Skip to main content
SpringerLink
Log in

Nonbonded Computations

  • Chapter
  • First Online:
Book cover Molecular Modeling and Simulation: An Interdisciplinary Guide

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 21))

Abstract

Reducing the cost of the nonbonded energy and force computations is of primary importance in molecular mechanics and dynamics simulations of biomolecules. This is because the direct evaluation of these nonbonded interactions involving all atom pairs has the complexity of \(\mathcal{O}({N}^{2})\) where N is the number of atoms. Recall that the bonded terms are local and thus have a linear computational complexity; see homework assignment 8 for a related exercise.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    (For lysozyme): nonbonded cutoffs via group-based electrostatic switch and atom-based Lennard-Jones switch functions, switch buffer 10 to 12 Ã…, pairlist buffer 12 to 13 Ã…, and SHAKE used for all bonds involving hydrogens. (For DNA dodecamer and BPTI): nonbonded cutoffs with periodic boundary conditions (PBC) via atom-based electrostatic and Lennard-Jones switch functions, switch buffer 10 to 12 Ã…, pairlist buffer 12 to 13 Ã…, and SHAKE used for all bonds involving hydrogens.

  2. 2.

    Each step entails an energy and gradient evaluation performed in the CHARMM program. The timings were made on a single Intel Xeon/3GHz processor of a Dell Linux machine.

  3. 3.

    We assume 1 fs timesteps.

  4. 4.

    These two components are also termed ‘fast’ and ‘slow’ because the short-range terms are rapidly varying in time while the long-range terms change more slowly with time; see Chapter 22.

  5. 5.

    A series \(S ={ \sum \nolimits }_{n=1}^{\infty }{a}_{n}\) is conditionally convergent if the infinite sum ∑ n a n converges but ∑ n | a n | diverges. It is also known that the sum for a conditionally convergent series depends on the order of summation. For a n = ( − 1)n + 1 ∕ n, the ‘alternating harmonic series’ \(1 -\frac{1} {2} + \frac{1} {3} -\frac{1} {4} + \cdots \) converges, but the harmonic series \(1 + \frac{1} {2} + \frac{1} {3} + \frac{1} {4} + \cdots \) diverges, though a n → 0 as n → ∞. To see that the sum for finite n terms can be as large as we please for the harmonic series, note that terms can be grouped so that each subsum is larger than \(\frac{1} {2}\): \({\sum \nolimits }_{n=1}^{\infty }\frac{1} {n} =\) \(1 + \left (\frac{1} {2} + \frac{1} {3}\right ) + \left (\frac{1} {4} + \frac{1} {5} + \frac{1} {6} + \frac{1} {7}\right ) + (\mathrm{next\ 8\ terms}) + \cdots > 1 + \frac{1} {2} + \frac{1} {2} + \frac{1} {2} + \cdots \).

  6. 6.

    Simeon Denis Poisson (1781–1840) was a brilliant mathematician whose name frequently appears in text books. The Poisson equation (1812) in potential theory is a result of his discovery that Laplace’s equation for the gravitational force holds only at points where no mass is located (see also Box 10.2).

  7. 7.

    For two functions of time f(t) and g(t) and corresponding Fourier transforms F(f) and F(g), we define the convolution of the two original functions f and g, f ∗ g, as: f ∗ g = ∫ − ∞ ∞ f(τ) g(t − τ)dτ. It can be shown that F(f ∗ g) = F(f) F(g). That is, the Fourier transform of the convolution of two functions (f ∗ g) is just the product of the individual Fourier transforms of those functions.

  8. 8.

    Physicists often refer to this equation as Gauss’ law while mathematicians tend to favor the term Poisson’s equation.

  9. 9.

    We can also write \(\frac{1} {{r}^{2}} \frac{d} {dr}\,\left ({r}^{2} \frac{d} {dr}\right )\Phi (r) = {\kappa }^{2}\,\Phi (r)\).

References

  1. B. Al-Lazikani, J. Jung, Z. Xiang, and B. Honig. Protein structure prediction. Curr.Opin. Struct. Biol., 5:51–56, 2001.

    Article  Google Scholar 

  2. C. R. Anderson. An implementation of the fast multipole algorithm without multipoles. SIAM J. Sci. Stat. Comput., 13:923–947, 1992.

    Article  MATH  Google Scholar 

  3. A. W. Appel. An efficient program for many body simulation. SIAM J. Sci. Stat. omput., 6:85–103, 1985.

    Article  MathSciNet  Google Scholar 

  4. P. Auffinger and E. Westhof. Molecular dynamics simulations of nucleic acids. In P. von Ragué Schleyer (Editor-in Chief), N. L. Allinger, T. Clark, J. Gasteiger, P. A. ollman, and H. F. Schaefer, III, editors, Encyclopedia of Computational Chem- istry, volume 3, pages 1628–1639. John Wiley & Sons, West Sussex, England, 1998.

    Google Scholar 

  5. N. Baker, M. Holst, and E. Wang. 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.

    Google Scholar 

  6. N. Baker, D. Sept, S. Joseph, M. J. Holst, and J. A. McCammon. Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc. Natl. Acad. Sci. SA, 98:10037–10041, 2001.

    Article  Google Scholar 

  7. D. Barash, X. Qian, L. Yang, and T. Schlick. Inherent speedup limitations in multiple-timestep/particle-mesh-Ewald algorithms. J. Comput. Chem., 24:77–88, 2003.

    Article  Google Scholar 

  8. J. Barnes and P. Hut. A hierarchical O(N logN) force-calculation algorithm. ature, 324:446–449, 1986.

    Google Scholar 

  9. D. Bashford and D. A. Case. Generalized Born models of macromolecular solvation effects. Ann. Rev. Phys. Chem., 51:129–152, 2000.

    Article  Google Scholar 

  10. P. Batcho, D. A. Case, and T. Schlick. Optimized particle-mesh Ewald / multiple-timestep integration for molecular dynamics simulations. J. Chem. Phys., 115:4003–4018, 2001.

    Article  Google Scholar 

  11. P. Batcho and T. Schlick. New splitting formulations for lattice summations. . Chem. Phys., 115:8312–8326, 2001.

    Google Scholar 

  12. D. Beard and T. Schlick. Inertial stochastic dynamics: I. long-timestep methods for langevin dynamics. J. Chem. Phys., 112:7313–7322, 2000.

    Google Scholar 

  13. D. Beard and T. Schlick. Inertial stochastic dynamics: II. influence of inertia on slow kinetic properties of supercoiled DNA. J. Chem. Phys., 112:7323–7338, 2000.

    Google Scholar 

  14. D. Beard and T. Schlick. Computational modeling predicts the structure and dynamics of the chromatin fiber. Structure, 9:105–114, 2001.

    Article  Google Scholar 

  15. D. Beard and T. Schlick. Modeling salt-mediated electrostatics of macromolecules: The algorithm DiSCO (Discrete Charge Surface Charge Optimization) and its application to the nucleosome. Biopolymers, 58:106–115, 2001.

    Article  Google Scholar 

  16. R. S. Berry, S. A. Rice, and J. Ross. Physical Chemistry. Wiley, New York, NY, 1980.

    Google Scholar 

  17. J. Board, A. John, Z. S. Hakura, W. D. Elliott, and W. T. Rankin. Scalable vari- ants of multipole-accelerated algorithms for molecular dynamics applications. n Proceedings, Seventh SIAM Conference on Parallel Processing for Scientific Computing, pages 295–300, Philadelphia, PA, 1995. SIAM.

    Google Scholar 

  18. J. Board, A. John, C. W. Humphres, C. G. Lambert, W. T. Rankin, and A. Y. oukmaji. Ewald and multipole methods for periodic N-body problems. In Proceedings, Eighth SIAM Conference on Parallel Processing for Scientific Computing, Philadelphia, PA, 1997. SIAM. CD-ROM.

    Google Scholar 

  19. J. A. Board, Jr., J. W. Causey, T. F. Leathrum, Jr., A.Windemuth, and K. Schulten. ccelerated molecular dynamics simulations with the parallel fast multiple algorithm. Chem. Phys. Lett., 198:89–94, 1992.

    Article  Google Scholar 

  20. S. Boresch, S. Ringhofer, P. H¨ochtl, and O. Steinhauser. Towards a better de- scription and understanding of biomolecular solvation. Biophys. Chem., 78:43–68, 1999.

    Google Scholar 

  21. A. H. Boschitsch, M. O. Fenley, and W. K. Olson. A fast adaptive multipole algo- rithm for calculating screened Coulomb (Yukawa) interactions. J. Comput. Phys., 151:212–241, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Brandt and A. A. Lubrecht. Multilevel matrix multiplication and fast solution of integral equations. J. Comput. Phys., 90:348–370, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  23. A. Br¨unger, C. L. Brooks, III, and M. Karplus. Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Lett., 105:495–500, 1982.

    Google Scholar 

  24. F. Bueche. The viscoelastic properties of plastics. J. Chem. Phys., 22:603–609, 1954.

    Article  Google Scholar 

  25. J. Chen and C. L. Brooks, III. Implicit modeling of nonpolar solvation for simu- lating protein folding and conformational transitions. Phys. Chem. Chem. Phys., 10:471–481, 2008.

    Article  Google Scholar 

  26. G. Chirico and J. Langowski. Brownian dynamics simulations of supercoiled DNA with bent sequences. Biophys. J., 71:955–971, 1996.

    Article  Google Scholar 

  27. C. J. Cramer. Essentials of Computational Chemistry: Theories and Models. John Wiley & Sons Inc., Hoboken, NJ, second edition, 2004.

    Google Scholar 

  28. D. Crothers and D. Eisenberg. Physical Chemistry with Applications to the Life Sciences. Benjamin/Cummings, Menlo Park, CA, 1979.

    Google Scholar 

  29. T. Darden, L. Perera, L. Li, and L. Pedersen. New tricks for modelers from the crystallography toolkit: The particle mesh Ewald algorithm and its use in nucleic acid simulations. Structure, 7:R55–R60, 1999.

    Article  Google Scholar 

  30. T. Darden, D. York, and L. Pedersen. Particle mesh Ewald: An N ·log(N) method for Ewald sums in large systems. J. Chem. Phys., 98:10089–10092, 1993.

    Article  Google Scholar 

  31. O. Norberto de Souza and R. L. Ornstein. Effect of periodic box size on aqueous molecular dynamics simulation of a DNA dodecamer with particle-mesh Ewald method. Biophys. J., 72:2395–2397, 1997.

    Article  Google Scholar 

  32. S.W. DeLeeuw, J.W. Perram, and E. R. Smith. Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constant. Proc. Roy. oc. Lond. A, 373:27–56, 1980.

    Article  MathSciNet  Google Scholar 

  33. P. Derreumaux and T. Schlick. Long-time integration for peptides by the dynamics driver approach. Proteins: Struc. Func. Gen., 21:282–302, 1995.

    Article  Google Scholar 

  34. P. Derreumaux and T. Schlick. The loop opening/closing motion of the enzyme triosephosphate isomerase. Biophys. J., 74:72–81, January 1998.

    Article  Google Scholar 

  35. M. Deserno, C. Holm, and S. May. Fraction of condensed counterions around a charged rod: Comparison of Poisson-Boltzmann theory and computer simulations. acromolecules, 33:199–206, 2000.

    Google Scholar 

  36. H. Q. Ding, N. Karasawa, and W. A. Goddard, III. Atomic level simulations on a million particles: The cell multipole method for Coulomb and London nonbond interactions. J. Chem. Phys., 97:4309–4315, 1992.

    Article  Google Scholar 

  37. H. Q. Ding, N. Karasawa, and W. A. Goddard, III. The reduced cell multipole method for Coulomb interactions in periodic systems with million-atom unit cells. hem. Phys. Lett., 196:6–10, 1992.

    Google Scholar 

  38. R. O. Dror, D. H. Arlow, D. W. Borhani, M.. Jensen, S. Piana, and D. E. Shaw. dentification of two distinct inactive conformations of the 2-adrenergic receptor reconciles structural and biochemical observations. Proc. Natl. Acad. Sci. USA., 106:4689–4694, 2009.

    Google Scholar 

  39. Y. Duan, C. Wu, S. Chowdhury, M. C. Lee, G. Xiong, W. Zhang, R. Yang, P. Cieplak, R. Luo, T. Lee, J. Caldwell, J. Wang, and P. Kollman. A point-charge force field for molecular mechanics simulations of proteins based on condensed- phase quantum mechanical calculations. J. Comput. Chem., 24:1999–2012, 2003.

    Article  Google Scholar 

  40. Z.-H. Duan and R. Krasny. An Ewald summation based multipole method. . Chem. Phys., 113:3492–3495, 2000.

    Google Scholar 

  41. Y. Erlich, K. Chang, A. Gordon, R. Ronen, O. Navon, M. Rooks, and G. J. Hannon. NA Sudoku—harnessing high-throughput sequencing for multiplexed specimen analysis. Gen. Res., 19:1243–1253, 2009.

    Article  Google Scholar 

  42. R. R. Ernst, G. Bodenhausen, and A. Wokaum. Principles of Nuclear Magnetic Resonance in One and Two Dimensions, volume 14 of International Series of Monographs on Chemistry. Clarendon Press, Oxford, New York, NY, 1987.

    Google Scholar 

  43. H. R. Faber and B.W. Matthews. A mutant lysozyme displays five different crystal conformations. Nature, 348:263–265, 1990.

    Article  Google Scholar 

  44. A. S. Fauci, M. I. Johnston, C.W. Dieffenbach, D. R. Burton, S. M. Hammer, J. A. oxie, M. Martin, J. Overbaugh, D. I. Watkins, A. Mahmoud, and W. C. Greene. IV vaccine research: The way forward. Science, 321:530–532, 2008.

    Google Scholar 

  45. G. Felsenfeld and M. Groudine. Controlling the double helix. Nature, 421: 448–453, 2003.

    Article  Google Scholar 

  46. J. Fiaux, E. B. Bertelsen, A. L Horwich, and K.W¨uthrich. NMR analysis of a 900K GroEL–GroES complex. Nature, 418:207–211, 2002.

    Google Scholar 

  47. D. Filmore. Taming the beast. Mod. Drug Dis., 4:40–46, 2001.

    Google Scholar 

  48. D. Fincham. Optimisation of the Ewald sum for large systems. Mol. Sim., 13:1–9, 1994.

    Article  Google Scholar 

  49. J. Flori´an, M. F. Goodman, and A. Warshel. Computer simulation of the chemical catalysis of DNA polymerases: Discriminating between alternative nu- cleotide insertion mechanisms for T7 DNA polymerase. J. Amer. Chem. Soc., 125:8163–8177, 2003.

    Google Scholar 

  50. P. J. Flory. Statistical Mechanics of Chain Molecules. Oxford University Press, New York, NY, 1988. (Reprinted version of the 1969 text with an added excerpt from Flory’s Nobel address).

    Google Scholar 

  51. P. L. Freddolino, S. Park, B. Roux, and K. Schulten. Force field bias in protein folding simulations. Biophys. J., 96:3772–3780, 2009.

    Article  Google Scholar 

  52. P. L. Freddolino and K. Schulten. Common structural Transitions in explicit- solvent simulations of villin headpiece folding. Biophys. J., 97:2338–2347, 2009. n Press.

    Google Scholar 

  53. P. E. Gill and M. W. Leonard. Reduced-Hessian quasi-Newton methods for unconstrained optimization. SIAM J. Optim., 12:209–237, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  54. P. Grayson, E. Tajkhorshid, and K. Schulten. Mechanisms of selectivity in chan- nels and enzymes studied with interactive molecular dynamics. Biophys. J., 85:36, 2003.

    Article  Google Scholar 

  55. P. Green. Whole-genome disassembly. Proc. Natl. Acad. Sci. USA, 99:4143–4144, 2002.

    Article  Google Scholar 

  56. L. Greengard. The Rapid Evaluation of Potential Fields in Particle Systems. MIT Press, Cambridge, Massachusetts, 1988.

    Google Scholar 

  57. L. Greengard. Fast algorithms for classical physics. Science, 265:909–914, 1994.

    MathSciNet  MATH  Google Scholar 

  58. L. Greengard and V. Rokhlin. A fast algorithm for particle simulation. J. Comput. hys., 73:325–348, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  59. U. H. E. Hansmann. Parallel-tempering algorithm for conformational studies of biological molecules. Chem. Phys. Lett., 281:140–150, 1997.

    Article  Google Scholar 

  60. T. E. Haran and U. Mohanty. The unique structure of A-tracts and intrinsic DNA bending. Quart. Rev. Biophys., 42:41–81, 2009.

    Article  Google Scholar 

  61. S. Hayward and B. L. deGroot. Normal modes and essential dynamics. Methods Mol. Biol., 443:89–106, 2008.

    Google Scholar 

  62. T. Hermann and D. J. Patel. Stitching together RNA tertiary architectures. J. Mol. iol., 294:828–849, 1999.

    Google Scholar 

  63. P. Hobza and J. ˇSponer. Structure, energetics, and dynamics of the nucleic acid base pairs: Nonempirical Ab Initio calculations. Chem. Rev., 99:3247–3276, 1999.

    Google Scholar 

  64. A. Holmgren and C.-I. Br¨anden. Crystal structure of chaperone protein PapD reveals an immunoglobulin fold. Nature, 342:248–251, 1989.

    Google Scholar 

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

    Article  Google Scholar 

  66. N. V. Hud and J. Feigon. Localization of divalent metal ions in the minor groove of DNA A-tracts. J. Amer. Chem. Soc., 119:5756–5757, 1997.

    Article  Google Scholar 

  67. D. E. Humphreys, R. A. Friesner, and B. J. Berne. A multiple-time-step molecu- lar dynamics algorithm for macromolecules. J. Phys. Chem., 98(27):6885–6892, 1994.

    Article  Google Scholar 

  68. J. Chen W. Im and C. L. Brooks, III. Application of torsion angle molecular dynamics for efficient sampling of protein conformations. J. Comput. Chem., 26:1565–1578, 2005.

    Google Scholar 

  69. R. M. Jendrejack, M. D. Graham, and J. J. de Pablo. Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations. J. Chem. Phys., 113:2894–2900, 2000.

    Article  Google Scholar 

  70. M. Ø Jensen, E. Tajkhorshid, and K. Schulten. The mechanism of glycerol conduction in aquaglyceroporins. Structure, 9:1083–1093, 2001.

    Google Scholar 

  71. H. Jian, T. Schlick, and A. Vologodskii. Internal motion of supercoiled DNA: Brownian dynamics simulations of site juxtaposition. J. Mol. Biol., 284:287–296, 1998.

    Article  Google Scholar 

  72. N. Kim, J. Sup Shin, S. Elmetwaly, H. H. Gan, and T. Schlick. RAGPOOLS: RNA- As-Graph-Pools —A web server for assisting the design of structured RNA pools for in vitro selection. Bioinfor., 10, 2007. doi: 10.1093/bioinformatics/btm439.

    Google Scholar 

  73. M. Kruithof, F.-T. Chen, A. Routh, C. Logie, D. Rhodes, and J. van Noort. Single- molecule force microscopy reveals a highly compliant helical folding for the 30-nm chromatin fiber. Nat. Struc. Mol. Biol., 16:534–540, 2009.

    Article  Google Scholar 

  74. C. Laing and T. Schlick. Analysis of four-way junctions in RNA structures. J. Mol. iol., 390:547–559, 2009.

    Article  Google Scholar 

  75. J. P. Lewis, N. H. Pawley, and O. F. Sankey. Theoretical investigation of the cyclic peptide system cyclo[(D-Ala-Glu-D-Ala-Gln)m=1−4]. J. Phys. Chem. B, 101:10576–10583, 1997.

    Article  Google Scholar 

  76. A. Liwo, C. Czaplewski, S. Oldziej, and H. A. Scheraga. Computational tech- niques for efficient conformational sampling of proteins. Curr. Opin. Struct. Biol., 18:134–139, 2008.

    Article  Google Scholar 

  77. R. J. Loncharich, B. R. Brooks, and R. W. Pastor. Langevin dynamics of peptides: The frictional dependence of isomerization rates of N-acetylalanyl-N’- methylamide. Biopolymers, 32:523–535, 1992.

    Article  Google Scholar 

  78. R. Ludwig. Water: From clusters to the bulk. Angew. Chem. Int. Ed., 40:1808– 1827, 2001.

    Article  Google Scholar 

  79. K. Luger, A. W. M¨ader, R. K. Richmond, D. F. Sargent, and T. J. Richmond. rystal structure of the nucleosome core particle at 2.8 A resolution. Nature, 389:251–260, 1997.

    Google Scholar 

  80. L. M. Luheshi, D. C. Crowther, and C. M. Dobson. Protein misfolding and disease: From the test tube to the organism. Curr. Opin. Chem. Biol., 12:25–31, 2008.

    Article  Google Scholar 

  81. J. Maddox. Statistical mechanics by numbers. Nature, 334:561, 1989.

    Google Scholar 

  82. J. D. McGhee, J. M. Nickol, G. Felsenfeld, and D. C. Rau. Higher order structure of chromatin: Orientation of nucleosomes within the 30 nm chromatin solenoid is independent of species and spacer length. Cell, 33:831–841, 1983.

    Article  Google Scholar 

  83. E. L. Mehler and F. Guarnieri. A self-consistent, microenvironment modulated screened Coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins. Biophys. J., 77:3–22, 1999.

    Article  Google Scholar 

  84. N. Nevins, J.-H. Lii, and N. L. Allinger. Molecular mechanics (MM4) calculations on conjugated hydrocarbons. J. Comput. Chem., 17:695–729, 1996.

    Google Scholar 

  85. M. Nilges, P. Markwick, T. Malliavin, W. Rieping, and M. Habeck. New fron- tiers in characterizing structure and dynamics by NMR. In T. Schwede and M. Peitsch, editors, Computational Structural Biology. Methods and Applications, pages 655–679. World Scientific, Singapore, 2008.

    Google Scholar 

  86. F. Noé and S. Fischer. Transition networks for modeling the kinetics of con- formational change in macromolecules. Curr. Opin. Struct. Biol., 8:154–162, 2008.

    Google Scholar 

  87. R. G. Parr and W. Yang. Density-functional theory of the electronic structure of molecules. Ann. Rev. Phys. Chem., 46:701–728, 1995.

    Article  Google Scholar 

  88. A. Pérez, J. Luque, and M. Orozco. Dynamics of B-DNA on the microsecond time scale. J. Amer. Chem. Soc., 129:14739–14745, 2007.

    Google Scholar 

  89. S. L. Pomeroy, P. Tamayo, M. Gaasenbeek, L. M. Sturla, M. Angelo, M. E. cLaughlin, J. Y. H. Kim, L. C. Goumnerova, P. M. Black, C. Lau, J. C. Allen, D. Zagzag, J.M. Olson, T. Curran, C.Wetmore, J. A. Biegel, T. Poggio, S. Mukher- jee, R. Rifkin, A. Califano, G. Stolovitzky, D. N. Louis, J. P. Mesirov, E. S. Lander, and T. R. Golub. Prediction of central nervous system embryonal tumour outcome based on gene expression. Nature, 415:436–442, 2002.

    Google Scholar 

  90. V. Pophristic and L. Goodman. Hyperconjugation not steric repulsion leads to the staggered structure of ethane. Nature, 411:565–568, 2001.

    Article  Google Scholar 

  91. N. V. Prabhu, J. S. Perkyns, H. D. Blatt, P. E. Smith, and B. M. Pettitt. Comparison of the potentials of mean force for alanine tetrapeptide between integral equation theory and simulation. Biophys. Chem., 78:113–126, 1999.

    Article  Google Scholar 

  92. L. J. Prins, D. N. Reinhoudt, and P. Timmerman. Nonvalent synthesis using hydrogen bonding. Angew. Chem. Int. Ed., 40:2382–2426, 2001.

    Article  Google Scholar 

  93. D. Pruss, B. Bartholomew, J. Persinger, J. Hayes, G. Arents E. N. Moudrianakis, and A. P. Wolffe. An asymmetric model for the nucleosome: A binding site for linker histones inside the DNA gyres. Science, 274:614–617, 1996.

    Google Scholar 

  94. A. M. Pyle and J. B. Green. RNA folding. Curr. Opin. Struct. Biol., 5:303–310, 1995.

    Article  Google Scholar 

  95. R. Radhakrishnan and T. Schlick. Orchestration of cooperative events in DNA synthesis and repair mechanism unraveled by transition path sampling of DNA polymerase β’s closing. Proc. Natl. Acad. Sci. USA, 101:5970–5975, 2004.

    Article  Google Scholar 

  96. R. Radhakrishnan and T. Schlick. Fidelity discrimination in DNA polymerase β: differing closing profiles for a mismatched G:A versus matched G:C base pair. . Amer. Chem. Soc., 127:13245–13252, 2005.

    Google Scholar 

  97. J. S. Read and G. F. Joyce. A ribozyme composed of only two different nucleotides. ature, 420:841–844, 2002.

    Google Scholar 

  98. R. J. Read and D. E. Wemmer. Biophysical methods. Bigger, better, faster and automatically too? (Editorial overview). Curr. Opin. Struct. Biol., 9:591–593, 1999.

    Google Scholar 

  99. D. R. Ripoll, J. A. Vila, and H. A. Scheraga. Folding of the villin headpiece sub- domain from random structures. Analysis of the charge distribution as a function of the pH. J. Mol. Biol., 339:915–925, 2004.

    Google Scholar 

  100. K. Rippe, P. H. von Hippel, and J. Langowski. Action at a distance: DNA-looping and initiation of transcription. Trends Bio. Sci., 20(12):500–506, Dec. 1996.

    Google Scholar 

  101. J. B. Ristaino, C. T. Groves, and G. R. Parra. PCR amplification of the Irish potato famine pathogen from historic specimens. Nature, 411:695–697, 2001.

    Article  Google Scholar 

  102. T. Rodinger, P. Howell, and R. Poms. Distributed replica sampling. J. Chem. Ther. omp., 2:725–731, 2006.

    Article  Google Scholar 

  103. eferences [1067] S. M. Ross. A Course in Simulation. Macmillan Publishing Company, New York, NY, 1990.

    Google Scholar 

  104. I. K. Roterman, M. H. Lambert, K. D. Gibson, and H. A. Scheraga. A comparison of the CHARMM, AMBER and ECEPP potentials for peptides. I. Conformational predictions for the tandemly repeated peptide (Asn-Ala-Asn-Pro)9. J. Biomol. truct. Dyn., 7:391–419, 1989.

    Google Scholar 

  105. M. Rueda, E. Cubero, C. A. Laughton, and M. Orozco. Exploring the counte- rion atmosphere around DNA: What can be learned from molecular dynamics simulations? Biophys. J., 87:800–811, 2004.

    Article  Google Scholar 

  106. K. Sakamoto, H. Gouzu, K. Komiya, D. Kiga, S. Yokoyama, T. Yokomori, and M. Hagiya. Molecular computation by DNA hairpin formation. Science, 288:1223–1226, 2000.

    Article  Google Scholar 

  107. K. Salehi-Ashtiani, A. Luptk, A. Litovchick, and J.W. Szostak. A genomewide search for ribozymes reveals an HDV-like sequence in the human CPEB3 gene. cience, 313:1788–1792, 2006.

    Google Scholar 

  108. eferences [1101] T. Schlick. Modeling and Minimization Techniques for Predicting Three- Dimensional Structures of Large Biological Molecules. PhD thesis, New York University, Courant Institute of Mathematical Sciences, New York, NY, October 1987.

    Google Scholar 

  109. T. Schlick. From macroscopic to mesoscopic models of chromatin folding. In J. Fish, editor, Bridging The Scales in Science in Engineering, pages 514–535. xford University Press, New York, NY, 2009.

    Google Scholar 

  110. T. Schlick, S. Figueroa, andM.Mezei. A molecular dynamics simulation of a water droplet by the implicit-Euler/Langevin scheme. J. Chem. Phys., 94:2118–2129, 1991.

    Google Scholar 

  111. T. Schlick and W. K. Olson. Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA. Science, 257:1110–1115, 1992.

    Article  Google Scholar 

  112. T. Schlick, W. K. Olson, T. Westcott, and J. P. Greenberg. On higher buckling transitions in supercoiled DNA. Biopolymers, 34:565–598, 1994.

    Article  Google Scholar 

  113. eferences [1131] T. Schlick and G. Parks. DOE computational sciences education project, 1994. hapter on Mathematical Optimization. URL: csep1.phy.ornl.gov/.

    Google Scholar 

  114. B. Schneider, K. Patel, and H. M. Berman. Hydration of the phosphate group in double-helical DNA. Biophys. J., 75:2422–2434, 1998.

    Article  Google Scholar 

  115. E. C. Sherer, S. A. Harris, R. Soliva, M. Orozco, and C. A. Laughton. Molecular dynamics studies of DNA A-tract structure and flexibility. J. Amer. Chem. Soc., 121:5981–5991, 1999.

    Article  Google Scholar 

  116. H. Shi and P. Moore. The crystal structure of yeast phenylalanine tRNA at 1.93 A resolution: A classic structure revisited. RNA, 6:1091–1105, 2000.

    Google Scholar 

  117. P. E. M. Siegbahn, M. R. A. Blomberg, and M. L. Blomberg. Theoretical study of the energetics of proton pumping and oxygen reduction in cytochrome oxidase. . Phys. Chem. B, 107:10946–10955, 2003.

    Google Scholar 

  118. S. Singh, B. K. Malik, and D. K. Sharma. Molecular drug targets and structure based drug design: A holistic approach. Bioinformation, 1:314–320, 2006.

    Article  Google Scholar 

  119. U.C. Singh and P.A. Kollman. An approach to computing electrostatic charges for molecules. J. Comput. Chem., 5:129–145, 1984.

    Article  Google Scholar 

  120. eferences [1198] R. D. Skeel, I. Tezcan, and D. J. Hardy. Multiple grid methods for classical molecular dynamics. J. Comput. Chem., 23:673–684, 2002.

    Google Scholar 

  121. A. Srinivasan and W. K. Olson. Polynucleotide conformation in real solution — a preliminary theoretical estimate. Fed. Amer. Soc. Exp. Bio., 39:2199, 1980.

    Google Scholar 

  122. D. K. Stammers, D. O’N. Somers, C. K. Ross, I. Kirby, P. H. Ray, J. E. Wilson, M. Norman, J. S. Ren, R. M. Esnouf, E. F. Garman, E. Y. Jones, and D. I. Stuart. rystals of HIV-1 reverse transcriptase diffracting to 2.2 A resolution. J. Mol. Biol., 242:586–588, 1994.

    Google Scholar 

  123. R. Steinbrook. The AIDS epidemic - A progress report from Mexico City. N. Engl.. Med., 359:885–887, 2008.

    Google Scholar 

  124. E. Stofer, C. Chipot, and R. Lavery. Free energy calculations ofWatson-Crick base pairing in aqueous solution. J. Amer. Chem. Soc., 121:9503–9508, 1999.

    Article  Google Scholar 

  125. W. B. Streett, D. J. Tildesley, and G. Saville. Multiple time step methods and an improved potential function for molecular dynamics simulations of molecular liq- uids. In Peter Lykos, editor, Computer Modeling of Matter, volume 86 of ACS Symposium Series, pages 144–158. ACS, Washington, D. C., 1978.

    Google Scholar 

  126. F. Tama, M. Valle, J. Frank, and C. L. Brooks, III. Dynamic reorganization of the functionally active ribosome explored by normal mode analysis and cryo-electron microscopy. Proc. Natl. Acad. Sci. USA, 100:9319–9323, 2003.

    Article  Google Scholar 

  127. J. T. Thomas. The scientific and humane legacy of Max Perutz (1914 – 2002). ngew. Chem. Int. Ed., 41:3155–3166, 2002.

    Google Scholar 

  128. M. M. Tirion. Large amplitude elastic motions in proteins from a single-parameter, atomic analysis. Phy. Rev. Lett., 77:1905–1908, 1996.

    Article  Google Scholar 

  129. J. J. Toulme, C. Di Primo, and D. Boucard. Regulating eukaryotic gene expression with aptamers. FEBS Lett., 567:55–62, 2004.

    Article  Google Scholar 

  130. A. Valouev, J. Ichikawa, T. Tonthat, J. Stuart, S. Ranade, H. Peckham, K. Zeng, J. A. Malek, G. Costa, K. McKernan, A. Sidow, A. Fire, and S. M. Johnson. A high-resolution, nucleosome position map of C. elegans reveals a lack of universal sequence-dictated positioning. Gen. Res., 18, 2008.

    Google Scholar 

  131. eferences [1304] C. T. Vogelson. Advances in drug delivery systems. Mod. Drug Dis., 4:49–52, 2001.

    Google Scholar 

  132. A. V. Vologodskii and N. R. Cozzarelli. Modeling of long-range electrostatic interactions in DNA. Biopolymers, 35:289–296, 1995.

    Article  Google Scholar 

  133. J. Vrebalov, D. Ruezinsky, V. Padmanabhan, R. White, D. Medrano, R. Drake, W. Schuch, and J. Giovannoni. A MADS-box gene necessary for fruit ripening at the tomato ripening-inhibitor (Rin) locus. Science, 296:343–346, 2002.

    Article  Google Scholar 

  134. J. ˇSponer, J. Leszczy´nski, and P. Hobza. Nature of nucleic acid-base stacking: Nonempirical ab Initio and empirical potential characterization of 10 stacked base dimers. Comparison of stacked and H-bonded base pairs. J. Phys. Chem., 100:5590–5596, 1996.

    Google Scholar 

  135. S.Wallin and H. S. Chan. Conformational entropic barriers in topology-dependent protein folding: perspectives from a simple native-centric polymer model. J. Phy. onden. Matter, 18:S307–S328, 2006.

    Article  Google Scholar 

  136. A.Warshel. Computer Modeling of Chemical Reactions in Enzymes and Solutions. ohn Wiley & Sons, New York, NY, 1991.

    Google Scholar 

  137. D. Xie, A. Tropsha, and T. Schlick. A data projection approach using the sin- gular value decomposition and energy refinement. J. Chem. Inf. Comput. Sci., 40(1):167–177, 2000.

    Article  Google Scholar 

  138. L. Yang, W. A. Beard, S. H. Wilson, S. Broyde, and T. Schlick. Polymerase β simulations suggest that Arg258 rotation is a slow step rather than large subdomain motion per se. J. Mol. Biol., 317:651–671, 2002.

    Article  Google Scholar 

  139. D. M. York, T.-S. Lee, and W. Yang. Quantum-mechanical study of aque- ous polarization effects on biological macromolecules. J. Amer. Chem. Soc., 118:10940–10941, 1996.

    Article  Google Scholar 

  140. C. Zhang and C. DeLisi. Estimating the number of protein folds. J. Mol. Biol., 284:1301–1305, 1998.

    Article  Google Scholar 

  141. K. Zhu, M. R. Shirts, R. A. Friesner, and M. P. Jacobson. Multiscale Optimization of a Truncated Newton Minimization Algorithm and Application to Proteins and Protein-Ligand Complexes. J. Chem. Theory Comput, 3:640–648, 2007.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences and Department of Chemistry, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Prof. Tamar Schlick

Authors
  1. Prof. Tamar Schlick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tamar Schlick .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Schlick, T. (2010). Nonbonded Computations. In: Molecular Modeling and Simulation: An Interdisciplinary Guide. Interdisciplinary Applied Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6351-2_10

Download citation

Publish with us

Policies and ethics

Search

Navigation