Note: Charge transfer in a hydrated peptide group is determined mainly by its intrinsic hydrogen-bond energetics Noemi G. Mirkin and Samuel Krimm Citation: The Journal of Chemical Physics 140, 046101 (2014); doi: 10.1063/1.4862900 View online: http://dx.doi.org/10.1063/1.4862900 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hofmeister anionic effects on hydration electric fields around water and peptide J. Chem. Phys. 136, 124501 (2012); 10.1063/1.3694036 Energy relaxation of the amide-I mode in hydrogen-bonded peptide units: A route to conformational change J. Chem. Phys. 128, 065101 (2008); 10.1063/1.2831508 A new scheme for determining the intramolecular seven-membered ring N – H O C hydrogen-bonding energies of glycine and alanine peptides J. Chem. Phys. 123, 024307 (2005); 10.1063/1.1979471 Orbital interactions and charge redistribution in weak hydrogen bonds: The Watson–Crick AT mimic adenine-2,4difluorotoluene J. Chem. Phys. 119, 4262 (2003); 10.1063/1.1592494 An effective potential function with enhanced charge-transfer-type interaction for hydrogen-bonding liquids J. Chem. Phys. 117, 3558 (2002); 10.1063/1.1495851

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THE JOURNAL OF CHEMICAL PHYSICS 140, 046101 (2014)

Note: Charge transfer in a hydrated peptide group is determined mainly by its intrinsic hydrogen-bond energetics Noemi G. Mirkin and Samuel Krimm LSA Biophysics, University of Michigan, 930 N. University Ave., Ann Arbor, Michigan 48109-1055, USA

(Received 5 November 2013; accepted 9 January 2014; published online 24 January 2014) [http://dx.doi.org/10.1063/1.4862900] Improved knowledge of the hydrogen-bond (HB) interactions of water molecules with the peptide group is basic to developing a deeper understanding of the detailed nature of protein solvation. In pursuing this goal, attention has been directed to the issue of charge transfer between the peptide group and its bonding water molecules, generally involving molecular mechanics and dynamics studies.1–5 When the interaction energy is considered, it is typically based on a common definition,6 viz., the difference between the (optimized) energy of the HB complex and the (optimized) energies of its isolated components. In this Note, we present results of a quantum-mechanical treatment of these interactions, utilizing an intrinsic definition of HB energy. The system studied was N-methylacetamide (NMA), CH3 CONHCH3 , the simplest model of a peptide group, with three water molecules hydrogen bonded to it. Its equilibrium structure is shown in Figure 1. The calculations were done with Gaussian 097 and a dispersion-corrected DFT (density functional theory) functional, the ωB97X-D8 (such a functional providing an optimum combination of HB and dispersion accuracy), and the 6-31++G** basis set. Energies were corrected for basis set superposition error (BSSE) with the counterpoise procedure9 (neither energies nor structures were significantly different from a BSSE-optimization calculation). Charge transfer was determined by 0.3 Å-grid dipole-moment-constrained potential-derived CHelpG atomic charges (natural population analysis (NPA) charges were also calculated, but these are not expected to satisfactorily reflect charge transfer10 ). A charge transfer calculation with the augcc-pVTZ basis set gave comparable, but a little larger, results. Interaction energies were determined by the above common procedure, but since it is acknowledged that combining components into the complex causes changes in their internal geometries,11 it is relevant to take into account the portion of the HB energy that is expended in altering these structures from their optimized values. Therefore, we also calculated this energy by subtracting the component energies based on their structures in the complex, so-called “dry” energies.12 In Table I, properties are given for individual peptidewater HB structures: C=O with water molecules only in position 1 or position 2 or in both, NH with a water molecule in position 3, and the complete NMA(H2 O)3 complex. Interaction energies are given for the common definition, E(opt), and for our modified one, E(dry). The charge transfer, q, is given for the NMA component of the complexes, and also the relevant HB distances. 0021-9606/2014/140(4)/046101/2/$30.00

A number of conclusions follow: (1) The (stabilizing) HB interaction energy, E(dry), is larger than that obtained by subtracting optimized components. This is expected since part of the intrinsic energy is expended in altering the structures of the optimized components. This amount varies with the type of complex and is in the range of 0.7–0.9 kcal/mol (and 4%–11% depending on the structure), a non-negligible quantity. (2) The energy of the CO-1,2 pair (17.09) is smaller than the sum of the individual HB energies: CO-1 + CO-2 = 18.68. Clearly, and not unexpectedly, the presence of both waters bonding with the O exhibits cooperativity, viz., a crossterm in their interaction. This is further emphasized by the fact that the charge transfer in the former case (0.18 electrons, e) is quite different from that in the latter (0.13 e). (3) The sum of the individual energies of CO-1,2 and NH-3 (23.29) is close to that of the NMA(H2 O)3 complex (23.68), suggesting essentially non-interaction. (4) The charge transfer of the peptide

FIG. 1. Structure of N-methylacetamide(H2 O)3 based on ωB97X-D/6 -31++G** optimization.

140, 046101-1

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046101-2

N. G. Mirkin and S. Krimm

J. Chem. Phys. 140, 046101 (2014)

TABLE I. N-methylacetamide-water interactions. Watera CO-1 CO-2 CO-1,2 NH-3 NMA-1,2,3

E(opt)b

E(dry)c

qd

H(1)· · ·Oe

8.58 8.49 16.17 5.51 22.75

9.40 9.28 17.09 6.20 23.68

0.09 0.04 0.18 0.02 0.19

1.8438

H(2)· · ·Oe

1.8614

1.8539 1.8695

1.8362

1.8500

H(3)· · ·Oe

1.9976 1.9549

a

NMA group and bonded water number. Interaction energy (kcal/mol) with optimized components. c Interaction energy (kcal/mol) with complex-based components. d Charge transfer of NMA (CHelpG, e). e Hydrogen bond length (Å). b

associated with the individual peptide-water hydrogen bonds increases (roughly linearly) with increasing E(dry), indicating that such transfer is a stabilizing factor of the complex. (The −0.02 e value of the water in NH-3, and its comparable value of −0.01 e in NMA-1,2,3, may simply reflect the errorlimit properties of the CHelpG protocol rather than the unexpected physical transfer of charge from the NH to water. The values, however, suggest that the transfer at this site is probably small.) (5) The HB lengths vary inversely with E(dry), as expected, and are consistent with a suggested exponential relation between charge transfer and these distances.2 (Our data give an acceptable fit to q = Aexp(−Br), but additional study is desirable to establish a reliable quantitative relation.) Since such transfer increases with the extent of overlap between acceptor and donor wave functions, it is not surprising that the short 1.8362 Å distance of the NMA(H2 O)3 complex would be the dominant contributor to its large q. The somewhat puzzling result that the large q of CO-1,2 is associated with slightly larger distances may point to structure-mediated interaction effects between the two C=O hydrogen bonds (for example, the H(1)OH(2) angle of CO-1,2 is 119.00◦ , while that of NMA-1,2,3 is 114.57◦ ). The implication of these results is that the final total peptide charge and its distribution must be determined by the action of charge transfer. The CO-1,2 structure produces a large q, 0.18 e, almost the same as that of the complete complex. On the other hand, the NH-3 structure results in a small q, 0.02 e, the result of the introduction of the NH· · ·O hydrogen bond. And as soon as CO-1,2 is added to the system q increases to its complete complex value, 0.19 e. Thus, the CO interactions are mainly responsible for the charge transfer, largely uninfluenced by charge transfer of the NH hydrogen bond (which results in only a relatively small re-distribution of NMA internal atomic charges). This suggests that charge transfer is dominated by specific HB interactions, a result that

is important in determining the relative stability of peptide conformations.12, 13 It has been noted that, although polarization is being increasingly incorporated, present molecular mechanics force fields do not take charge transfer explicitly into account.1–4 The effects of such transfer could be important in describing the detailed electrostatic environment of solvated peptide groups, and such inclusion should be implemented. A possible model would be through a charge flux14, 15 with dependence on the HB length, as was found needed to account for the vibrational spectroscopic properties of the water dimer.16 1 A.

van der Vaart and K. M. Merz, Jr., J. Am. Chem. Soc. 121, 9182 (1999). van der Vaart, B. D. Bursulaya, C. L. Brooks III, and K. M. Merz, Jr., J. Phys. Chem. B 104, 9554 (2000). 3 A. van der Vaart and K. M. Merz, Jr., J. Chem. Phys. 116, 7380 (2002). 4 M. D. Peraro, S. Raugei, P. Carloni, and M. L. Klein, ChemPhysChem 6, 1715 (2005). 5 B. Yogeswari, R. Kanakaraju, S. Boopathi, and P. Kolandaivel, J. Mol. Graphics Modell. 35, 11 (2012). 6 S. Scheiner, J. Phys. Chem. B 111, 11312 (2007). 7 M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., Gaussian 09, Revision A.2, Gaussian, Inc., Wallingford, CT, 2009. 8 J. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys. 10, 6615 (2008). 9 S. F. Boys and F. Bernardi, Mol. Phys. 19, 553 (1970). 10 J. Rigby and E. I. Izgorodina, Phys. Chem. Chem. Phys. 15, 1632 (2013). 11 S. Scheiner, Hydrogen Bonding, A Theoretical Perspective (Oxford University Press, New York, Oxford, 1997). 12 N. G. Mirkin and S. Krimm, Biopolymers 97, 789 (2012). 13 N. G. Mirkin and S. Krimm, “Charge-transfer differences in the hydrogen bonding of solvating waters are the dominant factors in determining the relative energetic stability of the polyproline II peptide conformation,” Biopolymers (to be published). 14 K. Palmo, B. Mannfors, N. G. Mirkin, and S. Krimm, Biopolymers 68, 383 (2003) 15 K. Palmo, B. Mannfors, N. G. Mirkin, and S. Krimm, Chem. Phys. Lett. 429, 628 (2006). 16 B. Mannfors, K. Palmo, and S. Krimm, J. Phys. Chem. A 112, 12667 (2008). 2 A.

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