J. Phys. Chem. 1981, 85,2433-2434
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Solvating Glycylglycine Zwitterion with Polarlzation Model Water Carl W. David Department of Chert’tISt,y,Unlvers#y of Connectlcut, Storrs, Connecticut 06268 (Received: April 1, 198 1; In Final Form: June 25, 198 1)
The polarization model is used to study the conformation of glycylglycine zwitterion in droplets of water. A solvent-stabilized conformation different from the absolute minimum energy conformation is obtained. The polarization model for water1 has proven itself to be reasonably successful. It is natural to attempt to extend the model to small peptides, as interest in the conformational states of peptides in aqueous medium is high. Already, accounts of computations on peptides in ST22water have been reported by V ~ v e l l e Rossky; ,~ and HaglerS5 Alternative approaches to including water in solution computations existe and we can expect to find such methodology applied to peptides Conformational analysis of peptides based on molecular mechanical principles has been hampered by the vacuum state assumption that has been required. Since the actual peptide molecules are rarely of interest in the gas phase, predictions of conformation based on isolated molecule interactions ignore a host of intermolecular interactions, some of which may actually play a role in determining peptide conformation. It is well-known that biologically interesting peptides interact with water; it is suspected that the influence of water as a solvent on protein secondary structure is both subtle and far reaching. Furthermore, it is known that peptides in aqueous medium suffer chemical effects due to pH. Both of these facts impinge in a meaningful way on the choice of the polarization model as our vehicle for simulating these systems. The polarization model is a lineal descendent of the Borna and Heisenberg model and the Rittnere model. Like its predecessor, the BNS’O model, the polarization model is an electrostatic model which uses fixed charges. Unlike many other water potentials, such as those due to Shipman and Scheraga,ll Campbell and Mezei,12 or Popkie et al.13 the polarization model is not pairwise additive.14 The polarization model specifically includes the polarizability of the water molecule and, as a result, shares its classification with the models of Campbell and Mezei15 and Berendsen and van der Velde.le The polarization model further differs from its prede(1)F.H. Stillinger and C. W. David, J. Chem. Phys., 69,1473(1978). (2)F.H. Stillinger and A. Rahman, J. Chem. Phys., 60,1545 (1974). (3)F. Vovelle and M. Ptak,Int. J. Peptide Protein Res., 13, 435 (1979). (4)P. J. Rossky, M. Karplus, and A. Rahman, Biopolymers, 18,825 (1979). .~ (6)A. T. Hagler and J. Moult, Nature (London),272, 222 (1978). (6)A. Warshel, J.Phys. Chem., 83,1640 (1979). (7)Z.I. Hodes, G. Nemethy, and H. A. Scheraga, Biopolymers, 18, 1565, 1611 (1979). (8)M. Born and W. Heisenberg, 2. Phys., 23, 388 (1924). (9)R. S. Rittner, J. Chem. Phys., 19, 1030 (1951). (10)A. Ben-Naim and F. H. Stillinger, “Aspects of the Statistical Mechanical Theory of Water”, in “Structure and Transport Processes in Water and Aqueous Solutions”, R. A. Horne, Ed., Wiley-Interscience, New York, 1972. (11)L.L.Shipman and H. A. Scheraga, J.Phys. Chem., 78,909(1974). (12)E.S.Campbell and M. Mezei, J. Chem. Phys., 67,2338 (1977). (13)H.PoDkie, H.Kistenmacher, and E. Clementi. J.Chem. Phvs.. - . 59, 1325 (1973). (14)F.T. Marchese, P. K. Mehrotra, and D. L. Beveridge, J. Phys. Chem., 86,1 (1981). (15)E.S.Campbell and M. Mezei, J. Chem. Phys., 67,2338 (1977). (16)H.J. C. Berendsen and G. A. van der Velde, “Molecular Dynamics and Monte Carlo Simulations on Water”, Report on the CECAM Workshop, held in Orsay, 1972,p 63. 0022-3654/81/2085-2433$01.25/0
cessors, first by being a central force model17in which every constituent of each molecule interacts with every other constituent of its own and every other molecule in the system, and second by being nonclassical in its electrostatic treatment of polarization. The total potential energy of a waterlike system is broken up by the model into two parts, a direct part, and a polarization part. The direct part was grafted onto the polarization part (after the latter had been evaluated) in such a manner as to force maximum agreement with existing knowledge about the system. The polarization part of the total potential energy is a nonpairwise additive term. Its presence in the model thoroughly complicates the computation of the energy, and inflicts a time penalty on the user which is considerable.’* On the road to calibrating a polarization model of peptides, we decided to create a “half-way” model which would allow us to treat water and peptide simultaneously, but not in a common manner. In order to do this we assume that the peptide presents a collection of polarizable charged points to the water solvent. The effect of the peptide on the water is to alter the electric field found at each nuclear site of the solvent. We compute the dipole moments of the water oxide anions on the basis of this “external” field, and then compute the water part of the energy of the system on the assumption that the water (perturbed) interacts only with water via the polarization model. The total energy of the system is then equal to the polarization model energy of the water solvent plus two terms, the self-energy of the peptide, computed by using the Scheraga ECWP program,l9and the interaction energy of the water with the peptide, computed by using the Clementi functions.20 This system of computations is self-consistent and results in reasonable energies for the system peptide/water. It has been checked by computing the energy and orientation of water molecules in the field of both a glycy121and a glycylglycine zwitterion. The only obvious source of inconsistency in the mixed model comes from the intrinsic structual flexibility which water possesses which is not included in the Clementi calibration of the peptide/water interaction energy. Thus, the computed peptide/water interaction, although phrased in terms of independent proton and oxide interactions with individual atoms of the peptide, is really only strictly applicable to rigid water molecules. We assume that the error we commit in the peptide/water computation is small when we allow the water structure to relax. In the computations using glycyl zwitterion and water we found that (17) F. H. Stillinger, Isr. J. Chem., 14,130(1975);H.L.Lemberg and F. H. Stillinger, J. Chem. Phys., 62,1677 (1975). (18)P. Barnes, J. L. Finney, J. D. Nicholas, and J. E. Quinn, Nature (London),282,459(1979).These authors highlight the need for polarization in these computations, even if they turn out therefore to be expensive. (19)H.A. Scheraga and co-workers,ECEPP, WPE,Program 286. (20) L. Carozzo, G. Corongiu, C. Petrongolo, and E. Clementi,J. Chem. Phys., 68,787 (1978). (21)C. W.David, Chem. Phys. Lett., 78,337 (1981).
@ 1981 American Chemical Society
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The Journal of Physical Chemistty, Vol. 85, No. 17, 798 1
Figure 1. A glycylglycine zwitterion at 35 K, surrounded by 18 waters of hydration (incomplete first solvent shell). Water protons are not shown.
a rather severe distortion did take place, in which two adjacent waters in the first solvent sheath “disproportionated” into the ion pairs hydronium-hydroxide. Such an ion pair, properly oriented as it was, offset the dipole moment of the glycyl zwitterion itself. The computations reported here were performed by using the simplest of all dipeptides, the glycylglycine zwitterion. The solid-state structure of this dipeptide is not known, but the structure of glycylglycine hydrochloride monohydrate is known.22 We have computed, at low temperature, the average conformation of the glycylglycine zwitterion in 18 waters of solvent, allowing all backbone angles in the peptide to vary. We find a minimum energy conformation for the system peptide/water which is different from the peptide minimum energy conformation itself. The resulting conformation is shown in Figure 1. The energy of this conformation is -18833.4 f 0.3 kcal/mol of system. This corresponds approximately to a peptide self-energy of 6.6 kcallmol of peptide, -86.3 kcallmol of peptide in waterlpeptide interaction, and (22)T.F.Koetzle and W. C. Hamilton, Acta Crystallogr., Sect. B, 28, 2083 (1972).
Letters
-18 753.9 kcal/l8 mol of water. This latter figure corresponds to approximately -9.0 kcal/mol of water divided between strain energy of water (positive) and hydrogen bonding energy (negative). The backbone conformationz3of the zwitterion corre) ~-73, (t))z = -145, while the minimum sponds to the ( 4 ~ = = 0, with energy gas-phase zwitterion has (4J)2 = -179, an energy of 4.6 kcal/mol of peptide. This corresponds approximately to the structure found in the crystal. The starting point for this computation was the same water configuration as that which ended our solvation study of the glycyl zwitterion. Several aspects of the final “minimum” energy structure presented here are noteworthy, in comparison with the structure found for its predecessor, where the glycyl zwitterion formed 6-mers; here we find one 5-mer, based on 0-4-0-3-0-7-0-13-0-15 (which is hidden slightly in the drawing). Two other 6mer8 are apparent. The short, highly distorted hydrogen bond between 0 - 5 and 0-10 which we observed in the glycyl zwitterion has normalized. The shortest H bond in the system is now between 0 - 8 and 0-1,the longest is between 0-14 and 0-16. There are a total of 20 intrawater hydrogen bonds in this structure. It is noteworthy that the COO-end of the peptide has not been successful in breaking hydrogen bonds and forcing water orientation about itself. We believe that this is the first documented instance of a prediction of zwitterionic peptide conformation which is solvent stabilized to the detriment of backbone interactions. To be sure, the partial solvation, and the droplet nature of the computation implies that the final solution structure might not correspond to the one we found. The partial hydrated structure nevertheless demonstrates the importance of including solvent in a discussion of backbone conformation.
Acknowledgment. It is a pleasure to acknowledge, with great thanks, the support of NIH Grant No. GM26525 which made this work possible. Grants of computer time from the University of Connecticut Research Computer Center are also acknowledged with gratitude. (23)J. C.Kendrew, W. Klyne, S. Lifson, T. Miyazawa, G. Nemethy, D. C.Phillips, G. N. Ramachandran, and H. A. Scheraga, Biochemistry, 9, 3947 (1970).
