The multiple roles of histidine in protein interactions
© Liao et al; licensee Chemistry Central Ltd. 2013
Received: 24 September 2012
Accepted: 27 November 2012
Published: 1 March 2013
Among the 20 natural amino acids histidine is the most active and versatile member that plays the multiple roles in protein interactions, often the key residue in enzyme catalytic reactions. A theoretical and comprehensive study on the structural features and interaction properties of histidine is certainly helpful.
Four interaction types of histidine are quantitatively calculated, including: (1) Cation-π interactions, in which the histidine acts as the aromatic π-motif in neutral form (His), or plays the cation role in protonated form (His+); (2) π-π stacking interactions between histidine and other aromatic amino acids; (3) Hydrogen-π interactions between histidine and other aromatic amino acids; (4) Coordinate interactions between histidine and metallic cations. The energies of π-π stacking interactions and hydrogen-π interactions are calculated using CCSD/6-31+G(d,p). The energies of cation-π interactions and coordinate interactions are calculated using B3LYP/6-31+G(d,p) method and adjusted by empirical method for dispersion energy.
The coordinate interactions between histidine and metallic cations are the strongest one acting in broad range, followed by the cation-π, hydrogen-π, and π-π stacking interactions. When the histidine is in neutral form, the cation-π interactions are attractive; when it is protonated (His+), the interactions turn to repulsive. The two protonation forms (and pKa values) of histidine are reversibly switched by the attractive and repulsive cation-π interactions. In proteins the π-π stacking interaction between neutral histidine and aromatic amino acids (Phe, Tyr, Trp) are in the range from -3.0 to -4.0 kcal/mol, significantly larger than the van der Waals energies.
The molecular interactions of histidine with other amino acids and metallic cations in proteins can be classified into the following five types. (1) Cation-π interaction[7–9]. The side chain imidazole of His is an aromatic ring. Histidine can take part in the cation-π interactions as the aromatic motif with metallic cations or organic cations (protonated amino acids, Lys+ and Arg+) [7, 9–11]. On the other hand, the protonated His+ is an organic cation, which can join the cation-π interactions as an organic cation with other aromatic amino acids (Phe, Tyr, and Trp) [12–16]. (2) π-π stacking interaction[17–20]. The imidazole structure of histidine side chain is a conjugative π-plane, which can make π-π stacking interactions with the aromatic side chains of other amino acids (Phe, Tyr, and Trp) [20, 21]. (3) hydrogen-π interaction[22, 23]. The polar hydrogen atom of histidine can form hydrogen-π bond with other aromatic amino acids in ‘T’ orientation. (4) Coordinate bond interaction[3, 24, 25]. The basic nitrogen atom in the imidazole of histidine has a lone electron pair that make it a coordinate ligand of metallic cations, such as Zn2+ and Ca2+[26, 27]. (5) Hydrogen bond interaction[28–31]. The polar hydrogen atom of the imidazole is a hydrogen-bond donor, and the basic nitrogen atom is a hydrogen-bond acceptor.
In protein interactions the roles of histidine are complicated by the five interaction types and two protonation forms. The unique behaviors of histidine have been discussed in literatures from different aspects [7, 32]. However, the quantitative interaction energies of five interaction types and the factors affecting the interaction energies still need more investigations. The influences of five interaction types to the protonation form (and pKa value) of histidine are still unclear. In this study the multiple roles of histidine in molecular interactions are quantitatively studied using quantum chemical calculations, and the factors, which influence the interaction energies and pKa value of histidine in proteins, are analyzed in detail.
Methods and materials
Comparison of three methods (DFT, CCSD, and CCSD(T)) for five interaction types (cation-π; π-π staking; hydrogen-π; hydrogen bond; and metallic cation-coordinate interaction
a π-π stack
From the data in Table 1 we find that the DFT method B3LYP cannot yield attractive interaction energy in C6H6-C6H6 π-π stacking interaction, completely failing in describing the π-π stacking interactions, which are dispersion dominated phenomenon. On the other hand the higher level method CCSD calculation produces attractive C6H6-C6H6 π-π stacking energy −1.883 kcal/mol. In this study the energy differences between B3LYP and CCSD are used as the dispersion contribution in the molecular interaction energies. In the hydrogen-π interaction more than 50% interaction energy is from the dispersion contribution. The interaction energies of other three interaction types (cation-π interactions, common hydrogen bond interactions, and metal cation-His coordinate interactions), obtained by using B3LYP and CCSD methods, have no remarkable difference. In above three interaction types the electrostatic (charge) interactions and orbital coordinate interactions make the main contributions, and the contribution of dispersion interactions are less than 10% [8, 41, 42]. In the C6H6CH3-H3O+ cation-π calculations the CPU time of three methods (B3LYP, CCSD, and CCSD(T)) are 1.08 hours, 50 days, and 86 days, respectively. However, the energy difference of cation-π interaction between B3LYP and CCSD(T) is only 1.08 kcal/mol, less than 6%.
In this study the π-π stacking interactions and the hydrogen-π interactions are calculated using CCSD/6-31+G(d,p) method, and the B3LYP/6-31+G(d,p) is used in the calculations of cation-π interactions and ligand-cation coordinate interactions. In recent years great efforts are made to make up the shortcoming of DFT in dispersion interactions, including design of new functional , or empirical correction terms [41, 42, 48–50]. , In this study the missing dispersion energies in DFT calculations are corrected by an empirical method suggested by Du et al . The interaction energies in solutions are calculated by using the polarizable continuum model (PCM) [50–53].
In this study most molecule monomers are optimized by using CCSD/6-31+G(d,p) methods. Some large amino acids, such as Tyr and Trp, first are optimized at B3LYP/6-31+G(d,p) level, then the side chains are optimized at CCSD/6-31+G(d,p) level. The geometry parameters of side-chain, obtained from CCSD calculations, are combined with the parameters of DFT optimizations. In this study the protonated His+ is simplified as the protonated imidazole (C3N2H4+), protonated Arg+ is simplified as CHNH2NH2+, and the protonated amino acid Lys+ is simplified as CH3NH3+, respectively, as shown in Figure 1C, D, and E. The structures of four interaction types (cation-π interaction, π-π stacking interaction, hydrogen-π interaction, and coordinate bond interaction) of His are shown in Figure 1F, G, H, and I, respectively. Usually amino acids have several stable structural conformations with different energies. In proteins the orientations of residue side chains and the structural conformations of peptide backbone are innumerous. The optimized structures of amino acids, shown in Figure 1, are only one of the possible conformations. In Figure 1 F the metallic cation can be put at the upside or at the downside of the aromatic planes. In the ‘Upside’ structure the cation-π interaction may be complicated by the interaction elements in peptide backbone. On the other hand, the ‘Downside’ structure is less affected by other interaction elements. In this study we focus on the ‘pure’ cation-π interactions, the ‘Downside’ structures. All calculations are performed on Sugon-5000A computer using Gaussian 09 software package . The detailed geometrical parameters of optimized molecular structures are stored in supporting material (Optimized-Mol.zip).
In this section all calculation results are reported and summarized using tables and figures. Brief comparisons and illustrations are provided following the calculation results. Four interaction types (cation-π, π-π stacking, hydrogen-π, and coordinate bond interaction) of histidine with other amino acids and metallic cations are calculated in gas phase and in solutions (water, acetonitrile, and cyclohexane). The hydrogen bonding interaction of histidine is not included in this study, because it is a familiar and well studied interaction type.
Cation-π interactions of Histidine
Cation-π interaction energies between amino acid His and cations in gas phase
His (Aromatic motif)
Cation-π interaction energies between histidine (His) and cations in three solvents (water, acetonitrile, and cyclohexane)
π-π stacking interactions of histidine
The π-π stacking interaction energies between His and aromatic amino acids in gas phase
The π-π stacking energies increase with the size of π-system. In Table 4 the π-π stacking energy (−4.035 kcal/mol) of His-Trp is larger than that of His-Phe and His-Tyr because of the larger π-system of Trp. In DNA the π-π stacking interactions have larger contributions than in proteins [41, 47–49]. The protonated amino group (CHNH2NH2+) of Arg+ forms a π-plane, and the larger π-π stacking energy (−5.0432 kcal/mol) of His-Arg+ may partially from the cation-π interaction. The lower part of Table 4 lists the π-π stacking interaction energies between the protonated His+ and three aromatic amino acids (Phe, Tyr, and Trp), which are remarkably larger than that in the up part of Table 4.
Hydrogen-π interactions of histidine
The hydrogen-π interaction energies between His and aromatic amino acids in gas phase
Comparing the data in Table 4 and Table 5, the energies of hydrogen-π interactions are larger than the corresponding energies of π-π stacking interactions. In proteins the energies of hydrogen-π interactions are in the range −5 to −8 kcal/mol, comparable to the common hydrogen bond interactions (−4 to −6 kcal/mol). Actually, the π-π stacking interaction energies of aromatic amino acids contain the contributions of hydrogen-π interactions from the polar hydrogen atoms in His and in Tyr.
Coordinate bonding interactions between His and cations
The coordinate bonding interaction energies between His and metallic ations in gas phase and in solutions
Water (ε =78.39)
Histidine is an ionizable amino acid with the acidic ionization constant around pKa=6.5, very close to neutral. An interesting finding in this study is that the protonation of histidine has closely relationship with the interaction types. The cation-π interactions of neutral histidine (His) are attractive, and the cation-π interactions of protonated histidine (His+) are repulsive. A reasonable deduction is that pH condition can reversibly switch the cation-π interactions of histidine from attractive to repulsive. Vice versa, the cation-π interactions can affect the two protonation forms of histidine. In proteins the pKa value of His can change in a broad range due to the influence of interaction environment, and histidine can play the roles of both proton donor or acceptor [58, 65, 66]. The stronger attractive cation-π interaction can make the pKa value of His lower, and the lower pH condition may turn the cation-π interaction from attractive to repulsive. For the same reason, other interaction types (coordinate interaction, hydrogen-π interaction, hydrogen bond and the π-π stacking interaction) may also affect the pKa value of histidine to some degree .
In protein hydrolysis reactions the pKa value of His is a critically important property. In the catalytic triads of lipase, the basic nitrogen of histidine is used to abstract a proton from threonine, serine, or cysteine to activate it as a nucleophile. In carbonic anhydrases, a histidine proton shuttle is utilized to rapidly transport protons away from a zinc-bound water molecule to quickly regenerate the active form of the enzyme [67, 68]. In the histidine proton shuttle, histidine abstracts a proton with its basic nitrogen to make a positively-charged intermediate, and then use another molecule, a buffer, to extract the proton from its acidic nitrogen. Our study illustrates that in the proton shuttle procedure, the histidine is not working by itself alone, but with the collaboration of environmental residues through the multiple interactions that affect the pKa value of histidine.
Based on our calculation results the energy order of five interaction types (cation-π interaction, π-π stacking interaction, hydrogen-π interaction, hydrogen-bond interaction, and coordinate bond interaction) is as follows, Ecoor>Ecation-π>EH-π≈EH-b>Eπ-π. The coordinate interaction (Ecoor) of His with metallic cations is the strongest interaction with long interaction distance, followed by the cation-π interaction (Ecation-π). In the cation-π interactions, when His is in neutral form (unprotonated), interaction energy is attractive. However, when His is protonated, the interaction energy turns to repulsive. The π-π stacking interactions are the π-plane to π-plane interactions, with much more interaction conformations than other interaction types. In proteins the energies of π-π stacking interactions (Eπ-π) can change in a broad range, because of different interaction orientations. The π-π stacking interactions between neutral His and aromatic amino acids (Phe, Tyr, and Trp) are in the range −3.0 to −4.0 kcal/mol, significantly larger than the van der Waals interactions. However, the π-π stacking energies of protonated histidine (His+) are much larger than the energies of neutral His.
The interaction strength of cation-π interactions in solutions is a controversial research topic [17, 65, 69]. Based on our calculations by using PCM method, the energies of cation-π interactions decrease sharply with the increase of the dielectric constant ε of solvents. In gas phase the cation-π interaction energies of metallic cations are larger than that of organic cations (Lys+ and Arg+). However, in solutions of polar solvents (water and acetonitrile) the cation-π interaction energies of organic cations (protonated amino acids) are lager than that of metallic cations. The PCM is a continuum medium model [50–53]. The calculated values of PCM may be not very accurate, but the qualitative order is meaningful. In aqueous solution the cation-π interactions between protonated amino acids and aromatic amino acids may be more important than that of metallic cations [17, 69, 70]. However, this does not mean that the cation-π interactions of metallic cations are not important in solutions. In aqueous solution the hydrophilic residues are explored on the surface, and the hydrophobic residues are hidden in the core region of protein structures. In the hydrophobic pockets of proteins the dielectric constants are smaller than that in bulk solution. Therefore, the cation-π interactions are still working in the hydrophobic pockets and in core region of proteins.
- Martínez A: Evidence for a functionally important histidine residue in human tyrosine hydroxylase. Amino Acids. 1995, 9: 285-292. 10.1007/BF00805959.View ArticleGoogle Scholar
- Uchida K: Histidine and lysine as targets of oxidative modification. Amino Acids. 2003, 25: 249-257. 10.1007/s00726-003-0015-y.View ArticleGoogle Scholar
- Remko M, Fitz D, Rode BM: Effect of metal ions (Li+, Na+, K+, Mg2+, Ca2+, Ni2+, Cu2+ and Zn2+) and water coordination on the structure and properties of l-histidine and zwitterionic l-histidine. Amino Acids. 2010, 39: 1309-1319. 10.1007/s00726-010-0573-8.View ArticleGoogle Scholar
- Li F, Fitz D, Fraser DG, Rode BM: Catalytic effects of histidine enantiomers and glycine on the formation of dileucine and dimethionine in the salt-induced peptide formation reaction. Amino Acids. 2010, 38: 287-294. 10.1007/s00726-009-0249-4.View ArticleGoogle Scholar
- Agnieszka M, Janina KW, Katarzyna KK: Five-membered heterocycles. Part III. Aromaticity of 1,3-imidazole in 5+n hetero-bicyclic molecules. J Mol Struc. 2003, 655: 397-403. 10.1016/S0022-2860(03)00282-5.View ArticleGoogle Scholar
- Doğan A, Özel AD, Kılıç E: The protonation equilibria of selected glycine dipeptides in ethanol–water mixture: solvent composition effect. Amino Acids. 2009, 36: 373-379. 10.1007/s00726-008-0054-5.View ArticleGoogle Scholar
- Priyakumar UD, Punnagai M, Krishna Mohan GP, Sastry GN: A computational study of cation-π interactions in polycyclic systems: exploring the dependence on the curvature and electronic factors. Tetrahedron. 2004, 60: 3037-3043. 10.1016/j.tet.2004.01.086.View ArticleGoogle Scholar
- Reddy AS, Sastry GN: Cation [M = H+, Li+, Na+, K+, Ca2+, Mg2+, NH4+, and NMe4+] interactions with the aromatic motifs of naturally occurring amino acids: A theoretical study. J Phys Chem A. 2005, 109: 8893-8903. 10.1021/jp0525179.View ArticleGoogle Scholar
- Engerer LK, Hanusa TP: Geometric Effects in Olefinic Cation−π Interactions with Alkali Metals: A Computational Study. J Org Chem. 2011, 76: 42-49. 10.1021/jo101307z.View ArticleGoogle Scholar
- Hunter CA, Lawson KR, Perkins J, Urch CJ: Aromatic interactions. J Chem Soc Perkin Trans. 2001, 2: 651-669.View ArticleGoogle Scholar
- Crowley PB, Golovin A: Cation–π interactions in protein–protein interfaces. Proteins. 2005, 59: 231-239. 10.1002/prot.20417.View ArticleGoogle Scholar
- Vijay D, Sastry GN: Exploring the size dependence of cyclic and acyclic π-systems on cation-π binding. Phys Chem Chem Phys. 2008, 10: 582-590. 10.1039/b713703f.View ArticleGoogle Scholar
- Matsumura H, Yamamoto T, Leow TC, Mori T, Salleh AB, Basri M, Inoue T, Kai Y, Zaliha RN, Rahman RA: Novel cation-π interaction revealed by crystal structure of thermoalkalophilic lipase. Proteins. 2008, 70: 592-598.View ArticleGoogle Scholar
- Reddy AS, Zipse H, Sastry GN: Cation-π Interactions of Bare and Coordinatively Saturated Metal Ions: Contrasting Structural and Energetic Characteristics. J Phys Chem B. 2007, 111: 11546-11553. 10.1021/jp075768l.View ArticleGoogle Scholar
- Schottel BL, Chifotides HT, Dunbar KR: Anion-π interactions.Chem Soc Rev. 2008, 37: 68-83. 10.1039/b614208g.View ArticleGoogle Scholar
- Burley SK, Petsko GA: Amino-aromatic interactions in proteins. FEBS Lett. 1986, 203: 139-143. 10.1016/0014-5793(86)80730-X.View ArticleGoogle Scholar
- Stefan G: Do special noncovalent π-π stacking interactions really exist?. Angew Chem Int Ed. 2008, 47: 3430-3434. 10.1002/anie.200705157.View ArticleGoogle Scholar
- Mignon P, Loverix S, Steyaert J, Geerlings P: Influence of the π–π interaction on the hydrogen bonding capacity of stacked DNA/RNA bases. Nucl Acids Res. 2005, 33: 1779-1789. 10.1093/nar/gki317.View ArticleGoogle Scholar
- Petitjean A, Khoury RG, Kyritsakas N, Lehn JM: Dynamic devices, shape switching and substrate binding in ion-controlled nanomechanical molecular tweezers. J Am Chem Soc. 2004, 126: 6637-6647. 10.1021/ja031915r.View ArticleGoogle Scholar
- Sygula A, Fronczek FR, Sygula R, Rabideau PW, Olmstead MM: A Double Concave Hydrocarbon Buckycatcher. J Am Chem Soc. 2007, 129: 3842-3843. 10.1021/ja070616p.View ArticleGoogle Scholar
- Janiak C: A critical account on π-π stacking in metal complexes with aromatic nitrogen-containing ligands. J Chem Soc Dalton Trans. 2000, 3885-3896.Google Scholar
- Meyer EA, Castellano RK, Diederich F: Interactions with aromatic rings in chemical and biological recognition. Angew Chem Int Ed. 2003, 42: 1210-1250. 10.1002/anie.200390319.View ArticleGoogle Scholar
- Hughes RM, Waters ML: Effects of lysine acylation in a β-hairpin peptide: comparison of an amide-π and a cation-π interaction. J Am Chem Soc. 2006, 128: 13586-13591. 10.1021/ja0648460.View ArticleGoogle Scholar
- Kang SO, Hossain MA, Bowman-James K: Influence of dimensionality and charge on anion binding in amide-based macrocyclic receptors. Coord Chem Rev. 2000, 250: 3038-3052.View ArticleGoogle Scholar
- Miessler GL, Tarr DA: Inorganic Chemistry. 2003, Upper Saddle River, NJ: Pearson Prentice Hall, 3Google Scholar
- Smith MB, March J: March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure. 2007, New York: Wiley-Interscience, 6Google Scholar
- Jackson WG, Josephine AM, Silvia C: Alfred Werner's inorganic counterparts of racemic and mesomeric tartaric acid: A milestone revisited. Inorg Chem. 2004, 43: 6249-6254. 10.1021/ic040042e.View ArticleGoogle Scholar
- Sirois SW, Proynov EI, Truchon JF, Tsoukas CM, Salahub DR: A density functional study of the hydrogen-bond network within the HIV-1 protease catalytic site cleft. J Comput Chem. 2003, 24: 1110-1119. 10.1002/jcc.10176.View ArticleGoogle Scholar
- Du QS, Li DP, Liu PJ, Huang RB: Molecular potential energies in dodecahedron cell of methane hydrate and dispersion correction for DFT. J Mol Graph Model. 2008, 27: 140-146. 10.1016/j.jmgm.2008.03.008.View ArticleGoogle Scholar
- Henry M: Thermodynamics of hydrogen bond patterns in supramolecular assemblies of water molecules. Chem Phys Chem. 2002, 3: 607-616. 10.1002/1439-7641(20020715)3:7<607::AID-CPHC607>3.0.CO;2-A.Google Scholar
- Henry M: Nonempirical quantification of molecular interactions in supramolecular assemblies. Chem Phys Chem. 2002, 3: 561-569. 10.1002/1439-7641(20020715)3:7<561::AID-CPHC561>3.0.CO;2-E.Google Scholar
- Andrews LJ, Keefer RM: Molecular complexes in organic chemistry. 1964, San Francisco: Holden-DayGoogle Scholar
- Mezey PG: Macromolecular density matrices and electron densities with adjustable nuclear geometries. J Math Chem. 1995, 18: 141-168. 10.1007/BF01164655.View ArticleGoogle Scholar
- Mezey PG: Quantum similarity measures and Löwdin's transform for approximate density matrices and macromolecular forces. Int J Quantum Chem. 1997, 63: 39-48. 10.1002/(SICI)1097-461X(1997)63:1<39::AID-QUA8>3.0.CO;2-3.View ArticleGoogle Scholar
- Sayyed FB, Suresh CH: Accurate prediction of cation−π interaction energy using substituent effects. J Phys Chem A. 2012, 116: 5723-5732. 10.1021/jp3034193.View ArticleGoogle Scholar
- Mohan N, Vijayalalakshmi KP, Koga N, Suresh CH: Comparison of aromatic NH…π, OH…π, and CH…π interactions of alanine using MP2, CCSD, and DFT methods. J Comput Chem. 2010, 31: 2874-2882.Google Scholar
- Gresh N, Kafafi SA, Truchon JF, Salahub DR: Intramolecular interaction energies in model alanine and glycine tetrapeptides. Evaluation of anisotropy, polarization, and correlation effects. A parallel ab initio HF/MP2, DFT, and polarizable molecular mechanics study. J Compt Chem. 2004, 25: 823-834. 10.1002/jcc.20012.View ArticleGoogle Scholar
- Jurecka P, Cerný J, Hobza P, Salahub DR: Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations. J Comput Chem. 2007, 28: 555-569. 10.1002/jcc.20570.View ArticleGoogle Scholar
- Van Mourik T, Gdanitz RJ: A critical note on density functional theory studies on rare-gas dimers. J Chem Phys. 2002, 116: 9620-9623. 10.1063/1.1476010.View ArticleGoogle Scholar
- Morgado C, Vincent MA, Hillier IH, Shan X: Can the DFT-D method describe the full range of noncovalent interactions found in large biomolecules?. Phys Chem Chem Phys. 2007, 9: 448-451. 10.1039/b615263e.View ArticleGoogle Scholar
- Von Lilienfeld OA, Tavernelli I, Rothlisberger U, Sebastiani D: Optimization of effective atom centered potentials for London dispersion forces in density functional theory. Phys Rev Lett. 2004, 93: 153004-153007.View ArticleGoogle Scholar
- Du Q-S, Liu P-J, Deng J: Empirical correction to molecular interaction energies in density functional theory (DFT) for methane hydrate simulation. J Chem Theory Comput. 2007, 3: 1665-1672. 10.1021/ct700026d.View ArticleGoogle Scholar
- Purvis GD, Bartlett RJ: A full coupled-cluster singles and doubles model: The inclusion of disconnected triples. J Chem Phys. 1982, 76: 1910-1919. 10.1063/1.443164.View ArticleGoogle Scholar
- Lee TJ, Rice JE: An efficient closed-shell singles and doubles coupled-cluster method. Chem Phys Lett. 1988, 23: 406-415.View ArticleGoogle Scholar
- Scuseria GE, Schaefer HF: Is coupled cluster singles and doubles (CCSD) more computationally intensive than quadratic configuration interaction (QCISD)?. J Chem Phys. 1989, 90: 3700-3703. 10.1063/1.455827.View ArticleGoogle Scholar
- Scuseria GE, Janssen CL, Schaefer HF: An efficient reformulation of the closed-shell coupled cluster single and double excitation (CCSD) equations. J Chem Phys. 1988, 89: 7382-7388. 10.1063/1.455269.View ArticleGoogle Scholar
- Grimme S: Semiempirical hybrid density functional with perturbative second-order correlation. J Chem Phys. 2006, 124: 034108-10.1063/1.2148954.View ArticleGoogle Scholar
- Zimmerli U, Parrinello M, Koumoutsakos P: Dispersion corrections to density functionals for water aromatic interactions. J Chem Phys. 2004, 120: 2693-2699. 10.1063/1.1637034.View ArticleGoogle Scholar
- Grimme S: Accurate description of van der Waals complexes by density functional theory including empirical corrections. J Comput Chem. 2004, 25: 1463-1473. 10.1002/jcc.20078.View ArticleGoogle Scholar
- Miertus S, Scrocco E, Tomasi J: Electrostatic interaction of a solute with a continuum. A direct utilization of ab initio molecular potentials for the prevision of solvent effects. Chem Phys. 1981, 55: 117-129. 10.1016/0301-0104(81)85090-2.View ArticleGoogle Scholar
- Amovilli C, Barone V, Cammi R, Cances E, Cossi M, Mennucci B, Pomelli CS, Tomasi J: Recent advances in the description of solvent effects with the polarizable continuum model. Adv Quant Chem. 1998, 32: 227-262.View ArticleGoogle Scholar
- Cossi M, Barone V: Analytical second derivatives of the free energy in solution by polarizable continuum models. J Chem Phys. 1998, 109: 6246-6254. 10.1063/1.477265.View ArticleGoogle Scholar
- Foresman JB, Keith TA, Wiberg KB, Snoonian J, Frisch MJ: Solvent effects. 5. influence of cavity shape, truncation of electrostatics, and electron correlation on ab initio reaction field calculations. J Phys Chem. 1996, 100: 16098-16104. 10.1021/jp960488j.View ArticleGoogle Scholar
- Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA: Gaussian 09, Revision B,01. 2010, Wallingford CT: Gaussian IncGoogle Scholar
- Zielkiewicz J: Structural properties of water: Comparison of the SPC, SPCE, TIP4P, and TIP5P models of water. J Chem Phys. 2005, 123: 104501-10.1063/1.2018637.View ArticleGoogle Scholar
- Markovitch O, Agmon N: Structure and energetics of the hydronium hydration shells. J Phys Chem A. 2007, 111: 2253-2256. 10.1021/jp068960g.View ArticleGoogle Scholar
- Du QS, Long SY, Meng JZ, Huang RB: Empirical formulation and parameterization of cation-π interactions for protein modeling. J Compt Chem. 2012, 33: 153-162. 10.1002/jcc.21951.View ArticleGoogle Scholar
- Du QS, Liao SM, Meng JZ, Huang RB: Energies and Physicochemical Properties of Cation-π Interactions in Biology Structures. J Mol Graph Model. 2012, 34: 38-45.View ArticleGoogle Scholar
- Olsson MHM, Søndergaard CR, Rostkowski M, Jensen JH: PROPKA3: consistent treatment of internal and surface residues in empirical pKa predictions. J Chem Theory Comput. 2011, 7: 525-537. 10.1021/ct100578z.View ArticleGoogle Scholar
- Huang RB, Du QS, Wang CH, Liao SM, Chou KC: A fast and accurate method for predicting pKa of residues in proteins. Protein Eeng Des Sel. 2010, 23: 35-42. 10.1093/protein/gzp067.View ArticleGoogle Scholar
- Ottiger P, Pfaffen C, Leist R, Leutwyler S, Bachorz RA, Klopper W: Strong N−H···π Hydrogen Bonding in Amide−Benzene Interactions. J Phys Chem B. 2009, 113: 2937-2943. 10.1021/jp8110474.View ArticleGoogle Scholar
- Steiner T, Koellner G: Hydrogen bonds with pi-acceptors in proteins: frequencies and role in stabilizing local 3D structures. J Mol Biol. 2001, 305: 535-557. 10.1006/jmbi.2000.4301.View ArticleGoogle Scholar
- Trakhanov S, Quiocho FA: Influence of divalent cations in protein crystallization. Protein Sci. 1995, 4: 1914-1919. 10.1002/pro.5560040925.View ArticleGoogle Scholar
- Fischer M, Pleiss J: The Lipase Engineering Database: a navigation and analysis tool for protein families. Nucleic Acids Res. 2003, 31: 319-321. 10.1093/nar/gkg015.View ArticleGoogle Scholar
- Bas DC, Rogers DM, Jensen JH: Very fast prediction and rationalization of pKa values for protein-ligand complexes. Proteins. 2008, 73: 765-783. 10.1002/prot.22102.View ArticleGoogle Scholar
- Li H, Robertson AD, Jensen JH: Very fast empirical prediction and rationalization of protein pKa values. Proteins. 2005, 6: 704-721.View ArticleGoogle Scholar
- Badger MR, Price GD: The role of carbonic anhydrase in photosynthesis. Annu Rev Plant Physio Plant Mol Bio. 1994, 45: 369-392. 10.1146/annurev.pp.45.060194.002101.View ArticleGoogle Scholar
- Lindskog S: Structure and mechanism of carbonic anhydrase. Pharmacol Ther. 1997, 74: 1-20. 10.1016/S0163-7258(96)00198-2.View ArticleGoogle Scholar
- Biot C, Buisine E, Rooman M: Free-energy calculations of protein-ligand cation-π and amino-π interactions: From vacuum to protein-like environments. J Am Chem Soc. 2003, 125: 13988-13994. 10.1021/ja035223e.View ArticleGoogle Scholar
- Crowley PB, Golovin A: Cation-π interactions in protein–protein interfaces. Proteins. 2005, 59: 231-239. 10.1002/prot.20417.View ArticleGoogle Scholar
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