot. Acetylcholinesterase inhibition by fasciculin: crystal structure of the complex. Cell, 83:503-512, 1995.

    Article  PubMed  CAS  Google Scholar 

  18. Angel E. Garcia. Large-amplitude nonlinear motions in proteins. Phys. Rev. Lett, 68:2696–2699, 1992.

    Article  PubMed  Google Scholar 

  19. T. Y. Shen, Kaihsu Tai, and J. Andrew McCammon. Statistical analysis of the fractal gating motions of the enzyme acetylcholinesterase. Phys. Rev. E, 63:041902, 2001.

    Google Scholar 

  20. D. M. Quirin. Acetylcholinesterase: Enzyme structure, reaction dynamics, and virtual transition states. Chem. Rev., 87:955-979, 1987.

    Article  Google Scholar 

  21. P. Nambi, A. Wierzbicki, and S.A. Allison. Intermolecular interaction between bovine pancreatic trypsin inhibitor moecules probed by brownian dynamics simulation. J. Phys. Chem., 95:9595–9600, 1991.

    Article  CAS  Google Scholar 

  22. S.H. Northrup, K.A. Thomasson, CM. Miller, P.D. Barker, L.D. Eltis, J.G. Guillemette, S.C. Inglis, and A.G. Mauk. Effects of charged amino acid mutations on the biomolecular kinetics of reduction of yeast iso-l-ferricytochrome c by bovine ferrocytochrome b5. Biochem., 32:6613–6623, 1993.

    Article  CAS  Google Scholar 

  23. R.E. Kozack, M.J. d’Mello, and S. Subramanium. Computer modeling of electrostatic steering and orientational effects in antibody-antigen association. Biophys. J., 68:807–814, 1995.

    Article  PubMed  CAS  Google Scholar 

  24. R.R. Gabdoulline and R.C. Wade. Simulation of the diffusional association of barnase and barstar. Biophys. J., 72:1917–1929, 1997.

    Article  PubMed  CAS  Google Scholar 

  25. A.H. Elcock, R.R. Gabdoulline, R.C. Wade, and J.A. McCammon. Computer simulation of protein-protein association kinetics: Acetylcholinesterase-Fasciculin. J. Mol. Biol, 291:149–162, 1999.

    Article  PubMed  Google Scholar 

  26. D. Sept, A. H. Elcock, and J. A. McCammon. Computer simulations of actin polymerization can explain the barbed-pointed end assymetry. J. Mol. Biol., 294:1181–1189, 1999.

    Article  PubMed  CAS  Google Scholar 

  27. A. H. Elcock, D. Sept, and J. A. McCammon. Computer simulation of protein-protein interactions. J. Phys. Chem., in press.

    Google Scholar 

  28. D. L. Ermak and J. A. McCammon. Brownian dynamics with hydrodynamic interactions. J. Chem. Phys., 69:1352–1360, 1978.

    Article  Google Scholar 

  29. S.H. Northrup, S.A. Allison, and J.A. McCammon. Brownian dynamics simulations of diffusion-influenced biomolecular reactions. J. Chem. Phys., 80:1517–1524, 1984.

    Article  CAS  Google Scholar 

  30. R.R. Gabdoulline and R.C. Wade. Effective charges for macromolecules in solvent. J. Phys. Chem., 100:3868–3878, 1996.

    Article  CAS  Google Scholar 

  31. K.C. Holmes, D. Popp, W. Gebhard, and W. Kabsch. Atomic model of the actin filament. Nature, 347:44–49, 1990.

    Article  PubMed  CAS  Google Scholar 

  32. M. E. Davis and J. A. McCammon. Electrostatics in biomolecular structure and dynamics. Chem. Rev., 94:7684–7692, 1990.

    Google Scholar 

  33. B. Honig and A. Nicholls. Classical electrostatics in biology and chemistry. Science, 268:1144–1149, 1995.

    Article  PubMed  CAS  Google Scholar 

  34. M. J. Holst, N. A. Baker, and F. Wang. Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I: algorithms and examples. J. Comput. Chem., 21:1319–1342, 2000.

    Article  CAS  Google Scholar 

  35. N. A. Baker, M. J. Hoist, and Wang. F. Adaptive multilevel finite element solution of the Poisson-Boltzmann equation II: refinement at solvent accessible surfaces in biomolecular systems. J. Comput. Chem., 21:1343–1352, 2000.

    Article  CAS  Google Scholar 

  36. N. A. Baker, D. Sept, M. J. Holst, and J. A. McCammon. The adaptive multilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers. IBM J. Research Develop., in press.

    Google Scholar 

  37. Michael J. Holst. Adaptive multilevel finite element methods on manifolds and their implementation in MC (In preparation; currently available as a UCSD Dept. of Mathematics technical report and user’s guide to the MC software).

    Google Scholar 

  38. . K. A. Sharp and B. Honig. Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation. J. Phys. Chem., 94:7684–7692, 1990.

    Article  CAS  Google Scholar 

  39. B. Lee and F. M. Richards. The interpretation of protein structures: estimation of static accessibility. J. Mol. Biol, 55:379–400, 1971.

    Article  PubMed  CAS  Google Scholar 

  40. O. Axelsson and V. A. Barker. Finite element solution of boundary value problems. Theory and computation. Academic Press, San Diego, CA, 1984.

    Google Scholar 

  41. D. Braess. Finite elements. Theory, fast solvers, and applications in solid mechanics. Cambridge Univ. Press, New York, 1997.

    Google Scholar 

  42. M. Hoist and F. Saied. Numerical solution of the nonlinear Possion-Boltzmann equation: developing more robust and efficient methods. J. Comput. Chem., 16:337–364, 1995.

    Article  CAS  Google Scholar 

  43. R. E. Bank and R. K. Smith. Parameter selection for Newton-like methods applicable to nonlinear partial differential equations. SIAM J. Numer. Anal, 17:806–822, 1980.

    Article  Google Scholar 

  44. R. E. Bank and R. K. Smith. Global approximate Newton methods. Numer. Math., 37:279–295, 1981.

    Article  Google Scholar 

  45. R. E. Bank and R. K. Smith. Analysis of a multilevel iterative method for nonlinear finite element equations. Math. Comp., 39:453–465, 1982.

    Article  Google Scholar 

  46. R. S Dembo, S. C. Eisenstat, and T. Steihaug. Inexact Newton methods. SIAM J. Numer. Anal, 19:400–408, 1982.

    Article  Google Scholar 

  47. M. Holst and D. Bernstein. Adaptive finite element solution of the initial-value problem in general relativity: Theory and algorithms. Comm. Math. Phys., submitted.

    Google Scholar 

  48. I. Babuška and W. C. Rheinboldt. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal, 15:736–754, 1978.

    Article  Google Scholar 

  49. I. Babuška and W. C. Rheinboldt. A posteriori error estimates for the finite element method. Int. J. Numer. Meth. Engrg., 12:1597–1615, 1978.

    Article  Google Scholar 

  50. R. Verfürth. A posteriori error estimates for nonlinear problems. Finite element discretization of elliptic equations. Math. Comp., 62:445–475, 1994.

    Article  Google Scholar 

  51. R. Verfürth. A review of a posteriori error estimation and adaptive mesh-refinement techniques. John Wiley, New York, 1996.

    Google Scholar 

  52. R. E. Bank and J. Xu. The hierarchical basis multigrid method and incomplete LU decomposition. In D. Keyes and J. Xu, editors, Seventh international symposium on domain decomposition methods for partial differential equations, pages 163–173. AMS, 1994.

    Google Scholar 

  53. A. Brandt. Algebraic multigrid theory: the symmetric case. Appl. Math. Comp., 19:23–56, 1986.

    Article  Google Scholar 

  54. A. Brandt, S. McCormick, and J. Ruge. Algebraic multigrid (AMG) for sparse matrix equations. In D. J. Evans, editor, Sparsity and its applications. Cambridge Univ. Press, 1984.

    Google Scholar 

  55. M. Holst and F. Saied. Multigrid solution of the Poisson-Boltzmann equation. J. Comput. Chem., 14:105–113, 1993.

    Article  Google Scholar 

  56. J. W. Ruge and K. Stuben. Algebraic multigrid (AMG). In S. F. McCormick, editor, Multigrid methods, volume 3 of Frontiers in applied mathematics, pages 73–130. SIAM, Philadelphia, 1987.

    Google Scholar 

  57. W. Hackbusch. Multi-grid methods and applications. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  58. J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Review, 34:581–613, 1992.

    Article  Google Scholar 

  59. R. E. Bank, T. F. Dupont, and H. Yserentant. The hierarchical basis multigrid method. Numer. Math., 52:427–458, 1988.

    Article  Google Scholar 

  60. M. Holst and S. Vandewalle. Schwarz methods: to symmetrize or not to symmetrize. SIAM J. Numer. Anal, 34:699–722, 1997.

    Article  Google Scholar 

  61. R. Bank and M. Holst. A new paradigm for parallel adaptive meshing algorithms. SIAM J. Sci. Comput., in press.

    Google Scholar 

  62. Jinchao Xu and Aihui Zhou. Local and parallel finite element algorithms based on two-grid discretizations. Math. Comp., 69:881–909, 2000.

    Article  Google Scholar 

  63. P. Dustin. Microtubules. Springer-Verlag, Berlin, 1984.

    Book  Google Scholar 

  64. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson. Molecular biology of the cell. Garland Publishing, New York, 1994.

    Google Scholar 

  65. E. Nogales, M. Whittaker, R. A. Milligan, and K. H. Downing. High-resolution model of the microtubule. Cell, 96:79–88, 1999.

    Article  PubMed  CAS  Google Scholar 

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Baker, N.A. et al. (2002). Mathematics and Molecular Neurobiology. In: Schlick, T., Gan, H.H. (eds) Computational Methods for Macromolecules: Challenges and Applications. Lecture Notes in Computational Science and Engineering, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56080-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-56080-4_2

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