Molecular Modeling of Nucleic Acid Structure: Electrostatics and Solvation

Christina Bergonzo1, Rodrigo Galindo‐Murillo1, Thomas E. Cheatham1

1 Department of Medicinal Chemistry, University of Utah, Salt Lake City, Utah
Publication Name:  Current Protocols in Nucleic Acid Chemistry
Unit Number:  Unit 7.9
DOI:  10.1002/0471142700.nc0709s55
Online Posting Date:  December, 2013
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This unit presents an overview of computer simulation techniques as applied to nucleic acid systems, ranging from simple in vacuo molecular modeling techniques to more complete all‐atom molecular dynamics treatments that include an explicit representation of the environment. The third in a series of four units, this unit focuses on critical issues in solvation and the treatment of electrostatics. UNITS 7.5 & 7.8 introduced the modeling of nucleic acid structure at the molecular level. This included a discussion of how to generate an initial model, how to evaluate the utility or reliability of a given model, and ultimately how to manipulate this model to better understand its structure, dynamics, and interactions. Subject to an appropriate representation of the energy, such as a specifically parameterized empirical force field, the techniques of minimization and Monte Carlo simulation, as well as molecular dynamics (MD) methods, were introduced as a way of sampling conformational space for a better understanding of the relevance of a given model. This discussion highlighted the major limitations with modeling in general. When sampling conformational space effectively, difficult issues are encountered, such as multiple minima or conformational sampling problems, and accurately representing the underlying energy of interaction. In order to provide a realistic model of the underlying energetics for nucleic acids in their native environments, it is crucial to include some representation of solvation (by water) and also to properly treat the electrostatic interactions. These subjects are discussed in detail in this unit. Curr. Protoc. Nucleic Acid Chem. 55:7.9.1‐7.9.27. © 2013 by John Wiley & Sons, Inc.

Keywords: nucleic acid chemistry; nucleic acid structure and folding; structural analysis of biomolecules; experimental determination of structure

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Table of Contents

  • Electrostatics and Solvation
  • In Vacuo Representations
  • Implicit Solvent Models
  • Simulations in Explicit Solvent
  • Summary
  • Acknowledgments
  • Literature Cited
  • Figures
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Literature Cited

  Aguilar, B., Shadrach, R., and Onufriev, A.V. 2010. Reducing the secondary structure bias in the generalized Born model via R6 effective radii. J. Chem. Theory Comput. 6:3613‐3630.
  Alden, C.J. and Kim, S.‐H. 1979. Solvent‐accessible surfaces of nucleic acids. J. Mol. Biol. 132:411‐434.
  Allen, M.P. and Tildesley, D.J. 1987. Computer Simulation of Liquids. Oxford University Press, Oxford.
  Allner, O., Nilsson, L., and Villa, A. 2012. Magnesium ion‐water coordination and exchange in biomolecular simulations. J. Chem. Theory Comput. 8:1493‐1502.
  Auffinger, P. and Beveridge, D.L. 1995. A simple test for evaluating the truncation effects in simulations of systems involving charged groups. Chem. Phys. Lett. 234:413‐415.
  Auffinger, P., Bielecki, L., and Westhof, E. 2003. The Mg2+ binding sites of the 5S rRNA loop E motif as investigated by molecular dynamics simulations. Chem. Biol. 10:551‐561.
  Auffinger, P., Cheatham, T.E. III, and Vaiana, A.C., 2007. Spontaneous formation of KCL aggregates in biomolecular simulations: A force field issue? J. Chem. Theory Comput. 3:1851‐1859.
  Aqvist, J. 1990. Ion‐water interaction potentials derived from free energy perturbation simulations. J. Phys. Chem. 94:8021‐8024.
  Bader, J.S. and Chandler, D. 1992. Computer simulation study of the mean forces between ferrous and ferric ions in water. J. Phys. Chem. 96:6423‐6427.
  Baker, N.A., Sept, D., Joseph, S., Holst, M.J., and McCammon, J.A. 2001. Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc. Natl. Acad. Sci. U.S.A. 98:10037‐10041.
  Bashford, D. and Case, D.A. 2000. Generalized Born models of macromolecular solvation effects. Annu. Rev. Phys. Chem. 51:129‐152.
  Bashford, D. and Karplus, M. 1990. pKa's of ionizable groups in proteins: Atomic detail from a continuum electrostatic model. Biochemistry 29:10219‐10225.
  Beck, D.A.C., Armen, R.S., and Daggett, V. 2005. Cutoff size need not strongly influence molecular dynamics results for solvated polypeptides. Biochemistry 44:609‐616.
  Beglov, D. and Roux, B. 1994. Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations. J. Chem. Phys. 100:9050‐9063.
  Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., DiNola, A., and Haak, J.R. 1984. Molecular dynamics with coupling to an external bath. J. Comp. Phys. 81:3684‐3690.
  Berendsen, H.J.C., Grigera, J.R., and Straatsma, T.P. 1987. The missing term in effective pair potentials. J. Phys. Chem. 91:6269‐6271.
  Berkowitz, M. and McCammon, J.A. 1982. Molecular dynamics with stochastic boundary conditions. Chem. Phys. Lett. 90:215‐217.
  Beveridge, D.L., Swaminathan, S., Ravishanker, G., Withka, J.M., Srinivasan, J., Prevost, C., Louise‐May, S., Langley, D.R., DiCapua, F.M., and Bolton, P.H. 1993. Molecular dynamics simulations on the hydration, structure and motions of DNA oligomers. In Water and Biological Molecules (E. Westhof, ed.) pp. 165‐225. Macmillan Press, New York.
  Beveridge, D.L., Cheatham, T.E. III, and Mezei, M. 2012. The ABCs of molecular dynamics simulations on B‐DNA, circa 2012. J. Biosci. 37:379‐397.
  Bewley, C.A., Gronenborn, A.M., and Clore, G.M. 2002. Minor groove‐binding architectural proteins: Structure, function, and DNA recognition. In Annual Reviews Collection. National Center for Biotechnology Information, Bethesda, Md.
  Biesiadecki, J.J. and Skeel, R.D. 1993. Dangers of multiple time step methods. J. Comp. Phys. 109:318‐328.
  Bogusz, S., Cheatham, T.E. III, and Brooks, B.R. 1998. Removal of pressure and free energy artifacts in charged periodic systems via net charge corrections to the Ewald potential. J. Chem. Phys. 108:7070‐7084.
  Boresch, S. and Steinhauser, O. 1997. Presumed versus real artifacts of the Ewald summation technique: The importance of dielectric boundary conditions. Ber. Bunsenges. Phys. Chem. 101:1019‐1029.
  Born, M. 1920. Volumen und Hydratationswärme der Ionen. Z. Phys. Chem. 1:45‐48.
  Bowman, J.C., Lenz, T.K., Hud, N.V., and Williams, L.D. 2012. Cations in charge: Magnesium ions in RNA folding and catalysis. Curr. Opin. Struct. Biol. 22:262‐272.
  Brooks, B.R., Brooks, C.L. III, Mackerell, A.D. Jr., Nilsson, L., Petrella, R.J., Roux, B., Won, Y., Archontis, G., Bartels, C., Boresch, S., Caflisch, A., Caves, L., Cui, Q., Dinner, A.R., Feig, M., Fischer, S., Gao, J., Hodoscek, M., Im, W., Kuczera, K., Lazaridis, T., Ma, J., Ovchinnikov, V., Paci, E., Pastor, R.W., Post, C.B., Pu, J.Z., Schaefer, M., Tidor, B., Venable, R.M., Woodcock, H.L., Wu, X., Yang, W., York, D.M., and Karplus, M. 2009 CHARMM: The biomolecular simulation program. J. Comp. Chem. 30:1545‐1614.
  Brooks, C.L. III and Karplus, M. 1983. Deformable stochastic boundaries in molecular dynamics. J. Chem. Phys. 79:6312‐6325.
  Brooks, C.L. III, Brünger, A., and Karplus, M. 1985. Active site dynamics in protein molecules: A stochastic boundary‐molecular dynamics approach. Biopolymers 24:843‐865.
  Brooks, C.L. III, Karplus, M., and Pettitt, B.M. 1988. Proteins: A theoretical perspective of dynamics, structure, and thermodynamics. In Advances in Chemical Physics, Vol. 71 (I. Prigogine and S.A. Rice, eds.). John Wiley & Sons, New York.
  Challacombe, M., White, C., and Head‐Gordon, M. 1997. Periodic boundary conditions and the fast multipole method. J. Chem. Phys. 107:10131‐10140.
  Cheatham, T.E. III and Kollman, P.A. 1998. Molecular dynamics simulation of nucleic acids in solution: How sensitive are the results to small perturbations in the force field environment? In Structure, Motion, Interactions and Expression of Biological Macromolecules (M. Sarma and R. Sarma, eds.) pp. 99‐116. Adenine Press, Schenectady, New York.
  Cheatham, T.E. III and Kollman, P.A. 2000. Molecular dynamics simulation of nucleic acids. Annu. Rev. Phys. Chem. 51:435‐471.
  Cheatham, T.E. III and Young, M.A. 2001. Molecular dynamics simulation of nucleic acids: Successes, limitations, and promise. Biopolymers 56:232‐256.
  Cheatham, T.E. III, Miller, J.L., Fox, T., Darden, T.A., and Kollman, P.A. 1995. Molecular dynamics simulations on solvated biomolecular systems: The particle mesh Ewald method leads to stable trajectories of DNA, RNA, and proteins. J. Am. Chem. Soc. 117:4193‐4194.
  Cheatham, T.E. III, Crowley, M.F., Fox, T., and Kollman, P.A. 1997. A molecular level picture of the stabilization of A‐DNA in mixed ethanol‐water solutions. Proc. Natl. Acad. Sci. U.S.A. 94:9626‐9630.
  Chen, A.A. and Pappu, R.V. 2007. Parameters of monovalent ions in the AMBER‐99 forcefield: Assessment of inaccuracies and proposed improvements. J. Phys. Chem. B. 111:11884‐11887.
  Cheng, Y.‐K. and Pettitt, B.M. 1992. Hoogsteen versus reversed-Hoogsteen base pairing: DNA triplex helices. J. Am. Chem. Soc. 114:4465‐4474.
  Cheng, Y.‐K. and Pettitt, B.M. 1995. Solvent effects on model d(CG.G)7 and d(TA.T)7 DNA triplex helices. Biopolymers 35:457‐473.
  Chocholoušová, J., and Feig, M. 2006. Implicit solvent simulations of DNA and DNA‐protein complexes: Agreement with explicit solvent vs experiment. J. Phys. Chem. B. 110:17240‐17251.
  Cramer, C.J. and Truhlar, D.G. 1995. Continuum solvation models: Classical and quantum mechanical implementations. In Reviews in Computational Chemistry, Vol. 6 (K.D. Lipkowitz and D.B. Boyd, eds.) pp. 1‐72. VCH Publishers, New York.
  Daggett, V., Kollman, P.A., and Kuntz, I.D. 1991. Molecular dynamics simulations of small peptides: Dependence on dielectric model and pH. Biopolymers 31:285‐304.
  Dang, L.X. and Pettitt, B.M. 1987. Chloride ion pairs in water. J. Am. Chem. Soc. 109:5531‐5532.
  Darden, T.A., York, D.M., and Pedersen, L.G. 1993. Particle mesh Ewald: An N • log(N) method for Ewald sums in large systems. J. Chem. Phys. 98:10089‐10092.
  Darden, T.A., Pedersen, L.G., Toukmaji, A.Y., Crowley, M.F., and Cheatham, T.E. III. 1997. Particle-mesh based methods for fast Ewald summation in molecular dynamics simulations. Proceedings of the Eighth SIAM conference on parallel processing for scientific computing, Minneapolis, Minn. Society for Industrial and Applied Mathematics, Philadelphia.
  Davis, M.E. and McCammon, J.A. 1990. Electrostatics in biomolecular structure and dynamics. Chem. Rev. 90:509‐521.
  DeLeeuw, S.W., Perram, J.M., and Smith, E.R. 1980. Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants. Proc. R. Soc. Lond. A 373:27‐56.
  de Pablo, J.J. 2011. Coarse‐grained simulations of macromolecules: From DNA to nanocomposites. Annu. Rev. Phys. Chem. 62:555‐574.
  de Souza, O.N. and Ornstein, R.L. 1997. Effect of periodic box size on aqueous molecular dynamics simulation of a DNA dodecamer with particle‐mesh Ewald method. Biophys. J. 72:2395‐2397.
  Dick, T.J. and Madura, J.D. 2005. A review of the TIP4P, TIP4P‐Ew, TIP5P, and TIP5P‐E water models. In Annual Reports in Computational Chemistry, Vol. 1 (D.C. Spellmeyer, ed.) pp. 59‐74. Elsevier, Amsterdam.
  Dill, K.A. 1990. Dominant forces in protein folding. Biochemistry 29:7133‐7155.
  Ding, H.‐Q., Karasawa, N., and Goddard, W.A. III. 1992. Atomic level simulations on a million particles: The cell multipole method for Coulomb and London nonbond interactions. J. Chem. Phys. 97:4309‐4315.
  Donchev, A.G., Ozrin, V.D., Subbotin, M.V., Tarasov, O.V., and Tarasov, V.I. 2005. A quantum mechanical polarizable force field for biomolecular interactions. Proc. Natl. Acad. Sci. U.S.A. 102:7829‐7834.
  Drew, H.R. and Dickerson, R.E. 1981. Structure of a B‐DNA dodecamer. III. Geometry of hydration. J. Mol. Biol. 151:535‐556.
  Eisenberg, D. and McLachlan, A.D. 1986. Solvation energy in protein folding and binding. Nature 319:199‐203.
  Essex, J.W. and Jorgensen, W.L. 1995. An empirical boundary potential for water droplet simulations. J. Comp. Chem. 16:951‐972.
  Essmann, U., Perera, L., Berkowitz, M.L., Darden, T., Lee, H., and Pedersen, L.G. 1995. A smooth particle mesh Ewald method. J. Chem. Phys. 103:8577‐8593.
  Ewald, P. 1921. Investigations of crystals by means of Roentgen rays. Ann. Phys. (Leipzig) 64:253‐264.
  Feller, S.E., Zhang, Y., Pastor, R.W., and Brooks, B.R. 1995. Constant pressure molecular dynamics simulation: The Langevin piston method. J. Chem. Phys. 103:4613‐4621.
  Feller, S.E., Pastor, R.W., Rojnuckarin, A., Bogusz, S., and Brooks, B.R. 1996. Effect of electrostatic force truncation on interfacial and transport properties of water. J. Phys. Chem. 100:17011‐17020.
  Figueirido, F., Del Buono, G.S., and Levy, R.M. 1997. On finite‐size corrections to the free energy of ionic hydration. J. Phys. Chem. 101:5622‐5623.
  Fogolari, F., Brigo, A., and Molinari, H. 2002. The Poisson‐Boltzmann equation for biomolecular electrostatics: A tool for structural biology. J. Mol. Recognit. 15:377‐392.
  Fox, T. and Kollman, P.A. 1996. The application of different solvation and electrostatic models in molecular dynamics simulations of ubiquitin: How well is the X‐ray structure “maintained.” Proteins 25:315‐334.
  Fraczkiewicz, R. and Braun, W. 1998. Exact and efficient analytical calculation of the accessible surface areas and their gradients for macromolecules. J. Comp. Chem. 19:319‐333.
  Friedman, H. 1975. Image approximation to the reaction field. Mol. Phys. 29:1533‐1543.
  Friedman, R.A. and Honig, B. 1992. The electrostatic contribution to DNA base-stacking interactions. Biopolymers 32:145‐159.
  Friedman, R.A. and Honig, B. 1995. A free energy analysis of nucleic acid base stacking in aqueous solution. Biophys. J. 69:1528‐1535.
  Fritsch, V., Ravishanker, G., Beveridge, D.L., and Westhof, E. 1993. Molecular dynamics simulations of poly(dA).poly(dT): Comparisons between implicit and explicit solvent representations. Biopolymers 33:1537‐1552.
  Gaillard, T. and Case, D.A. 2011. Evaluation of DNA force fields in implicit solvation. J. Chem. Theory. Comp. 7:3181‐3198.
  Gallicchio, E. and Levy, R.M. 2004. AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high‐resolution modeling. J. Comput. Chem. 25:479‐499.
  Gilson, M.K. 1995. Theory of electrostatic interactions in macromolecules. Curr. Opin. Struct. Biol. 5:216‐223.
  Gilson, M.K. and Honig, B. 1991. The inclusion of electrostatic hydration energies in molecular mechanics calculations. J. Comp. Aided Mol. Des. 5:5‐20.
  Gilson, M.K., Sharp, K.A., and Honig, B.H. 1988. Calculating the electrostatic potential of molecules in solution: Method and error assessment. J. Comp. Chem. 9:327‐335.
  Gilson, M.K., Davis, M.E., Luty, B.A., and McCammon, J.A. 1993. Computation of electrostatic forces on solvated molecules using the Poisson‐Boltzmann equation. J. Phys. Chem. 97:3591‐3600.
  Goh, G.B., Knight, J.L., and Brooks, C.L. III. 2013a. pH‐dependent dynamics of complex RNA macromolecules. J. Chem. Theory Comput. 9:935‐943.
  Goh, G.B., Knight, J.L., and Brooks, C.L. III. 2013b. Towards accurate prediction of protonation equilibrium of nucleic acids. J. Phys. Chem. Lett. 4:760‐766.
  Gong, Z., Xiao, Y., and Xiao, Y. 2010. RNA stability under different combinations of Amber force fields and solvation models. J. Biomol. Struct. Dyn. 28:431‐441.
  Greengard, L. 1988. The Rapid Evaluation of Potential Fields in Particle Systems. MIT Press, Cambridge, Mass.
  Greengard, L. 1994. Fast algorithms for classical physics. Science 265:909‐914.
  Greengard, L. and Rokhlin, V. 1989. On the evaluation of electrostatic interactions in molecular modeling. Chem. Scrip. 29A:139‐144.
  Greengard, L.F. and Huang, J. 2002. A new version of the fast multipole method for screened Coulomb interactions in three dimensions. J. Computat. Phys. 180:642‐658.
  Guillot, B. 2002. A reappraisal of what we have learnt during three decades of computer simulations on water. J. Mol. Liq. 101:219‐260.
  Harvey, S.C. 1989. Treatment of electrostatic effects in macromolecular modeling. Proteins 5:78‐92.
  Hawkins, G.D., Lynch, G.C., Giesen, D.J., Rossi, I., Storer, J.W., Liotard, D.A., Cramer, C.J., and Thular, D.G. 1996a. AMSOL. QCPE Bull. 16:11‐13.
  Hawkins, G.D., Cramer, C.J., and Truhlar, D.G. 1996b. Parameterized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. J. Phys. Chem. 100:19824‐19839.
  Hawkins, G.D., Cramer, C.J., and Truhlar, D.G. 1997. Parameterized model for aqueous free energies of solvation using geometry‐dependent atomic surface tensions with implicit electrostatics. J. Phys. Chem. B. 101:7147‐7157.
  Henriksen, N.M., Davis, D.R., and Cheatham, T.E. III. 2012. Molecular dynamics re‐refinement of two different small RNA loop structures using the original NMR data suggest a common structure. J. Biomol. NMR 53:321‐339.
  Hingerty, B.E., Ritchie, R.H., Ferrell, T.L., and Turner, J.E. 1985. Dielectric effects in biopolymers: The theory of ionic saturation revisited. Biopolymers 24:427‐439.
  Hockney, R.W. and Eastwood, J.W. 1981. Computer Simulation Using Particles. McGraw‐Hill, New York.
  Horn, H.W., Swope, W.C., Pitera, J.W., Madura, J.D., Dick, T.J., Hura, G.L., and Head‐Gordon, T. 2004. Development of an improved four‐site water model for biomolecular simulations: TIP4P‐Ew. J. Chem. Phys. 120:9665‐9678.
  Hoover, W.G. 1995. Canonical dynamics: Equilibrium phase distributions. Phys. Rev. A. 31:1695‐1697.
  Hummer, G., Soumpasis, D.M., and Neumann, M. 1993. Computer simulations do not support Cl‐Cl pairing in aqueous NaCl solution. Mol. Phys. 81:1155‐1163.
  Hummer, G., Pratt, L.R., and Garcia, A. 1997. Ion sizes and finite‐size corrections for ionic‐solvation free energies. J. Chem. Phys. 107:9275‐9277.
  Jayaram, B. and Beveridge, D.L. 1996. Modeling DNA in aqueous solutions: Theoretical and computer simulation studies on the ion atmosphere of DNA. Annu. Rev. Biophys. Biomol. Struct. 25:367‐394.
  Jorgensen, W.L. and Tirado‐Rives, J. 2005. Potential energy functions for atomic‐level simulations of water and organic and biomolecular systems. Proc. Natl. Acad. Sci. U.S.A. 102:6665‐6670.
  Jorgensen, W.L., Chandrasekhar, J., Madura, J.D., Impey, R.W., and Klein, M.L. 1983. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79:926‐935.
  Joung, I.S. and Cheatham, T.E. III. 2008. Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations. J. Phys. Chem. B. 112:9020‐9041.
  Kang, Y.K., Gibson, K.D., Nemethy, G., and Scheraga, H.A. 1988. Free energies of hydration of solute molecules. 4. Revised treatment of the hydration shell model. J. Chem. Phys. 92:4739‐4742.
  Kastenholtz, M.A. and Hünenberger, P.H. 2006. Computation of methodology‐independent ionic solvation free energies from molecular simulations. II. The hydration free energy of the sodium cation. J. Chem. Phys. 124:224501‐224522.
  King, G. and Warshel, A. 1989. A surface constrained all‐atom solvent model for effective simulations of polar solutions. J. Chem. Phys. 91:3647‐3661.
  Kirkwood, J.G. 1939. The dielectric polarization of liquids. J. Chem. Phys. 7:911‐919.
  Kirmizialtin, S., and Elber, R. 2010. Computational exploration of mobile ion distributions around RNA duplex. J. Phys. Chem. B. 114:8207‐8220.
  Kirmizialtin, S., Silalahi, A.R., Elber, R., and Fenley, M.O. 2012. The ionic atmosphere around A‐RNA: Poisson‐Boltzmann and molecular dynamics simulations. Biophys. J. 102:829‐838.
  Koehl, P. 2006. Electrostatics calculations: Latest methodological advances. Curr. Opin. Struct. Biol. 16:142‐151.
  Lavery, R., Zakrzewska, K., Beveridge, D., Bishop, T.C., Case, D.A., Cheatham, T.E. III, Dixit, S., Jayaram, B., Lankas, F., Laughton, C., Maddocks, J.H., Michon, A., Osman, R., Orozco, M., Pérez, A., Singh, T., Spacková, N., and Sponer, J. 2010. A systematic molecular dynamics study of nearest‐neighbor effects on base pair and base pair step conformations and fluctuations in B‐DNA. Nucleic Acids Res. 38:299‐313.
  Lawrence, C.P. and Skinner, J.L. 2003. Flexible TIP4P model for molecular dynamics simulation of liquid water. Chem. Phys. Lett. 372:842‐847.
  Lebrun, A. and Lavery, R. 1996. Modelling extreme stretching of DNA. Nucleic Acids Res. 24:2260‐2267.
  Lebrun, A., Shakked, Z., and Lavery, R. 1997. Local DNA stretching mimics the distortion caused by the TATA box‐binding protein. Proc. Natl. Acad. Sci. U.S.A. 94:2993‐2998.
  Lee, F.S., Chu, Z.T., and Warshel, A. 1993. Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs. J. Comp. Chem. 14:161‐185.
  Lee, M.S., Salsbury, F.R. Jr., and Brooks, C.L. III. 2002. Novel generalized Born methods. J. Chem. Phys. 116:10606‐10614.
  Lee, M.S., Feig, M., Salsbury, F.R. Jr., and Brooks, C.L. III. 2003. New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations. J. Comput. Chem. 24:1348‐1356.
  Lee, M.S., Salsbury, F.R. Jr., and Olson, M.A. 2004. An efficient hybrid explicit/implicit solvent method for biomolecular simulations. J. Comput. Chem. 25:1967‐1978.
  Le Grand, S.M. and Merz, K.M. Jr. 1993. Rapid approximation to molecular surface area via the use of Boolean logic and look‐up tables. J. Comp. Chem. 14:349‐352.
  Levitt, M. 1983. Computer simulation of DNA double‐helix dynamics. Cold Spring Harbor Symp. Quant. Biol. 47:251‐262.
  Levitt, M., Hirshberg, M., Sharon, R., and Daggett, V. 1995. Potential energy function and parameters for simulations of the molecular dynamics of proteins and nucleic acids in solution. Comp. Phys. Comm. 91:215‐231.
  Luo, R., Moult, J., and Gilson, M.K. 1997. Dielectric screening treatment of electrostatic solvation. J. Phys. Chem. B. 101:11226‐11236.
  Luty, B.A., Tironi, I.G., and van Gunsteren, W.F. 1995. Lattice‐sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys. 103:3014‐3021.
  MacKerell, A.D. Jr. 1997. Influence of magnesium ions on duplex DNA structural, dynamic, and solvation properties. J. Phys. Chem. B 101:646‐650.
  MacKerell, A.D. Jr. and Banavali, N. 2000. All‐atom empirical force field for nucleic acids. 2. Application to molecular dynamics simulations of DNA and RNA in solution. J. Comp. Chem. 21:105‐120.
  MacKerell, A.D. Jr. and Nilsson, L. 2008. Molecular dynamics simulations of nucleic acid‐protein complexes. Curr. Opin. Struct. Biol. 18:194‐199.
  MacKerell, A.D. Jr., Wiorkiewicz‐Kuczera, J., and Karplus, M. 1995. An all‐atom empirical energy function for the simulation of nucleic acids. J. Am. Chem. Soc. 117:11946‐11975.
  Madura, J.D., Briggs, J.M., Wade, R.C., Davis, M.E., Luty, B.A., Ilin, A., Antosiewicz, J., Gilson, M.K., Bagheri, B., Scott, L.R., and McCammon, J.A. 1995. Electrostatics and diffusion of molecules in solution: Simulations with the University of Houston Brownian dynamics program. Comp. Phys. Commun. 91:57‐95.
  Mahoney, M.W. and Jorgensen, W.L. 2000. A five‐site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J. Chem. Phys. 112:8910‐8922.
  Mahoney, M.W. and Jorgensen, W.L. 2001. Diffusion constant of the TIP5P model of liquid water. J. Chem. Phys. 114:363‐366.
  Manning, G.S. 1978. The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides. Quart. Rev. Biophys. 2:179‐246.
  McConnell, K.J., Nirmala, R., Young, M.A., Ravishanker, G., and Beveridge, D.L. 1994. A nanosecond molecular dynamics trajectory for a B DNA double helix: Evidence for substates. J. Am. Chem. Soc. 116:4461‐4462.
  Minasov, G., Tereshko, V., and Egli, M. 1999. Atomic‐resolution crystal structures of B‐DNA reveal specific influences of divalent metal ions on conformation and packing. J. Mol. Biol. 291:83‐99.
  Misra, V.K. and Honig, B. 1996. The electrostatic contribution to the B to Z transition of DNA. Biochemistry 35:1115‐1124.
  Misra, V.K., Sharp, K.A., Friedman, R.A., and Honig, B. 1994. Salt effects on ligand‐DNA binding. Minor groove binding antibiotics. J. Mol. Biol. 238:245‐263.
  Mobley, D.L., Dumont, E., Chodera, J.D., and Dill, K.A. 2007. Comparison of charge models for fixed‐charge force fields: Small‐molecule hydration free energies in explicit solvent. J. Phys. Chem. B. 111:2242‐2254.
  Mohanty, D., Elber, R., Thirumalai, D., Beglov, D., and Roux, B. 1997. Kinetics of peptide folding: Computer simulations of SYPFDV and peptide variants in water. J. Mol. Biol. 272:423‐442.
  Mongan, J., Simmerling, C., McCammon, J.A., Case, D.A., and Onufriev, A. 2007. Generalized Born model with a simple, robust molecular volume correction. J. Chem. Theor. Comput. 1:156‐169.
  Neumann, M. 1983. Dipole moment fluctuation formulas in computer simulations of polar systems. Mol. Phys. 50:841‐858.
  Norberg, J. and Nilsson, L. 1995. NMR relaxation times, dynamics, and hydration of a nucleic acid fragment from molecular dynamics simulations. J. Phys. Chem. 99:14876‐14884.
  Norberg, J. and Nilsson, L. 1996. Glass transition in DNA from molecular dynamics simulations. Proc. Natl. Acad. Sci. U.S.A. 93:10173‐10176.
  Norberg, J., and Nilsson, L. 2000. On the truncation of long‐range electrostatic interactions in DNA. Biophys. J. 79:1537‐1553.
  Nosé, S. 1984. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52:255‐268.
  Okur, A., Wickstrom, L., Layten, M., Geney, R., Song, K., Hornak, V., and Simmerling, C. 2006. Improved efficiency of replica exchange simulations through use of a hybrid explicit/implicit solvation model. J. Chem. Theory Comput. 2:420‐433.
  Onsager, L. 1936. Electric moments of molecules in liquids. J. Am. Chem. Soc. 58:1486‐1493.
  Onufriev, A. 2008. Implicit solvent models in molecular dynamics simulations: A brief overview. In Annual Reports in Computational Chemistry, Vol. 4 (R.A. Wheeler and D.C. Spellmeyer, eds.) pp. 125‐137. Elsevier, Amsterdam.
  Onufriev, A., Bashford, D., and Case, D.A. 2004. Exploring protein native states and large‐scale conformational changes with a modified generalized Born model. Proteins 55:383‐394.
  Ooi, T., Oobatake, M., Némethy, G., and Scheraga, H.A. 1987. Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides. Proc. Natl. Acad. Sci. U.S.A. 84:3086‐3090.
  Paesani, F., Zhang, W., Case, D.A., Cheatham, T.E. III, and Voth, G.A. 2006. An accurate and simple quantum model for liquid water. J. Chem. Phys. 125:184507.
  Papazyan, A. and Warshel, A. 1997. Continuum and dipole‐lattice models of solvation. J. Phys. Chem. B. 101:11254‐11264.
  Paulsen, R.B., Seth, P.P., Swayze, E.E., Griffey, R.H., Skalicky, J.J., Cheatham, T.E. III, and Davis, D.R. 2010. Inhibitor‐induced structural change in the HCV IRES domain IIa RNA. Proc. Natl. Acad. Sci. U.S.A. 107:7263‐7268.
  Pérez, A., Luque, F.J. and Orozco, M. 2012. Frontiers in molecular dynamics simulations of DNA. Acc. Chem. Res. 45:196‐205.
  Petersen, H.G. 1995. Accuracy and efficiency of the particle mesh Ewald method. J. Chem. Phys. 103:3668‐3679.
  Petrella, R.J. and Karplus, M. 2005. Electrostatic energies and forces computed without explicit interparticle interactions: A linear time complexity formulation. J. Comp. Chem. 26:755‐787.
  Price, D.J. and Brooks, C.L. III. 2004. A modified TIP3P water potential for simulation with Ewald summation. J. Chem. Phys. 121:10096‐10103.
  Pollock, E.L. and Glosli, J. 1996. Comments on P3M, FMM, and the Ewald method for large periodic Coulombic systems. Comp. Phys. Commun. 95:93‐110.
  Ramstein, J. and Lavery, R. 1988. Energetic coupling between DNA bending and base pair opening. Proc. Natl. Acad. Sci. U.S.A. 85:7231‐7235.
  Ren, P., Chun, J., Thomas, D.G., Schnieders, M.J., Marucho, M., Zhang, J., and Baker, N.A. 2012. Biomolecular electrostatics and solvation: A computational perspective. Q. Rev. Biophys. 45:427‐491.
  Rick, S.W. 2004. A reoptimization of the five‐site water potential (TIP5P) for use with Ewald sums. J. Chem. Phys. 120:6085‐6093.
  Riihimäki, E.‐S., Martinez, J.M., and Kloo, L. 2006. An evaluation of non‐periodic boundary condition models in molecular dynamics simulations using prion octapeptides as probes. J. Mol. Struct. Theochem. 760:91‐98.
  Roberts, J.E. and Schnitker, J. 1995. Boundary conditions in simulations of aqueous ionic solutions: A systematic study. J. Phys. Chem. 99:1322‐1331.
  Rueda, M., Cubero, E., Laughton, C.A., and Orozco, M. 2004. Exploring the counterion atmosphere around DNA: What can be learned from molecular dynamics simulations? Biophys. J. 87:800‐811.
  Ruscio, J.Z. and Onufriev, A. 2006. A computational study of nucleosomal DNA flexibility. Biophys. J. 91:4121‐4132.
  Ryckaert, J.‐P., Ciccotti, G., and Berendsen, H.J.C. 1977. Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n‐alkanes. J. Comput. Phys. 23:327‐341.
  Sagui, C. and Darden, T. 2001. Multigrid methods for classical molecular dynamics simulations of biomolecules. J. Chem. Phys. 114:6578‐6591.
  Sambrinski, E.J., Schwartz, D.C., and de Pablo, J.J. 2009. A mesoscale model of DNA and its renaturation. Biophys. J. 96:1675‐1690.
  Sarai, A., Mazur, J., Nussinov, R., and Jernigan, R.L. 1988. Origin of DNA helical structure and its sequence dependence. Biochemistry 27:8498‐8502.
  Savelyev, A. and Papoian, G.A. 2007. Inter‐DNA electrostatics from explicit solvent molecular dynamics simulations. J. Am. Chem. Soc. 129:6060‐6061.
  Schiffer, C.A., Caldwell, J.W., Kollman, P.A., and Stroud, R.M. 1993. Protein structure prediction with a combined solvation free energy‐molecular mechanics force field. Mol. Sim. 10:121‐149.
  Schmidt, K.E. and Lee, M.A. 1997. Multipole Ewald sums for the fast multipole method. J. Stat. Phys. 89:411‐424.
  Schreiber, H. and Steinhauser, O. 1992a. Cutoff size does strongly influence molecular dynamics results on solvated polypeptides. Biochemistry 31:5856‐5860.
  Schreiber, H. and Steinhauser, O. 1992b. Taming cut‐off induced artifacts in molecular dynamics studies of solvated polypeptides: The reaction field method. J. Mol. Biol. 228:909‐923.
  Seibel, G.L., Singh, U.C., and Kollman, P.A. 1985. A molecular dynamics simulation of double‐helical B‐DNA including counterions and water. Proc. Nat. Acad. Sci. U.S.A. 82:6537‐6540.
  Shan, Y., Klepeis, J.L., Eastwood, M.P., Dror, R.O., and Shaw, D.E. 2005. Gaussian split Ewald: A fast Ewald mesh method for molecular simulation. J. Chem. Phys. 122:54101.
  Sharp, K.A. 1991. Incorporating solvent and ion screening into molecular dynamics using the finite‐difference Poisson‐Boltzmann method. J. Comp. Chem. 12:454‐468.
  Sharp, K.A. and Honig, B. 1990. Electrostatic interactions in macromolecules: Theory and applications. Annu. Rev. Biophys. Biophys. Chem. 19:301‐332.
  Singh, U.C., Weiner, S.J., and Kollman, P.A. 1985. Molecular dynamics simulations of d(C‐G‐C‐G‐A)‐d(T‐C‐G‐C‐G) with and without “hydrated” counterions. Proc. Natl. Acad. Sci. U.S.A. 82:755‐759.
  Skeel, R.D., Tezcan, I., and Hardy, D.J. 2002. Multiple grid methods for classical molecular dynamics. J. Comput. Chem. 23:673‐684.
  Smith, P.E. and Pettitt, B.M. 1991. Peptides in ionic solutions: A comparison of the Ewald and switching function techniques. J. Chem. Phys. 95:8430‐8441.
  Smith, P.E. and Pettitt, B.M. 1996. Ewald artifacts in liquid state molecular dynamics simulations. J. Chem. Phys. 105:4289‐4293.
  Smith, P.E., Blatt, H.D., and Pettitt, B.M. 1997. On the presence of rotational Ewald artifacts in the equilibrium and dynamical properties of a zwitterionic tetrapeptide in aqueous solution. J. Phys. Chem. B 101:3886‐3890.
  Solvason, D., Kolafa, J., Petersen, H.G., and Perram, J.W. 1995. A rigorous comparison of the Ewald method and the fast multipole method in two dimensions. Comp. Phys. Comm. 87:307‐318.
  Sorin, E.J., Rhee, Y.M., Nakatani, B.J., and Pande, V.S. 2003. Insights into nucleic acid conformational dynamics from massively parallel stochastic simulations. Biophys. J. 85:790‐803.
  Spacková, N., Cheatham, T.E. III, Ryjácek, F., Lankas, F., Van Meervelt, L., Hobza, P., and Sponer, J. 2003. Molecular dynamics simulations and thermodynamics analysis of DNA‐drug complexes. Minor groove binding between 4′,6‐diamidino‐2‐phenylindole and DNA duplexes in solution. J. Am. Chem. Soc. 125:1759‐1769.
  Spolar, R.S. and Record, M.T. Jr. 1994. Coupling of local folding to site‐specific binding of proteins to DNA. Science 263:777‐784.
  Sponer, J., and Spacková, N. 2007. Molecular dynamics simulations and their application to four‐stranded DNA. Methods 43:278‐290.
  Sponer, J., Cang, X. and Cheatham, T.E. III. 2012. Molecular dynamics simulations of G‐DNA and perspectives on the simulation of nucleic acid structures. Methods 57:25‐39.
  Sprous, D., Young, M.A., and Beveridge, D.L. 1998. Molecular dynamics studies of the conformational preferences of a DNA double helix in water and an ethanol/water mixture: Theoretical considerations of the A‐B transition. J. Phys. Chem. B. 102:4658‐4667.
  Sridharan, S., Nicholls, A., and Sharp, K.A. 1995. A rapid method for calculating derivatives of solvent accessible surface areas of molecules. J. Comp. Chem. 16:1038‐1044.
  Steinbach, P.J. and Brooks, B.R. 1994. New spherical‐cutoff methods for long‐range forces in macromolecular simulation. J. Comput. Chem. 15:667‐683.
  Still, W.C., Tempczyk, A., Hawley, R.C., and Hendrickson, T. 1990. Semi analytical treatment of solvation for molecular mechanics and dynamics. J. Am. Chem. Soc. 112:6127‐6128.
  Tapia, O. and Velazquez, I. 1997. Molecular dynamics simulations of DNA with protein's consistent GROMOS force field and the role of counterions’ symmetry. J. Am. Chem. Soc. 119:5934‐5938.
  Tereshko, V., Minasov, G., and Egli, M. 1999a. The Dickerson‐Drew B‐DNA dodecamer revisited at atomic resolution. J. Am. Chem. Soc. 121:470‐471.
  Tereshko, V., Minasov, G., and Egli, M. 1999b. A “hydrat‐ion” spine in a B‐DNA minor groove. J. Am. Chem. Soc. 121:3590‐3595.
  Tironi, I.G., Sperb, R., Smith, P.E., and van Gunsteren, W.F. 1995. A generalized reaction field method for molecular dynamics simulations. J. Chem. Phys. 102:5451‐5459.
  Tironi, I.G., Luty, B.A., and van Gunsteren, W.F. 1997. Space‐time correlated reaction field: A stochastic dynamical approach to the dielectric continuum. J. Chem. Phys. 106:6068‐6075.
  Toukmaji, A.Y. and Board, J.A. Jr. 1996. Ewald summation techniques in perspective: A survey. Comp. Phys. Comm. 95:73‐92.
  Tsui, V. and Case, D.A., 2000a. Molecular dynamics simulations of nucleic acids with a generalized Born solvation model. J. Am. Chem. Soc. 122:2489‐2498.
  Tsui, V. and Case, D.A. 2000b. Theory and applications of the generalized Born solvation model in macromolecular simulations. Biopolymers 56:275‐291.
  Tuckerman, M., Berne, B.J., and Martyna, G.J. 1992. Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97:1990‐2001.
  Valleau, J.P. and Whittington, S.G. 1977. A guide to Monte Carlo for statistical mechanics: 1. Highways. In Modern Theoretical Chemistry, Vol. 5: Statistical Mechanics Part A: Equilibrium Techniques (B.J. Berne, ed.) pp. 137‐168 Plenum Press, New York and London. (B.J. Berne, ed.) pp. 137‐168. Plenum Press, New York.
  van Gunsteren, W.F., Berendsen, H.J.C., and Rullman, J.A.C. 1978. Inclusion of reaction fields in molecular dynamics: Applications to liquid water. Faraday Disc. 66:58‐70.
  Várnai, P. and Zakrzewska, K. 2004. DNA and its counterions: A molecular dynamics study. Nucleic Acids Res. 32:4269‐4280.
  von Kitzing, E. and Diekmann, S. 1987. Molecular mechanics calculations of dA12 • dT12 and the curved molecule of d(GCTCGAAAAA)4 • d(TTTTTCGAGC)4. Eur. Biophys. J. 15:13‐26.
  Warshel, A. and Aqvist, J. 1991. Electrostatic energy and macromolecular function. Annu. Rev. Biophys. Biophys. Chem. 20:267‐298.
  Warshel, A. and Levitt, M. 1976. Theoretical studies of enzyme reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol. 103:227‐249.
  Warshel, A. and Russell, S.T. 1984. Calculation of electrostatic interactions in biological systems and in solution. Quart. Rev. Biophys. 17:283‐422.
  Weber, W., Hünenberger, P.H., and McCammon, J.A. 2000. Molecular dynamics simulations of a polyalanine octapeptide under Ewald boundary conditions: Influence of artificial periodicity on peptide conformation. J. Phys. Chem. B. 104:3668‐3675.
  Wesson, L. and Eisenberg, D. 1992. Atomic solvation parameters applied to molecular dynamics of proteins in solution. Prot. Sci. 1:227‐235.
  Williams, R.L., Vila, J., Perrot, G., and Scheraga, H.A. 1992. Empirical solvation models in the context of conformational energy searches: Application to bovine pancreatic trypsin inhibitor. Proteins 14:110‐119.
  Wong, V. and Case, D.A. 2008. Evaluating rotational diffusion from protein MD simulation. J. Phys. Chem. B. 112:6013‐6024.
  Wu, X. and Brooks, B.R. 2005. Isotropic periodic sum: A method for the calculation of long‐range interactions. J. Chem. Phys. 122:44107.
  York, D. and Yang, W. 1994. The fast Fourier Poisson method for calculating Ewald sums. J. Chem. Phys. 101:3298‐3300.
  Zacharias, M. and Sklenar, H. 1997. Analysis of the stability of looped‐out and stacked‐in conformations of an adenine bulge in DNA using a continuum model for solvent and ions. Biophys. J. 73:2990‐3003.
  Zauhar, R.J. 1991. The incorporation of hydration forces determined by continuum electrostatics into molecular mechanics simulations. J. Comp. Chem. 12:575‐583.
  Zhurkin, V.B., Ulyanov, N.B., Gorin, A.A., and Jernigan, R.L. 1991. Static and statistical bending of DNA evaluated by Monte Carlo simulations. Proc. Natl. Acad. Sci. U.S.A. 88:7046‐7050.
Internet Resources
  Ascona B‐DNA Consortium Web site.
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