Abstract
Molecular mechanics attempts to represent intermolecular interactions in terms of classical physics. Initial efforts assumed a point charge located at the atom center and coulombic interactions. It is been recognized over multiple decades that simply representing electrostatics with a charge on each atom failed to reproduce the electrostatic potential surrounding a molecule as estimated by quantum mechanics. Molecular orbitals are not spherically symmetrical, an implicit assumption of monopole electrostatics. This perspective reviews recent evidence that requires use of multipole electrostatics and polarizability in molecular modeling.
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Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO, Eastwood MP, Bank JA, Jumper JM, Salmon JK, Shan Y, Wriggers W (2010) Atomic-level characterization of the structural dynamics of proteins. Science 330(6002):341–346
Dror RO, Jensen MO, Borhani DW, Shaw DE (2010) Exploring atomic resolution physiology on a femtosecond to millisecond timescale using molecular dynamics simulations. J Gen Physiol 135(6):555–562
Dror RO, Pan AC, Arlow DH, Borhani DW, Maragakis P, Shan Y, Xu H, Shaw DE (2011) Pathway and mechanism of drug binding to g-protein-coupled receptors. Proc Natl Acad Sci USA 108(32):13118–13123
Shan Y, Kim ET, Eastwood MP, Dror RO, Seeliger MA, Shaw DE (2011) How does a drug molecule find its target binding site? J Am Chem Soc 133(24):9181–9183
Shan Y, Seeliger MA, Eastwood MP, Frank F, Xu H, Jensen MO, Dror RO, Kuriyan J, Shaw DE (2009) A conserved protonation-dependent switch controls drug binding in the abl kinase. Proc Natl Acad Sci USA 106(1):139–144
Borhani DW, Shaw DE (2012) The future of molecular dynamics simulations in drug discovery. J Comput Aided Mol Des 26(1):15–26
Yue K, Fiebig KM, Thomas PD, Chan HS, Shakhnovich EI, Dill KA (1995) A test of lattice protein folding algorithms. Proc Natl Acad Sci USA 92(1):325–329
Dill KA (1999) Polymer principles and protein folding. Protein Sci Publ Protein Soc 8(6):1166–1180
Vanommeslaeghe K, Hatcher E, Acharya C, Kundu S, Zhong S, Shim J, Darian E, Guvench O, Lopes P, Vorobyov I, Mackerell AD Jr (2010) Charmm general force field: a force field for drug-like molecules compatible with the charmm all-atom additive biological force fields. J Comput Chem 31(4):671–690
Thomas JL, Tobias DJ, Mackerell AD Jr (2007) Direct comparisons of experimental and calculated neutron structure factors of pure solvents as a method for force field validation. J Phys Chem B 111(45):12941–12944
MacKerell AD, Bashford D, Bellott M, Dunbrack RL, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, et al. (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–3616
Jorgensen WL, Maxwell DS, Tirado-Rives J (1996) Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids. J Am Chem Soc 118(45):11225–11236
Wang J, Wolf RM, Caldwell JW, Kollman PA, Case DA (2004) Development and testing of a general amber force field. J Comput Chem 25(9):1157–1174
Nicholls A, Mobley DL, Guthrie JP, Chodera JD, Bayly CI, Cooper MD, Pande VS (2008) Predicting small-molecule solvation free energies: an informal blind test for computational chemistry. J Med Chem 51(4):769–779
Buckingham AD, Fowler PW (1983) Do electrostatic interactions predict structures of van der waals molecules? J Chem Phys 76:6426–6428
Volkov A, Gatti C, Abramov Y, Coppens P (2000) Evaluation of net atomic charges and atomic and molecular electrostatic moments through topological analysis of the experimental charge density. Acta Crystallogr Sect A Found Crystallogr 56(Pt 3):252–258
Cisneros GA, Piquemal JP, Darden TA (2006) Generalization of the gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods. J Chem Phys 125(18):184101
Cisneros GA, Piquemal JP, Darden TA (2006) Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions. J Phys Chem B 110(28):13682–13684
Cisneros GA, Piquemal JP, Darden TA (2005) Intermolecular electrostatic energies using density fitting. J Chem Phys 123(4):044109
Sagui C, Pedersen LG, Darden TA (2004) Towards an accurate representation of electrostatics in classical force fields: efficient implementation of multipolar interactions in biomolecular simulations. J Chem Phys 120(1):73–87
Sagui C, Darden TA (1999) Molecular dynamics simulations of biomolecules: long-range electrostatic effects. Annu Rev Biophys Biomol struct 28:155–179
Fenn TD, Schnieders MJ, Brunger AT, Pande VS (2010) Polarizable atomic multipole X-ray refinement: hydration geometry and application to macromolecules. Biophys J 98(12):2984–2992
Fenn TD, Schnieders MJ, Mustyakimov M, Wu C, Langan P, Pande VS, Brunger AT (2011) Reintroducing electrostatics into macromolecular crystallographic refinement: application to neutron crystallography and DNA hydration. Structure 19(4):523–533
Elking D, Darden T, Woods RJ (2007) Gaussian induced dipole polarization model. J Comput Chem 28(7):1261–1274
Elking DM, Perera L, Duke R, Darden T, Pedersen LG (2010) Atomic forces for geometry-dependent point multipole and gaussian multipole models. J Comput Chem 31(15):2702–2713
Elking DM, Perera L, Duke R, Darden T, Pedersen LG (2011) A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank. J Comput Chem 32(15):3283–3295
Dominiak PM, Volkov A, Dominiak AP, Jarzembska KN, Coppens P (2009) Combining crystallographic information and an aspherical-atom data bank in the evaluation of the electrostatic interaction energy in an enzyme-substrate complex: influenza neuraminidase inhibition. Acta Crystallogr D Biol Crystallogr 65(Pt 5):485–499
Muddana HS, Gilson MK (2012) Calculation of host-guest binding affinities using a quantum-mechanical energy model. J Chem Theory Comput 8(6):2023–2033
Muddana HS, Gilson MK (2012) Prediction of sampl3 host-guest binding affinities: evaluating the accuracy of generalized force-fields. J Comput Aided Mol Des 26(5):517–525
Ren P, Ponder JW (2003) Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B 107:5933–5947
Miyazawa S, Jernigan RL (1996) Residue-residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading. J Mol Biol 256(3):623–644
Zimmermann MT, Leelananda SP, Kloczkowski A, Jernigan RL (2012) Combining statistical potentials with dynamics-based entropies improves selection from protein decoys and docking poses. J Phys Chem B 116(23):6725–6731
Stone AJ (2008) Intermolecular potentials. Science 321(5890):787–789
Williams DE (1988) Representation of the molecular electrostatic potential by atomic multipole and bond dipole models. J Comput Chem 9(7):745–763
Williams DE (2007) Net atomic charge and multipole models for the ab initio molecular electric potential. In: Lipkowitz KB, Boyd DB (eds) Reviews in computational chemistry, vol 2. Wiley, USA
Hunter CA, Sanders JKM (1990) The nature of pi–pi interactions. J Am Chem Soc 112(14):5525–5534
Hunter CA (1994) Meldola lecture.The role of aromatic interactions in molecular recognition. Chem Soc Rev 23:101–109
Hunter CA, Low CM, Rotger C, Vinter JG, Zonta C (2002) Substituent effects on cation-pi interactions: a quantitative study. Proc Natl Acad Sci USA 99(8):4873–4876
Cockroft SL, Hunter CA (2006) Chemical double-mutant cycles: dissecting non-covalent interactions. Chem Soc Rev 36:172–188
Stone AJ, Price SL (1988) Some new ideas in the theory of inter molecular forces—anisotropic atom atom potentials. J Phys Chem 92(12):3325–3335
Price SL, Harrison RJ, Guest MF (1988) An ab initio distributed multipole study of the electrostatic potential around an undecapeptide cyclosporine derivative and comparison with point-charge electrostatic models. J Comput Chem 10(4):552–567
Vinter JG (1994) Extended electron distributions applied to the molecular mechanics of some intermolecular interactions. J Comput-Aided Mol Des 8:653–668
Sherrill CD (2012) Energy component analysis of pi interactions. Acc chem res
Quinonero D, Garau C, Frontera A, Ballester P, Costa A, Deya PM (2005) Structure and binding energy of anion-pi and cation-pi complexes: a comparison of mp2, ri-mp2, dft, and df-dft methods. J Phys Chem A 109(20):4632–4637
Chessari G, Hunter CA, Low CM, Packer MJ, Vinter JG, Zonta C (2002) An evaluation of force-field treatments of aromatic interactions. Chemistry 8(13):2860–2867
Cheeseright TJ, Mackey MD, Melville JL, Vinter JG (2008) Fieldscreen: virtual screening using molecular fields. Application to the dud data set. J Chem Inf Model 48(11):2108–2117
Apaya RP, Lucchese B, Price SL, Vinter JG (1995) The matching of electrostatic extrema: a useful method in drug design? A study of phosphodiesterase iii inhibitors. J Comput Aided Mol Des 9(1):33–43
Vinter JG, Trollope KI (1995) Multiconformational composite molecular potential fields in the analysis of drug action. I. Methodology and first evaluation using 5-ht and histamine action as examples. J Comput-Aided Mol Des 9:297–307
Cramer RD III, Patterson DE, Bunce JD (1989) Recent advances in comparative molecular field analysis (comfa). Prog Clin Biol Res 291:161–165
Reynolds CA, Wade RC, Goodford PJ (1989) Identifying targets for bioreductive agents: using grid to predict selective binding regions of proteins. J Mol Graph 7(2):103–108
Perez C, Pastor M, Ortiz AR, Gago F (1998) Comparative binding energy analysis of hiv-1 protease inhibitors: äâ incorporation of solvent effects and validation as a powerful tool in receptor-based drug design. J Med Chem 41(6):836–852
Lozano JJ, Pastor M, Cruciani G, Gaedt K, Centeno NB, Gago F, Sanz F (2000) 3d-qsar methods on the basis of ligand-receptor complexes. Application of combine and grid/golpe methodologies to a series of cyp1a2 ligands. J Comput Aided Mol Des 14(4):341–353
Ballante F, Musmuca I, Marshall GR, Ragno R (2012) Comprehensive models of wild-type and mutant hiv-1 reverse transciptases. J Comp-Aided Mol Design 26(8):907–919
Silvestri L, Ballante F, Mai A, Marshall GR, Ragno R (2012) Histone deacetylase inhibitors: structure-based modeling and isoform-selectivity prediction. J Chem Inf Model 52(8):2215–2235
Halgren TA, Damm W (2001) Polarizable force fields. Curr Opin Struct Biol 11(2):236–242
Morozov AV, Kortemme T, Tsemekhman K, Baker D (2004) Close agreement between the orientation dependence of hydrogen bonds observed in protein structures and quantum mechanical calculations. Proc Natl Acad Sci USA 101(18):6946–6951
Truchon JF, Nicholl’s A, Grant JA, Iftimie RI, Roux B, Bayly CI (2010) Using electronic polarization from the internal continuum (epic) for intermolecular interactions. J Comput Chem 31(4):811–824
Dudek MJ, Ponder JW (1995) Accurate modeling of the intramolecular electrostatic energy of proteins. J Comput Chem 16(7):791–816
Grossfield A, Ren P, Ponder JW (2003) Ion solvation thermodynamics from simulation with a polarizable force field. J Am Chem Soc 125(50):15671–15682
Ponder JW, Case DA (2003) Force fields for protein simulations. Adv Protein Chem 66:27–85
Ren P, Ponder JW (2002) Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations. J Comput Chem 23(16):1497–1506
Ponder JW (2011) Tinker—software tools for molecular design, version 6.0. http://www.dasher.wustl.edu/ffe/distribution/doc
Ponder JW, Wu C, Ren P, Pande VS, Chodera JD, Schnieders MJ, Haque I, Mobley DL, Lambrecht DS, DiStasio RA Jr, Head-Gordon M et al (2010) Current status of the amoeba polarizable force field. J Phys Chem B 114(8):2549–2564
Shi Y, Wu C, Ponder JW, Ren P (2011) Multipole electrostatics in hydration free energy calculations. J Comput Chem 32(5):967–977
Ren P, Wu C, Ponder JW (2011) Polarizable atomic multipole-based molecular mechanics for organic molecules. J Chem Theory Comput 7(10):3143–3161
Schnieders MJ, Fenn TD, Pande VS, Brunger AT (2009) Polarizable atomic multipole X-ray refinement: application to peptide crystals. Acta Crystallogr D Biol Crystallogr 65(Pt 9):952–965
Jiao D, Zhang J, Duke RE, Li G, Schnieders MJ, Ren P (2009) Trypsin-ligand binding free energies from explicit and implicit solvent simulations with polarizable potential. J Comput Chem 30(11):1701–1711
Riemen AJ, Waters ML (2009) Design of highly stabilized beta-hairpin peptides through cation-pi interactions of lysine and n-methyllysine with an aromatic pocket. Biochemistry 48(7):1525–1531
Allfrey VG, Faulkner R, Mirsky AE (1964) Acetylation and methylation of histones and their possible role in the regulation of rna synthesis. Proc Natl Acad Sci USA 51:786–794
Dvir H, Silman I, Harel M, Rosenberry TL, Sussman JL (2010) Acetylcholinesterase: from 3d structure to function. Chem Biol Interact 187(1–3):10–22
Zheng X, Wu C, Ponder JW, Marshall GR (2012) Molecular dynamics of beta-hairpin models of epigenetic recognition motifs. J Am Chem Soc 134(38):15970–15978
Macias AT, Mackerell AD Jr (2005) Ch/pi interactions involving aromatic amino acids: refinement of the charmm tryptophan force field. J Comput Chem 26(14):1452–1463
Mackerell AD Jr (2004) Feig M, Brooks CL, 3rd: extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J Comput Chem 25(11):1400–1415
Ren P, Ponder JW (2004) Temperature and pressure dependence of the amoeba water model. J Phys Chem B 108:13427–13437
Walsh TR, Liang T (2009) A multipole-based water potential with implicit polarization for biomolecular simulations. J Comput Chem 30(6):893–899
Kramer C, Gedeck P, Meuwly M (2012) Atomic multipoles: electrostatic potential fit, local reference axis systems, and conformational dependence. J Comput Chem 33(20):1673–1688
Chourasia M, Sastry GM, Sastry GN (2011) Aromatic-aromatic interactions database, a2id: an analysis of aromatic [pi]-networks in proteins. Int J Biol Macromol 48(4):540–552
Meyer EA, Castellano RK, Diederich F (2003) Interactions with aromatic rings in chemical and biological recognition. Angew Chem Int Ed Engl 42(11):1210–1250
Salonen LM, Ellermann M, Diederich F (2011) Aromatic rings in chemical and biological recognition: energetics and structures. Angew Chem Int Ed Engl 50(21):4808–4842
Burley SK, Petsko GA (1986) Amino-aromatic interactions in proteins. FEBS Lett 203:139–143
Crowley PB, Golovin A (2005) Cation-pi interactions in protein–protein interfaces. Proteins 59(2):231–239
Greenberg DA, Barry CD, Marshall GR (1978) Investigation and parameterization of a molecular dielectric function. J Am Chem Soc 100:4020–4026
Marshall GR (2012) Limiting assumptions in structure-based design: binding entropy. J Comput Aided Mol Des 26(1):3–8
Lane TJ, Bowman GR, Beauchamp K, Voelz VA, Pande VS (2011) Markov state model reveals folding and functional dynamics in ultra-long md trajectories. J Am Chem Soc 133(45):18413–18419
Acknowledgments
Many have contributed to what we have collectively attempted in computer-aided molecular design; my thanks for sharing the dream. In particular I need to thank my colleagues, Drs. Xiange Zheng, for her MD simulations comparing monopole force fields with AMOEBA, and Dan Kuster for his analysis of high-resolution protein helices. Many (too numerous to mention) have generously pointed out critical mistakes along my ultimate path to humility. This includes the referees of the first draft of this manuscript. A long association with Prof. Andy Vinter (a founding editor of JCAMD) opened my eyes to the problems with monopole electrostatics, and generated a noticeable avoidance of modeling nucleic acids and membranes on my part due to their high charge density. In particular, however, my proximity to Prof. Jay Ponder during his development of AMOEBA has taught me the necessity to swim upstream, i. e. to do what is scientifically justified without concern for the myopia of the field. Hopefully, the validation of AMOEBA has reached an acceptable level of maturity, and the molecular-modeling community can reap the benefits in its application. Discussion on the problems of representing electrostatics with Prof. Anthony Stone of Cambridge University has clarified many of the issues. My thanks also to Prof. Rino Ragno and the Sapienza Università di Roma for being my host during the preparation of this perspective. Finally, my thanks to the Editors of JCAMD for providing me this opportunity to pontificate, so appropriate considering my location in Rome.
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Marshall, G.R. Limiting assumptions in molecular modeling: electrostatics. J Comput Aided Mol Des 27, 107–114 (2013). https://doi.org/10.1007/s10822-013-9634-x
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DOI: https://doi.org/10.1007/s10822-013-9634-x