Abstract
pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.
Similar content being viewed by others
References
Alder BJ, Wainwright TE (1959) Studies in molecular dynamics. I. General method. J Chem Phys 31 (2):459–466
Alexov EG, Gunner MR (1997) Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties. Biophys J 74:2075–2093
Alexov E, Mehler EL, Baker N, Baptista A, Huang Y, Milletti F, Nielsen JE, Farrell D, Carstensen T, Olsson MHM, Shen JK, Warwicker J, Williams S, Word JM (2011) Progress in the prediction of pKa values in proteins. Proteins 79(12):3260–3275
Allen MP, Tildesley DJ (1989) Computer Simulation of Liquids. Oxford University Press, Oxford
Anandakrishnan R, Aguilar B, Onufriev AV (2012) H++ 3.0: automating pK prediction and the preparation of biomolecular structures for atomistic molecular modeling and simulation. Nucleic Acids Res 40(W1):E537—541
Andermatt S, Cha J, Schiffmann F, VandeVondele J (2016) Combining linear-scaling DFT with subsystem DFT in Born-Oppenheimer and Ehrenfest molecular dynamics simulations: From molecules to a virus in solution. J Chem Theory Comput 12:3214–3227
André I, Kesvatera T, Jönsson B, Åerfeldt KS, Linse S (2004) The role of electrostatic interactions in calmodulin-peptide complex formation. Biophys J 87:1929–1938
Antonsiewicz J, McCammon JA, Gilson MK (1994) Prediction of pH-dependence properties of proteins. J Mol Biol 238:415–436
Antonsiewicz J, McCammon JA, Gilson MK (1996) The determinants of pK as in proteins. Biochemistry 35:7819–7833
Archontis G, Simonson T (2005) Proton binding to proteins: A free-energy component analysis using a dielectric continuum model. Biophys J 88:3888–3904
Atkins PW (1995) Physical Chemistry, 5th edn. Oxford University Press, London
Autreto PAS, Figueiredo FV, Nonato MC, Barroso da Silva FL (2003) Application of the Poisson–Boltzmann approach on structural biology: An initial study of the complex trypsin-BPTI. Braz J Pharm Sci Supl 2(39):203
Bacquet RJ, McCammon JA, Allison SA (1988) Ionic strength dependence of enzyme-substrate interactions. Monte Carlo and Poisson–Boltzmann results for the superoxide dismutase. J Phys Chem 92(25):7134–7141
Baker NA, Sept D, Joseph S, Holst MJ, McCammon JA (2001) Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc Natl Acad Sci USA 98:10,037–10,041
Baptista AM (2002) Comment on ”explicit-solvent molecular dynamics simulation at constant pH: Methodology and application to small amines. J Chem Phys 116(17):7766–7768. J Chem. Phys. 114, 9706 (2001)
Baptista AM, Soares CM (2001) Some theoretical and computational aspects of the inclusion of proton isomerism in the protonation equilibrium of proteins. J Phys Chem B 105:293–309
Baptista AM, Marte PJ, Petersen SB (1997) Simulation of protein conformational freedom as a function of pH: Constant-pH molecular dynamics using implicit titration. Proteins: Struc Func, and Genetics 27:523–544
Baptista AM, Teixeira VH, Soares CM (2002) Constant-pH molecular dynamics using stochastic titration. J Chem Phys 117(9):293–309
Barroso da Silva FL (1999) Statistical Mechanical Studies of Aqueous solutions and Biomolecular Systems. Reproenheten SLU Alnarp, Lund University, Sweden
Barroso da Silva FL (2013) Peculiaridades nos mecanismos moleculares de proteínas em solução aquosa: Exemplo da importância do equilíbrio ácido-base para aplicações em biotecnologia. Química 131 (oct-dez):43–48
Barroso da Silva FL, Jönsson B (2009) Polyelectrolyte–protein complexation driven by charge regulation. Soft Matter 5(15):2862–2868
Barroso da Silva FL, Jönsson B, Penfold R (2001) A critical investigation of the Tanford-Kirkwood scheme by means of Monte Carlo simulations. Prot Sci 10:1415–1425
Barroso da Silva FL, Bogren D, Söderman O, Jönsson B (2002) Titration of fatty acids solubilized in cationic, nonionic and anionic micelles: Theory and experiment. J Phys Chem B 106:3515–3522
Barroso da Silva FL, Linse S, Jönsson B (2005) Binding of charged ligands to macromolecules. Anomalous salt dependence. J Phys Chem B 109:2007–2013
Barroso da Silva FL, Lund M, Jönsson B, Åkesson T (2006) On the complexation of proteins and polyelectrolytes. J Phys Chem B 110:4459–4464
Barroso da Silva FL, Boström M, Persson C (2014) Effect of charge regulation and ion–dipole interactions on the selectivity of protein–nanoparticle binding. Langmuir 30(14):4078–4083
Barroso da Silva FL, Pasquali S, Derreumaux P, Dias LG (2016) Electrostatics analysis of the mutational and pH effects of the n-terminal domain self-association of the major ampullate spidroin. Soft Matter 12:5600–5612
Barroso da Silva FL, Derreumaux P, Pasquali S (2017a) Fast coarse-grained model for RNA titration. J Chem Phys 146(3):035,101 +
Barroso da Silva FL, MacKernan D (2017b) Benchmarking a fast proton titration scheme in implicit solvent for biomolecular simulations. J Chem Theory Comput 13(6):2915–2929
Barroso da Silva FL, Derreumaux P, Pasquali S (2017c) Protein-RNA complexation driven by the charge regulation mechanism, Biochem. Biophys. Res. Commun., in press
Bartik K, Redfield C, Dobson CM (1994) Measurement of the individual pKa values of acidic residues of hen and turkey lysozymes by two-dimensional 1H NMR. Biophys J 66(4):145
Bashford D (1988) An object-oriented programming suite for electrostatic effects in biological molecules. an experience report on the mead project. ISCOPE meeting
Bashford D (1997) An object-oriented programming suite for electrostatic effects in biological molecules. An experience report on the MEAD project. Springer Berlin Heidelberg, Berlin, pp 233–240
Bashford D, Gerwert K (1992) Electrostatic calculations of the pK a values of ionizable groups in Bacteriorhodopsin. J Mol Biol 224:473–486
Bashford D, Karplus M (1990) pKa’s of ionizable groups in proteins: Atomic detail from a continuum electrostatic model. Biochemistry 29:10,219–10,225
Bashford D, Karplus M, Canters GW (1988) Electrostatic effects of charge perturbations introduced by metal oxidation in proteins—a theoretical analysis. J Mol Biol 203:507–510
Becconi O, Ahlstrand E, Salis A, Friedman R (2017) Protein–ion interactions: Simulations of bovine serum albumin in physiological solutions of NaCl, KCl and LiCl. Isr J Chem 57(5):403– 412
Bell RP (1959) The Proton in Chemistry. Cornell University Press, New York
Bennett WD, Chen AW, Donnini S, Groenhof G, Tieleman DP (2013) Constant pH simulations with the coarse-grained martini model—application to oleic acid aggregates. Can J Chem 91:839–846
Berendsen HJC, Postma JPM, van Gunsteren WF, Hermans J (1981) Interactions models for water in relation to protein hydration. In: Pullman B (ed) Intermolecular Forces. Reidel, Dordrecht, pp 331–342
Beresford-Smith B, Chan DYC (1983) Electrical double-layer interactions in concentrated colloidal systems. Faraday Disc Chem Soc 76:65–75
Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE (2000) The protein data bank. Nucleic Acids Res 28:235–242
Beroza P, Fredkin DR, Okamura MY, Feher G (1991) Protonation of interacting residues in a protein by a Monte Carlo method: Application to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides. Proc Natl Acad Sci USA 88:5804–5808
Bhattacharjee N, Rani P, Biswas P (2013) Capturing molten globule state of α-lactalbumin through constant pH molecular dynamics simulations. J Chem Phys 138:095,101
Börjesson U, Hünenberger P H (2001) Explicit-solvent molecular dynamics simulation at constant pH: Methodology and application to small amines. J Chem Phys 114:9706– 9719
Boese A, Doltsinis N, Handy N, Sprik M (2000) New generalized gradient approximation functionals. J Chem Phys 112:1670– 1678
Borkovec M, Jönsson B, Koper G (2001) Ionization processes and proton binding in polyprotic systems: Small molecules, proteins, interfaces, and polyelectrolytes. In: Matijević E (ed) Surface and Colloid Science, Surface and Colloid Science, vol 16, Springer US, pp 99–339
Böttcher C J F (1973) Theory of Electric Polarization. Elsevier, Amsterdam
Brémond E, Ciofini I, Sancho-García J, Adamo C (2016) Nonempirical double-hybrid functionals: An effective tool for chemists. Acc Chem Res 49:1503–1513
Burger SK, Ayers PW (2011) A parameterized, continuum electrostatic model for predicting protein pKa values. Proteins 79:2044–2052
Calixto T M R (2010) Análises de propriedades eletrostáticas e estruturais de complexos de proteínas para o desenvolvimento de preditores de complexação em larga escala, Master thesis, University of So Paulo, Ribeirão Preto, SP
Campos SRR, Machuqueiro M, Baptista AM (2010) Constant-pH molecular dynamics simulations reveal a β-rich form of the human prion protein. J Phys Chem B 114(39):12,692–12,700
Capelle K (2006) A bird’s-eye view of density-functional theory. Braz J Phys 36:6378–6396
Carlsson F, Linse P, Malmsten M (2001a) Monte Carlo simulations of polyelectrolyte–protein complexation. J Phys Chem B 105:9040–9049
Carlsson F, Malmsten M, Linse P (2001b) Monte Carlo simulations of lysozyme self-association in aqueous solution. J Phys Chem B 105:12,189–12,195
Carlsson F, Hyltner E, Arnebrant T, Malmsten M, Linse P (2004) Lysozyme adsorption to charged surfaces. A Monte Carlo study. J Phys Chem B 108:9871–9881
Carnal F, Claviera A, Stoll S (2015) Modelling the interaction processes between nanoparticles and biomacromolecules of variable hydrophobicity: Monte Carlo simulations. Environ Sci: Nano 2:327–339
Carstensen T, Farrell D, Huang Y, Baker NA, Nielsen JE (2011) On the development of protein pka calculation algorithms. Proteins 79(12):3287–3298
Casasnovas R, Ortega-Castro J, Frau J, Donoso J, Munoz F (2014) Theoretical pka calculations with continuum model solvents, alternative protocols to thermodynamic cycles. Int J Quantum Chem 114:1350–1363
Case D, Darden T, Cheatham T III, Simmerling C, Wang J, Duke R, Luo R, Merz K, Pearlman D, Crowley M, Walker R, Zhang W, Wang B, Hayik S, Roitberg A, Seabra G, Wong K, Paesani F, Wu X, Brozell S, Tsui V, Gohlke H, Yang L, Tan C, Mongan J, Hornak V, Cui G, Beroza P, Mathews D, Schafmeister C, Ross W, Kollman P (2006) Amber 9. University of California, San Francisco
Chen Y, Roux B (2015) Constant-pH hybrid nonequilibrium molecular dynamics Monte Carlo simulation method. J Chem Theory Comput 11:3919–3931
Chen J, Brooks CL III, Khandogin J (2008) Recent advances in implicit solvent-based methods for biomolecular simulations. Curr Opin Struct Biol 18:140–148
Chen K, Xu Y, Rana S, Miranda OR, Dubin PL, Rotello VM, Sun L, Guo X (2011) Electrostatic selectivity in protein–nanoparticle interactions. Biomacromolecules 12(7):2552–2561
Chen W, Wallace JA, Yue Z, Shen JK (2013) Introducing titratable water to all-atom molecular dynamics at constant pH. Biophys J 105:L15—L17
Chen W, Morrow BH, Shi C, Shen JK (2014) Recent development and application of constant pH molecular dynamics. Mol Sim 40:830–838
Chen W, Huang Y, Shen JK (2016) Conformational activation of a transmembrane proton channel from constant pH molecular dynamics. J Phys Chem Lett 7(19):3961–3966
Creighton TE (1983) Proteins—Structures and Molecular Principles. W. E. Freeman and Company, New York
Dashti DS, Meng Y, Roitberg AE (2012) pH-Replica exchange molecular dynamics in proteins using a discrete protonation method. J Phys Chem B 116:8805–8811
Davies MN, Toseland CP, Moss DS, Flower DR (2006) Benchmarking pKa prediction. BMC Biochemistry 7(1):1–12
Davis ME, McCammon JA (1990) Electrostatics in biomolecular structure and dynamics. Chem Rev 90:509–521
Davis ME, Madura JD, Luty BA, McCammon JA (1991) Electrostatics and diffusion of molecules in solution. Simulations with the University-of-Houston-Brownian dynamics program. Comp Phys Commun 62:187–197
de Carvalho SJ, Ghiotto RT, Barroso da Silva FL (2006) Monte Carlo and modified Tanford–Kirkwood results for macromolecular electrostatics calculations. J Phys Chem B 110:8832– 8839
de Carvalho SJ, Fenley MO, Barroso da Silva FL (2008) Protein–ion binding process on finite macromolecular concentration. A Poisson–Boltzmann and Monte Carlo study. J Phys Chem B 112(51):16,766–16,776
Degrève L, Barroso da Silva FL (1999a) Large ionic clusters in concentrated aqueous NaCl solution. J Chem Phys 111:5150–5156
Degrève L, Barroso da Silva FL (1999b) Structure of concentrated aqueous NaCl solution: a Monte Carlo study. J Chem Phys 110(6):3070–3078
Degrève L, Barroso da Silva FL (2000) Detailed microscopic study of 1M aqueous NaCl solution by computer simulations. J Mol Liquids 87:217–232
Degrève L, Lozada-Cassou M, Sánchez E, González-Tovar E (1993) Monte Carlo simulation for a symmetrical electrolyte next to a charged spherical colloid particle. J Chem Phys 98(11):8905–8909
De Groot BL, Frigato T, Helms V, Grubmuller H (2003) The mechanism of proton exclusion in the aquaporin-1 water channel. J Mol Biology 333(2):279–293
Delboni L, Barroso da Silva FL (2016) On the complexation of whey proteins. Food Hydrocolloids 55:89–99
Demchuk E, Wade RC (1996) Improving the continuum dielectric approach to calculating p K as of ionizable groups in proteins. J Phys Chem B 100:17,373–17,387
Derjaguin BV, Landau L (1941) Acta Phys Chim URSS 14:633
Devlin T M (ed) (1997) Textbook of Biochemistry with Clinical Correlations. Wiley-Liss, New York
Dobrev P, Donnini S, Groenhof G, Grubmüller H (2017) Accurate three states model for amino acids with two chemically coupled titrating sites in explicit solvent atomistic constant ph simulations and pKa calculations. J Chem Theory Comput 13:147–160
Donnini S, Tegeler F, Groenhof G, Grubmüller H (2011) Constant pH simulations with the coarse-grained martini model—application to oleic acid aggregates. J Chem Theory Comput 7:1962– 1978
Donnini S, Ullmann RT, Groenhof G, Grubmüller H (2016) Charge-neutral constant pH molecular dynamics simulations using a parsimonious proton buffer. J Chem Theory Comput 12:1040–1051
Dudev T, Lim C (2000) Metal binding in proteins: The effect of the dielectric medium. J Phys Chem B 104:3692–3694
Egan T, O’Riordan D, O’Sullivan M, Jacquier JC (2014) Cold-set whey protein microgels as pH modulated immobilisation matrices for charged bioactives. Food Chem 156:197–203
Eike BHMDM, Murch BP, Koenig PH, Shen JK (2014) Predicting proton titration in cationic micelle and bilayer environments. J Chem Phys 141:084,714
Enciso M, Schutte C, Site LD (2013) A pH-dependent coarse-grained model for peptides. Soft Matter 9:6118–6127
Evans DF, Wennerström H (1994) The Colloidal Domain. VCH Publishers, New York
Fennell CJ, Li L, Dill KA (2012) Simple liquid models with corrected dielectric constants. J Phys Chem B 116(23):6936–6944
Fernández M S, Fromherz P (1977) Lipoid pH indicators as probes of electrical potential and polarity in micelles. J Phys Chem 81:1755–1761
Fernández DP, Mulev Y, Goodwin ARH, Levelt-Sengers JMH (1995) A database for the static dielectric constant of water and steam. J Phys Chem Ref Data 24(1):33–70
Florián J, Warshel A (1997) Langevin dipoles model for ab initio calculations of chemical processes in solution: Parametrization and application to hydration free energies of neutral and ionic solutes and conformational analysis in aqueous solution. J Phys Chem B 101:5583–5595
Forsyth WR, Gilson MK, Antonsiewicz J, Jaren OR, Robertson AD (1998) Theoretical and experimental analysis of ionization equilibria in ovomucoid third domain. Biochemistry 37:8643–8652
Freitas A, Shimizu K, Dias L, Quina F (2007) A computational study of substituted flavylium salts and their quinonoidal conjugate- bases: S0 ®;s1 electronic transition, absolute pka and reduction potential calculations by DFT and semiempirical methods. J Braz Chem Soc 18:1537–1546
Friedman HL (1977) Introduction. Faraday Discuss of the Chem Soc 64:7–15
Friedman HL (1981) Electrolyte solutions at equilibrium. Ann Rev Phys Chem 32:179–204
Fuentes-Azcatl R, Barbosa MC (2016) Thermodynamic and dynamic anomalous behavior in the tip4p/ 𝜖 water model. Physica A 444:86–94
Garcia-Moreno B (1995) Probing structural and physical basis of protein energetics linked to protons and salt. Methods in Enzymnology 259:512–538
Garrett R, Grisham C (1999) Biochemistry. Harcourt Brace & Company, EUA
Genova A, Ceresoli D, Kishtal A, Andreussi O, DiStasio RA Jr, Pavanello M (2017) eQE: An open-source density functional embedding theory code for the condensed phase. Int J Quantum Chem pp e25,401–n/a, e25401
Goh GB, Knight JL, Brooks CL (2013a) pH-dependent dynamics of complex RNA macromolecules. J Chem Theory Comput 9(2):935–943
Goh GB, Knight JL, Brooks CL (2013b) Toward accurate prediction of the protonation equilibrium of nucleic acids. J Phys Chem Lett 4(5):760–766
González-Tovar E, Lozada-Cassou M (1989) The spherical double layer: A hypernetted chain mean spherical approximation calculation for a model spherical colloid particle. J Phys Chem 93:3761–3768
Gordon M, Fedorov D, Pruitt S, Slipchenko L (2012) Fragmentation methods: A route to accurate calculations on large systems. Chem Rev 112:632–672
Greberg H, Kjellander R (1994) Electric double-layer properties calculated in the anisotropic reference hypernetted chain approximation. Mol Phys 83:789–801
Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27:1787–1799
Gu W, Frigato T, Straatsma TP, Helms V (2007) Dynamic protonation equilibrium of solvated acetic acid. Angew Chem Int Ed (English) 46(16):2939–2943
Guillot B (2002) A reappraisal of what we have learnt during three decades of computer simulations on water. J Mol Liquids 101(1-3):219–260
Harano Y, Kinoshita M (2006) On the physics of pressure denaturation of proteins. J Phys: Condens Matter 18:L107—L113
Harris TK, Turner GJ (2002) Structural basis of perturbed pK a values of catalytic groups in enzyme active sites. Life 53:85–98
Harvey SC (1989) Treatment of electrostatic effects in macromolecular modeling. Proteins: Struc. Func and Genetics 5:78–92
Hassanali A, Prakash MK, Eshet H, Parrinello M (2011) On the recombination of hydronium and hydroxide ions in water. Proc Natl Acad Sci USA 108(51):20,410–20,415
Havranek JJ, Harbury PB (1999) Tanford–Kirkwood electrostatics for protein modeling. Proc Natl Acad Sci USA 96:11,145–11,150
He X, Jr KM (2010) Divide and conquer Hartree–Fock calculations on proteins. J Chem Theory Comput 6:405–411
He Y, Xu J, Pan XM (2007) A statistical approach to the prediction of pK a values in proteins. Proteins: Struc Func, and Bioinformatics 69:75–82
Hess B, van der Vegt NFA (2006) Hydration thermodynamic properties of amino acid analogues: a systematic comparison of biomolecular force fields and water models. J Phys Chem B 110(35):17,616–17,626
Hill TL (1955) Approximate calculations of the electrostatic free energy of nucleic acids and other cylindrical macromolecules. Arch Biochem Biophys 57:229–239
Hill TL (1956a) Influence of electrolyte on effective dielectric constants in enzymes, proteins and other molecules. J Chem Phys 60:253–255
Hill TL (1956b) Statistical Mechanics. McGraw-Hill, New York
Hill TL (1986) An Introduction to Statistical Thermodynamics. Dover Publications Inc., New York
Ho J, Coote M (2009a) pka calculation of some biologically important carbon acids—an assessment of contemporary theoretical procedures. J Chem Theory Comput 5:295–306
Ho J, Coote M (2009b) A universal approach for continuum solvent pka calculations: are we there yet Theor Chem Acc 125:3–21
Ho J, Ertem M (2016) Calculating free energy changes in continuum solvation models. J Phys Chem B 120:1319–1329
Holst M (1993) Multilevel methods for the Poisson–Boltzmann equation. PhD thesis, Numerical Computing Group, Department of Computer Science. University of Illinois at Urbana-Champaign, USA
Honig B, Nicholls A (1995) Classical electrostatics in biology and chemistry. Science 268:1144–1149
Horinek D, Mamatkulov SI, Netz RR (2009) Rational design of ion force fields based on thermodynamic solvation properties. J Chem Phys 130:124,507
Hünenberger P H, McCammon JA (1999) Ewald artifacts in computer simulations of ionic solvation and ion–ion interactions: A continuum study. J Chem Phys 110:1856–1872
Hurtley SM (2015) New players in Lou Gehrig’s disease. Science 347(6229):1432
Hyltegren K, Skepö M (2017) Adsorption of polyelectrolyte-like proteins to silica surfaces and the impact of pH on the response to ionic strength. A Monte Carlo simulation and ellipsometry study. J Colloid Interface Sci 494:266–273
Jin Y, Hoxie RS, Street TO (2017) Molecular mechanism of bacterial hsp90 ph-dependent ATPase activity. Protein Sci 26(6):1206–1213
Jönsson B (1981) The Thermodynamics of Ionic Amphiphilie–Water Systems—A Theoretical Analysis. PhD thesis. Lund University, Sweden
Jönsson B, Åkesson T, Woodward C (1996) Theory of interactions in charged colloids. In: Arora AK, Tata BVR (eds) Ordering and phase transitions in charged colloids, VCH, New York, pp 295–313
Jönsson B, Lund M, Barroso da Silva FL (2007) Electrostatics in macromolecular solution. In: Dickinson E, Leser M E (eds) Food Colloids: Self-Assembly and Material Science, Royal Society of Chemistry, Londres, pp 129–154
Juffer AH (1992) Melc—The Macromolecular Electrostatics Computer program. Laboratory of Physical Chemistry. University of Groningen, The Netherlands
Juffer AH (1993) On the modelling of solvent mean force potentials—from liquid argon to solvated macromolecules. PhD thesis, Rijkuniversiteit Groningen, The Netherlands
Juffer AH (1998) Theoretical calculations of acid-dissociation constants of proteins. Biochem Cell Biol 76:198–209
Juffer AH, Botta EFF, van Keulen BAM, van der Ploeg A, Berendsen HJC (1991) The electric potential of a macromolecule in a solvent: A fundamental approach. J Comp Phys 97:144–171
Kamerlin SL, Haranczyk M, Warshel A (2009) Progresses in ab initio QM/MM free energy simulations of electrostatic energies in proteins: Accelerated QM/MM studies of pKa, redox reactions and solvation free energies. J Phys Chem B 113:1253–1272
Karplus M, McCammon JA (1979) Protein structural fluctuations during a period of 100 ps. Nature 277:578
Karplus M, Gelin BR, McCammon JA (1977) Dynamics of folded proteins. Nature 267:585–590
Kesvatera T, Jönsson B, Thulin E, Linse S (1996) Measurement and modelling of sequence-specific pK a values of calbindin D 9k. J Mol Biol 259:828
Kesvatera T, Jönsson B, Thulin E, Linse S (1999) Ionization behavior of acidic residues in calbindin D 9k. Proteins: Struc Func, and Genetics 37:106–115
Kesvatera T, Jönsson B, Thulin E, Linse S (2001) Focusing of the electrostatic potential at EF-hands of calbindin D 9k: Titration of acidic residues. Proteins: Struc Func, and Genetics 45:129–135
Khandogin J, Brooks CL III (2005) Constant pH molecular dynamics with proton tautomerism. Biophys J 89:141–157
Kim MO, McCammon JA (2016) Computation of pH-dependent binding free energies. Biopolymers 105:43–49
King G, Lee FS, Warshel A (1991) Microscopic simulations of macroscopic dielectric constants of solvated proteins. J Chem Phys 95:4366–4377
Kirkwood JG (1934a) Solutions containing zwitterions: Erratum. J Chem Phys 2:713
Kirkwood JG (1934b) Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J Chem Phys 2:351–361
Kirkwood JG, Shumaker JB (1952) Forces between protein molecules in solution arising from fluctuations in proton charge and configuration. Proc Natl Acad Sci USA 38:863–871
Kirkwood JG, Westheimer FH (1938) The electrostatic influence of substituents on the dissociation constant of organic acids. I J Chem Phys 6:506–512
Klamt A (1995) Conductor-like screening model for real solvents: A new approach to the quantitative calculation of solvation phenomena. J Phys Chem 99:2224–2235
Ko J, Murga LF, Wei Y, Ondrechen MJ (2005) Prediction of active sites for protein structures from computed chemical properties. Bioinformatics 21(suppl 1):i258—i265
Kong X, Brooks CL III (1996) λ-dynamics: a new approach to free energy calculations. J Chem Phys 105:128–141
Koukiekolo R, Sagan SM, Pezacki JP (2007) Effects of pH and salt concentration on the siRNA binding activity of the RNA silencing suppressor protein p19. FEBS Lett 581:3051–3056
Krieger E, Nielsen JE, Spronk CAEM, Vriend G (2006) Fast empirical pKa prediction by Ewald summation. J Mol Graph Model 25:481–486
Kukic P, Farrell D, McIntosh LP, García-Moreno JKS, Toleikis Z, Teilum K, Nielsen JE (2013) Protein dielectric constants determined from NMR chemical shift perturbations. J Am Chem Soc 135 (45):16,968–16,976
Kurut A, Persson BA, Åkesson T, Forsman J, Lund M (2012) Anisotropic interactions in protein mixtures: Self assembly and phase behavior in aqueous solution. J Phys Chem Lett 3(6):731–734
Kurut A, Dicko C, Lund M (2015) Dimerization of terminal domains in spiders silk proteins is controlled by electrostatic anisotropy and modulated by hydrophobic patches. ACS Biomater Sci Eng 1(6):363–371
Labbez C, Jönsson B (2007) A new Monte Carlo method for the titration of molecules and minerals. In: gström B K (ed) Lecture Notes in Computer Science. Springer-Verlag, Berlin, pp 66–72
Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci USA 99:12,562–12,566
Lee MS, Jr FRS, Brooks CL (2004) Constant-pH molecular dynamics using continuous titration coordinates. Proteins 56:738–752
Lee J, Miller BT, Damjanovi A, Brooks BR (2015) Enhancing constant-pH simulation in explicit solvent with a two-dimensional replica exchange method. J Chem Theory Comput 11:2560–2574
Lee J, Miller BT, Brooks BR (2016) Computational scheme for pH-dependent binding free energy calculation with explicit solvent. Prot Sci 25:231–243
Legault P, Pardi A (1994) In situ probing of adenine protonation in RNA by 13C NMR. J Am Chem Soc 116(18):8390–8391
Levesque D, Weis JJ, Hansen JP (1986) Simulation of classical fluids. In: Binder K (ed) Monte Carlo Methods in Statistical Physics, vol 5. Springer-Verlag, Berlin, pp 47–119
Levitt M, Lifson S (1969) Refinement of protein conformations using a macromolecular energy minimization procedure. J Mol Biol 46:269
Lewis M, Bamforth C (2006) Essays in Brewing Science. Springer
Li H, Hains A, Everts J, Robertson A, Jensen J (2002) The prediction of protein pka’s using qm/mm: The pka of lysine 55 in turkey ovomucoid third domain. J Phys Chem B 106:3486–3494
Li H, Robertson AD, Jensen JH (2005) Very fast empirical prediction and rationalization of protein pKa values. Proteins: Struct Funct Bioinf 61(4):704–721
Lill MA, Helms V (2001) Molecular dynamics simulation of proton transport with quantum mechanically derived proton hopping rates (Q-HOP MD). J Chem Phys 115(17):7993–8005
Linderstrøm-Lang K (1924) Om proteinstoffernes ionisation. C R Trav Lab Carlsberg [Meddelelser fra Carlsberg Lab] 15(7):1–28
Linse P, Jönsson B (1983) A Monte Carlo study of the electrostatic interaction between highly charged aggregates. A test of the cell model applied to micellar systems. J Chem Phys 78:3167–3176
Linse P, Lobaskin V (1999) Electrostatic attraction and phase separation in solutions of like-charge colloidal particles. submitted
Linse S, Jönsson B, Chazin WJ (1995) The effect of protein concentration on ion binding. Proc Natl Acad Sci USA 92:4748–4752
Lizatović R, Aurelius O, Stenström O, Drakenberg T, Akke M, Logan DT, André I (2016) A de novo designed coiled-coil peptide with a reversible ph-induced oligomerization switch. Structure 24(6):946–955
Löffler G, Screiber H, Steinhauser O (1997) Calculation of the dielectric properties of a protein and its solvent: Theory and a case study. J Mol Biol 270:520–534
Lovett RA, Mou CY, Buff FP (1976) The structure of the liquid–vapor interface. J Chem Phys 65:570–572
Lund M, Jönsson B (2003) A mesoscopic model for protein–protein interactions in solution. Biophys J 85:2940–2947
Lund M, Jönsson B (2005) On the charge regulation of proteins. Biochemistry 44(15):5722–5727
Lund M, Jönsson B (2013) Charge regulation in biomolecular solution. Q Rev Biophys 46:265–281
Lyklema J (1991) Fundamentals of Interface and Colloid Science. Academic Press, San Diego
Lyubartsev AP, Laaksonen A (1996) Concentration effects in aqueous NaCl solutions. A molecular dynamics simulation. J Phys Chem 100:16,410–16,418
Machuqueiro M, Baptista AM (2007) The pH-dependent conformational states of kyotorphin: A constant-pH molecular dynamics study. Biophys J 92:1836–1845
Machuqueiro M, Baptista AM (2011) Is the prediction of pka values by constant-pH molecular dynamics being hindered by inherited problems?. Proteins: Struct Funct Bioinf 79(12):3437– 3447
Madura JD et al (1994) Biological applications of electrostatic calculations and Brownian dynamics simulations. In: Lipkowitz K B, Boyd D B (eds) Reviews in Computational Chemistry, vol 5. VCH Publishers, Inc, New York, pp 229–267
Magalhães P R, Oliveira ASF, Campos SRR, Soares CM, Baptista AM (2017) Effect of a pH gradient on the protonation states of cytochrome c oxidase: A continuum electrostatics study. J Chem Inf Model 57 (2):256–266
Mahadevan TS, Garofalini SH (2008) Dissociative water potential for molecular dynamics simulations. J Phys Chem B 111(30):8919–8927
Marenich A, Cramer C, Truhlar D (2009) Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J Phys Chem B 113:6378–6396
McQuarrie DA (1976) Statistical Mechanics. Harper Collins, New York
Medda L, Barse B, Cugia F, Boström M, Parsons DF, Ninham BW, Monduzzi M, Salis A (2012) Hofmeister challenges: Ion binding and charge of the BSA protein as explicit examples. Langmuir 28:16,355–16,363
Meyer TD, Ensing B, Rogge S, Clerck KD, Meijer E, Speybroeck VV (2016) Acidity constant (pKa) calculation of large solvated dye molecules: Evaluation of two advanced molecular dynamics methods. ChemPhysChem 17:3447–3459
Mongan J, Case DA (2005) Biomolecular simulations at constant pH. Curr Opin Struct Biol 15:157–163
Mongan J, Case DA, McCammon JA (2004) Constant pH molecular dynamics in generalized born implicit solvent. J Comp Chem 25:2038–2048
Mukerjee P, Banerjee K (1964) A study of the surface pH of micelles using solubilized indicator dyes. J Phys Chem 68:3567–3574
Noid WG (2013) Perspective: Coarse-grained models for biomolecular systems. J Chem Phys 139:090,901
Northrup SH, McCammon JA (1980) Simulation methods for protein structure fluctuations. Biopolymers 19:1001–1016
Nozaki Y, Tanford C (1967) Examination of titratation behavior. Methods Enzymol 11:715–734
Nylander KHT, Lund M, Skepö M (2017) Adsorption of the intrinsically disordered saliva protein histatin 5 to silica surfaces. A Monte Carlo simulation and ellipsometry study. J Colloid Interface Sci 467:280–290
Oliveira ASF, Campos SRR, Baptista AM, Soares CM (2016) Coupling between protonation and conformation in cytochrome c oxidase: Insights from constant-pH MD simulations. Biochimica et Biophysica Acta 1857:759–771
Olsson MH, Sondergard CR, Rostkowski M, Jensen JH (2011) PROPKA3: Consistent treatment of internal and surface residues in empirical pKa predictions. J Chem Theory Comput 7(2):525–537
Orttung WH (1977) Direct solution of the Poisson equation for biomolecules of arbitrary shape, polarizability density and charge distribution. Ann N Y Acad Sci 303:22–37
Outhwaite C, Bhuiyan L (1991) A modified Poisson–Boltzmann analysis of the electric double layer around an isolated spherical macroion. Mol Phys 74(2):367–381
Overbeek JTG (1982) A fascinating subject: Introductory lecture in Colloidal Dispersion. The Royal Society of Chemistry. Ed. J. W. Goodwin, London
Pechlaner M, Donghi D, Zelenay V, Sigel RKO (2015) Protonation-dependent base flipping at neutral pH in the catalytic triad of a self-splicing bacterial group II intron. Angew Chem Int Ed Engl 54(33):9687–9690
Penfold R, Warwicker J, Jönsson B (1998) Electrostatic models for calcium binding proteins. J Phys Chem B 102:8599–8610
Persson B, Lund M, Forsman J, Chatterton DEW, Åkesson T (2010) Molecular evidence of stereo-specific lactoferrin dimers in solution. Biophys Chem 3(3):187–189
Perutz MF (1978) Electrostatic effects in proteins. Science 201:1187–1191
Piper DW, Fenton BH (1965) pH stability and activity curves of pepsin with special reference to their clinical importance. Gut 6:506–508
Project CSE (1995) Direct and Inverse Bioelectric Field Problems. http://csep1.phy.ornl.gov/bf/bf.html
Radak BK, Roux B (2016) Efficiency in nonequilibrium molecular dynamics Monte Carlo simulations. J Chem Phys 145:124,109
Reitz JR, Milford FJ, Christy RW (1986) Fundamentos da teoria eletromagnética. Rio de Janeiro, Editora Campus
Rossini E, Knapp EW (2016) Proton solvation in protic and aprotic solvents. J Comput Chem 37:1082–1091
Roxby R, Tanford C (1971) Hydrogen ion titration curve of lysozyme in 6 M guanidine hydrochloride. Biochemistry 10:3348–3352
Russel WB, Saville DA, Schowalter WR (1989) Colloidal Dispersions. Cambridge University Press, Cambridge
Sakalli I, Knapp EW (2015) pKa in proteins solving the Poisson–Boltzmann equation with finite elements. J Comput Chem 36(29):2147–2157
Santos HAF, Cosa DVV, Teixeira VH, Baptista AM, Machuqueiro M (2015) Constant-pH MD simulations of DMPA/DMPC lipid bilayers. J Chem Theory Comput 11(12):5973–5979
Schaller W, Robertson AD (1995) pH, ionic strength, and temperature dependences of ionization equilibria for the carboxyl groups in turkey ovomucoid third domain. Biochemistry 34(14):4714–4723
Schlichter CP (1980) Principles of Magnetic Resonance. Springer, Berlin
Schmitz KS (ed) (1994) Macro-ion Characterization: From Dilute Solutions to Complex Fluids. American Chemistry Society, Washington
Schönichen A, Webb BA, Jacobson MP, Barber DL (2013) Considering protonation as a posttranslational modification regulating protein structure and function. Annu Rev Biophys 42:289–314
Schutz CN, Warshel A (2001) What are the dielectric “constants” of proteins and how to validate electrostatic models?. Proteins: Struc Func, and Genetics 44:400–417
Sham YY, Chu ZT, Warshel A (1997) Consistent calculations of pK a’s of ionizable residues in proteins: Semi-microscopic and microscopic approaches. J Phys Chem B 101:4458–4472
Sharp KA, Honig B (1990) Calculating total electrostatic energies with the nonlinear Poisson–Boltzmann equation. J Phys Chem 94:7684–7692
Sharp KA, Fine R, Honig B (1987) Computer simulations of the diffusion of a substrate to an active site of an enzyme. Science 236:1460–1463
Shaw DJ (1992) Introduction to Colloid and Surface Chemistry, 4th edn. Butterworths, London
Sheinerman FB, Norel R, Honig B (2000) Curr Opin Struct Biol 10:153–159
Shimizu K, Freitas AA, Farah JPS, Dias LG (2005) Predicting hydration free energies of neutral compounds by a parametrization of the polarizable continuum model. J Phys Chem A 109:11,322–11,327
Shukla A, Mylonas E, Di Cola E, Finet S, Timmins P, Narayanan T, Svergun DI (2008) Absence of equilibrium cluster phase in concentrated lysozyme solutions. Proc Natl Acad Sci USA 105(13):5075–5080
Simonson T (2013) What is the dielectric constant of a protein when its backbone is fixed J Chem Theory Comput 9(10):4603–4608
Simonson T, Perahia D (1995) Microscopic dielectric properties of cytochrome c from molecular dynamics simulations in aqueous solution. J Am Chem Soc 117:7987–8000
Simonson T, Brooks CL III (1996) Charge screening and the dielectric constant of proteins: Insights from molecular dynamics. J Am Chem Soc 118:8452–8458
Smith N, Witham S, Sarkar S, Zhang J, Li L, Li C, Alexov E (2012) Delphi web server v2: Incorporating atomic-style geometrical figures into the computational protocol. Bioinformatics 28(12):1655–1657
Soares RO, Torres PHM, da Silva ML, Pascutti PG (2016) Unraveling HIV protease flaps dynamics by constant pH molecular dynamics simulations. J Structural Biology 195:261–226
Socher E, Stich H (2016) Mimicking titration experiments with MD simulations: A protocol for the investigation of pH-dependent effects on proteins. Scientific Reports 22523:1–12
Sorensen SPL (1909) Biochem Z 21:131
Sorensen SPL, Hempel MHJ, Palitzsch S (1917) Studies on proteins. II. the capacity of egg-albumin to combine with acids or bases. C R Trav Lab Carlsberg [Meddelelser fra Carlsberg Lab] 12:68–163
Srivastava D, Santiso E, Gubbins KE, Barroso da Silva FL (2017) Computationally mapping pKa shifts due to the presence of a polyelectrolyte chain around whey proteins. http://dx.doi.org/https://doi.org/10.1021/acs.langmuir.7b02271
Stanton CL, Houk KN (2008) Benchmarking pKa prediction methods for residues in proteins. J Chem Theory Comput 4(6):951–966
Steiner E, Gastl M, Becker T (2011) Protein changes during malting and brewing with focus on haze and foam formation: a review. Eur Food Res Technol 232:191–204
Stern HA (2007) Molecular simulation with variable protonation states at constant pH. J Chem Phys 126:164,112
Stigter D, Dill KA (1990) Charge effects on folded and unfolded proteins. Biochemistry 29:1262–1271
Stoll S (2014) Computer simulations of soft nanoparticles and their interactions with DNA-like polyelectrolytes. In: Callejas-Fernandez J (ed) Soft Nanoparticles for Biomedical Applications. Royal Society of Chemistry, Londres, pp 342–371
Svensson B, Jönsson B, Woodward CE (1990) Electrostatic contributions of the binding of Ca 2+ in calbindin mutants. A Monte Carlo study. Biophys Chem 38:179–183
Svensson BR, Woodward CE (1988) Widom’s method for uniform and non-uniform electrolyte solutions. Mol Phys 64:247–259
Swails JM, York DM, Roitberg AE (2014) Constant pH replica exchange molecular dynamics in explicit solvent using discrete protonation states: Implementation, testing, and validation. J Chem Theory Comput 10:1341–1352
Szabo A, Ostlund NS (1989) Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. McGraw-Hill, New York
Takano Y, Houk KN (2005) Benchmarking the conductor-like polarizable continuum model (CPCM) for aqueous solvation free energies of neutral and ionic organic molecules. J Chem Theory Comput 1:70–77
Tanford C (1957a) The location of electrostatic charges in Kirkwood’s model of organic ions. J Am Chem Soc 79:5348–5352
Tanford C (1957b) Theory of protein titration curves II. Calculations for simple models at low ionic strength. J Am Chem Soc 79:5340–5347
Tanford C, Kirkwood JG (1957) Theory of protein titration curves I. General equations for impenetrable spheres. J Am Chem Soc 79:5333–5339
Tanford C, Roxby R (1972) Interpretation of protein titration curves. Application to lysozyme. Biochemistry 11:2192–2198
Tang CL, Alexov E, Pyle AM, Honig B (2007) Calculation of pKas in RNA: on the structural origins and functional roles of protonated nucleotides. J Mol Biol 366(5):1475–1496
Taylor D, Ángyán J, Galli G, Zhang C, Gygi F, Hirao K, Song J, Rahul K, von Lilienfeld A, Podeszwa R, Bulik I, Henderson T, Scuseria G, Toulouse J, Peverati R, Truhlar D, Szalewicz K (2016) Blind test of density-functional-based methods on intermolecular interaction energies. J Chem Phys 145:124,105
Teixeira AA, Lund M, Barroso da Silva FL (2010) Fast proton titration scheme for multiscale modeling of protein solutions. J Chem Theory Comput 6(10):3259–3266
Teleman O, Svensson B, Jönsson B (1991) Efficiency in statistical mechanical simulations of biomolecules—computer programs for molecular and continuum modelling. Comput Phys Commun 62(2-3):307–326
Terán L M, Dí az-Herrera E, Lozada-Cassou M, Saavedra-Barrera R (1989) A comparison of numerical methods for solving nonlinear integral equations found in liquid theories. J Comp Phys 84:326–342
Thaplyal P, Bevilacqua PC (2014) Experimental approaches for measuring pKa’s in RNA and DNA. Methods Enzymol 549:189–219
Thurlkill RL, Grimsley GR, Scholtz JM, Pace CN (2006) pK values of the ionizable groups of proteins. Prot Sci 15:1214–1218
Tironi IG, Sperb R, Smith PE, van Gunsteren WF (1995) A generalized reaction field method for molecular dynamics simulations. J Chem Phys 102:5451–5459
Tummanapelli A, Vasudevan S (2015) Ab initio molecular dynamics simulations of amino acids in aqueous solutions: Estimating pka values from metadynamics sampling. J Phys Chem B 119:12,249–12,255
Usui S (1984) Electrical double layer. In: Kitahara A, Watanabe A (eds) Electrical Phenomena at Interfaces – Fundamentals, Measurements, and Applications. Marcel Dekker, Inc., New York, pp 15–46
van Gunsteren WF, Berendsen HJC (1990) Computer simulation of molecular dynamics: Methodology, applications, and perspective in chemistry. Angew Chem Int Ed Engl 29:992–1023
Varma S, Jakobsson E (2004) Ionization states of residues in OmpF and mutants: Effects of dielectric constant and interactions between residues. Biophys J 86(2):690–704
Verlet L (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard–Jones molecules. Phys Rev 159(1):98–103
Verwey EJW, Overbeek JTG (1948) Theory of the Stability of Lyophobic Colloids. Elsevier Publishing Company Inc., Amsterdam
Vicatos S, Roca M, Warshel A (2009) Effective approach for calculations of absolute stability of proteins using focused dielectric constants. Proteins 77(3):670–684
Vila-Viçosa D V V, Campos SRR, Baptista AM, Machuqueiro M (2012) Reversibility of prion misfolding: Insights from constant-pH molecular dynamics simulations. J Phys Chem B 116(30):8812–8821
Wagoner T, Vardhanabhuti B, Foegeding EA (2016) Designing whey protein–polysaccharide particles for colloidal stability. Annu Rev Food Sci Technol 7:93–116
Wallace JA, Shen JK (2009) Predicting pKa values with continuous constant pH molecular dynamics. Methods Enzymol 466:455–475
Wallace JA, Shen JK (2011) Continuous constant pH molecular dynamics in explicit solvent with pH-based replica exchange. J Chem Theory Comput 7:2617–2629
Wallace JA, Shen JK (2012) Unraveling a trap-and-trigger mechanism in the ph-sensitive self-assembly of spider silk proteins. J Phys Chem Lett 3(5):658–662
Wang L, Li L, Alexov E (2015) pKa predictions for proteins, RNAs, and DNAs with the Gaussian dielectric function using DelPhi pKa. Proteins 83:2186–2197
Wang L, Zhang M, Alexov E (2016) DelPhiPKa web server: predicting pKa of proteins, RNAs and DNAs. Bioinformatics 34(4):614– 615
Warshel A (1981) Calculations of enzymatic reactions: Calculations of pKa, proton transfer reactions, and general acid catalysis reactions in enzymes. Biochemistry 20:3167–3177
Warshel A (2014) Multiscale modeling of biological functions: From enzymes to molecular machines (Nobel Lecture). Angew Chem Int Ed 53:10020–10031
Warshel A, Åqvist J (1991) Electrostatic energy and macromolecular function. Annu Rev Biophys Biophys Chem 20:267–298
Warshel A, Levitt M (1976) Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biology 103(2):227– 249
Warshel A, Papazyan A (1998) Electrostatic effects in macromolecules: Fundamental concepts and practical modeling. Curr Opin Struct Biol 8:211–217
Warshel A, Russel ST, Churg AK (1984) Macroscopic models for studies of electrostatic interactions in proteins: Limitations and applicability. Proc Natl Acad Sci USA 81:4785–4789
Warshel A, Sharma PK, Kato M, Parson WW (2006) Modeling electrostatic effects in proteins. Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics 1764(11):1647–1676
Warwicker J (1999) Simplified methods for pK a and acid pH-dependent stability estimation in proteins: Removing dielectric and counterion boundaries. Prot Sci 8:418–425
Warwicker J, Watson HC (1982) Calculation of the electric potential in the active site cleft due to α-helix dipoles. J Mol Biol 157:671– 679
Westheimer FH, Kirkwood JG (1938) The electrostatic influence of substituents on the dissociation constant of organic acids. II. J Chem Phys 6:513–517
Williams SL, de Oliveira CAF, McCammon JA (2010) Coupling constant ph molecular dynamics with accelerated molecular dynamics. J Chem Theory Comput 6:560–568
Woodward CE, Svensson B (1991) Potentials of mean force in charged systems: Application to Superoxide Dismutase. J Phys Chem 95:7471–7477
Xiao K, Yu H (2016) Rationalising pKa shifts in Bacillus circulans xylanase with computational studies. Phys Chem Chem Phys 18:30,305–30,312
Ye K, Malinina L, Patel D (2003) Recognition of small interfering RNA by a viral suppressor of RNA silencing. Nature 426:874– 878
You TJ, Bashford D (1995) Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility. Biophys J 69(5):1721–1733
Yu W, Lopes PEM, Roux B, MacKerell Jr AD (2013) Six-site polarizable model of water based on the classical drude oscillator. J Chem Phys 138:034,508
Acknowledgements
This work was supported in part by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Fapesp 2015/16116-3 (FLBDS), Fapesp 2013/08166-5 and 2017/03204-7 (LGD)], the University Global Partnership Network (UGPN) Research Collaboration Fund (FLBDS) and the University College Dublin (UCD) through a visiting professors grant - Seed Funding (FLBDS). FLBDS also thanks the support of the University of São Paulo through the NAP-CatSinQ (Research Core in Catalysis and Chemical Synthesis), the computing hours at Rice University through the international collaboration program with USP and at The Swedish National Infrastructure for Computing (SNIC 2015/10-6), and the hospitality of the UCD School of Physics, UCD Institute for Discovery and CECAM/IRL. It is also a pleasure to acknowledge the collaboration in previous works and/or fruitful discussions with Bo Jönsson, Bo Svensson, Torbjörn Åkesson (in memoriam), Mikael Lund, Aatto Laaksonen, Erik Santiso, Samuela Pasquali, Philippe Derreumaux, Catherine Etchebest, and Donal MacKernan.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
Fernando Luís Barroso da Silva declares that he has no conflicts of interest. Luis Gustavo Dias declares that he has no conflicts of interest.
Additional information
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
This article is part of a Special Issue on ‘Latin America’ edited by Pietro Ciancaglini and Rosangela Itri.
Rights and permissions
About this article
Cite this article
Barroso daSilva, F., Dias, L. Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems. Biophys Rev 9, 699–728 (2017). https://doi.org/10.1007/s12551-017-0311-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12551-017-0311-5