J. Am. Chem. SOC.1993, 115, 1964-1970
1964
Free Energy Calculations Involving Internal Coordinate Constraints to Determine Puckering of a Six-Membered Ring Molecule L. Young and Carol Beth Post* Contribution from the Department of Medicinal Chemistry, Purdue University, West h f a y e t t e , Indiana 47907. Received August 31, 1992
Abstract: The free energy of boatlike puckering is examined for dihydropyridine(DHP) and dihydronicotinamidemononucleoside (NMSH) by thermodynamic simulations with an empirical force field. The interest in the conformation of the dihydropyridine ring stems from the question of a nonplanar ring conformation to facilitate hydride transfer between the cofactor NADH (reduced nicotinamide adenine dinucleotide) and the substrate in enzyme complexes. To investigate this question we secure a set of empirical force field parameters for the nonaromatic six-membered ring molecule dihydropyridine. A reaction coordinate comprising two dihedral angles is used to constrain the ring in a given boat conformation to calculate the free energy of ring puckering. In agreement with small molecule crystallographic structures, the free energy minimum lies close to a planar ring, but importantly, a broad minimum exists which would allow a range of boat conformations. In addition to the bonding interactions of the dihydropyridine ring, the NMSH free energy profile for puckering depends on nonbonded interactions between the ribose and base as determined by the anti or syn orientation of the glycosidic bonds and pyramidalization of the ring nitrogen. The parameters and computational approach reported here will be useful in calculations on any of the wealth of enzyme complexes involving the cofactor NADH.
Introduction A description of the conformational equilibrium of molecules is necessary for a complete understanding of the function of biological systems. Multiple conformations with similar energies contribute to the thermodynamic properties of the system, and a description in terms of the average conformation may not be adequate. Even proteins with a well-ordered 3-dimensional structure exhibit conformational flexibility in active-site loopsla2 and the binding of ligands. We report a molecular dynamics study on the conformational equilibrium of the flexible-ring molecules dihydropyridine (DHP) and dihydronicotinamide mononucleoside (NMSH). D H P and N M S H are fragments of the cofactor reduced nicotinamide adenine dinucleotide (NADH). The pyridine cofactors NADH and NADPH are ubiquitous in living systems and are involved in a larger number of enzymic reactions than any other c ~ f a c t o r . ~ Their function is in stereospecific hydride transfer by reduction and oxidation of C4 of the pyridine/dihydropyridine ring (Figure 1a). Glycolysis, the tricarboxylic acid cycle, ethanol metabolism, and purine synthesis are a few of the many essential processes requiring pyridine nucleotide cofactors. There is much interest in trying to understand the significance of conformational factors of N A D H in enzyme catalysis and stereo~pecificity.~-' The ring conformation is one such factor; it has been proposed that a boatlike conformation is the transition-state structure for hydride transfer from C4 with the pseudoaxial hydrogen being the transferring h y d r ~ g e n . ~ * 'In ~ ~a boatlike conformation the pseudoaxial positions for the hydrogen and N1 lone pair electrons facilitate transfer by allowing the appropriate overlap of ?r orbitals on opposite sides of the ring. Although experiments play an invaluable role in studying structure, the information they provide is generally limited to a
description of the average conformation. A more complete understanding can be gained from additional information provided by thermodynamic sim~lationsl@'~ on the range of energetically accessible conformations. As such, the tendency toward boatlike puckering of the flexible dihydropyridine ring was investigated by calculating the free energy of ring pucker with thermodynamic simulation methods and intemal-coordinateconstrainedmolecular dynamics. For systems separated in configuration space, the free energy difference as a function of an internal coordinate is determined by configurational perturbations and simulations in which the internal coordinate is held constant by holonomic cons t r a i n t ~ . ' ~ This * ~ ~ procedure ~'~ has been successfully applied to dihedral angle coordinates in a dipeptidei0 and an enzyme-bound inhibitor. In the first step toward studies on the conformational flexibility of the dihydronicotinamide ring in an enzyme active site, we investigate the ring puckering of these isolated fragments of NADH. Our investigation finds no tendency toward stabilization of the putative transition-state structure for hydride transfer in the isolated DHP and NMSH. However, the free energy profile as a function of ring pucker is nearly flat over a 20'-30' range in pucker angles, and the energy for N1 inversion is small. In the next section we describe the parameterization of the CHARMM molecular force field. A description of the reaction coordinate and protocol for the free energy profile calculation follow. In Results, we examine the accuracy and convergence of the constraint algorithm for flexible ring molecules and free energy profiles for ring puckering and discuss structural features related to hydride transfer, including ring nitrogen pyramidalization. Parameters
The parameters required for the potential function of the programis are atomic partial charges qi, van der Waals constants Eh,, and Rmin,and the equilibrium geometry values for bond lengths, bond angles, and dihedral angles with their associated force constants. N o explicit hydrogen-bond term was CHARMM
(1) James, M.; Sielecki, A. R. J . Mol. Biol. 1983, 163, 229. (2) Ringe, D.; Petsko, G. A. Study of Protein Dynamics by X-Ray Diffraction. In Merhods in Enzymology; Hirs, C., Timasheff, S.,Eds.; Academic: New York, 1986; Vol. 131, pp 389-433. (3) You, K. CRC Crii. Reu. Biochem. 1985, 17, 313. (4) Donkersloot, M. C. A.; Buck, H. M. J . Am. Chem. SOC.1981, 103, 6554. (5) Benner, S. A . Experienrio 1982, 38, 633. (6) Nambiar, K. P.; Stauffer, D. M.; Kolodziej, P. A,; Benner, S. A. J . Am. Chem. SOC.1983, 105, 5886. (7) Wu, Y.; Houk, K. N . J . Am. Chem. SOC.1991, 113, 2353. (8) Wu, Y.; Houk, K. N., submitted for publication. (9) Rob, F.; Van Ramesdonk, H. J.; Van Gerresheim, W.; Bosma, P.; Scheele, J . J.; Verhoeven, J . W. J . Am. Chem. SOC.1984, 106, 3826.
(10) Tobias, D. J.; Brooks, C. L., I11 J . Chem. Phys. 1988, 89, 5515. (11) Straatsma, T.; McCammon, J. A. J . Chem. Phys. 1989, 90, 3300. (12) Tobias, D. J.; Brooks, C. L., 111; Fleischman, S.H. Chem. Phys. Lett. 1989, 156, 256. (13) Wade, R. C.; McCammon, J. A. J . Mol. Biol. 1992, 225, 679. (14) Tobias, D. J.; Brooks, C. L., I11 Chem. Phys. Leu. 1987, 142, 472. (15) Brooks, B.; Bruccoleri, R.; Olafson, B.; States, D.; Swaminathan, S.; Karplus, M. J . Compur. Chem. 1983, 4, 187.
0002-7863/93/1515-1964$04.00/00 1993 American Chemical Society
J . Am. Chem. SOC.,Vol. 115, No. 5, 1993
Free Energy of Puckering in the 6-Membered Ring of NADH
1965
Table 11. Interaction Energies for DHP-Water Dimers'
complexb (water--DHP)
6-31G* AE
empirical AE
0.-H 1 H-*N1 0*-H2 H-C2 0-H3 H-423 O*-C4
-3.84 -3.66 -3.64 -4.42 -1.40 -0.65 -2.62 -3.32 -0.70 -0.62 -2.71 -2.63 -0.16 -0.03 "Interaction energies in kcal/mol. *Atoms used to define the direction of approach in the complex.
H1
Table 111. Bond Parameters
bond N1-Hl C2-H2 C3-H3 C4-H4A C4-H4B C5-H5 C6-H6
equilibrium force length constant 1.01 1.09 1.09 1.11 1.11 1.09 1.09
474.0 350.0 350.0 317.0 317.0 350.0 350.0
bond Nl-C2 C2-C3 C3-C4 C4-C5 C5-C6 C6-N1
equilibrium force length constant 1.372 1.337 1.516 1.516 1.337 1.372
302.0 552.0 214.8 214.8 552.0
302.0
OH
OH
Figure 1. (a) Structure of dihydropyridine (DHP). (b) Structure of dihydronicotinamidemononucleoside (NMSH). Table I . Partial Charges and van der Waals Constants for
Di hydropyridine atom charge N1 HI C2 H2 C3 H3 C4
E,,, -0.48 -0.20 0.28 -0,046 0.06 -0.09 0.04 -0.0078 -0.02 -0.09 0.05 -0.0078 -0.10 -0.1562
R,,, 3.7 0.499 3.6 2.936 3.6 2.936 3.6
atom charge H4A
H4B C5 H5 C6 H6
0.02 0.02 -0.02 0.05 0.06 0.04
E,,, -0.0078 -0.0078 -0.09 -0.0078 -0.09 -0.0078
R,,, 2.936 2.936 3.6 2.936 3.6 2.936
included since the attraction between hydrogen-bonding atoms is adequately modeled by appropriate Coulombic and van der Waals potential terms. Partial charges and dihedral angle terms were determined for the base DHP, as described below. Other parameters are from crystallographic results or the CHARMMZ2 all-hydrogen potential function.I6 Partial charges, q,, of dihydropyridine were found by fitting the molecular dynamics intermolecular potential energy for a DHP-water dimer to corresponding a b initio intermolecular energies. Ab initio calculations were performed with the program GAUSSIAN 8817 and a 6-31G* basis set. This basis set was chosen because of previous success in describing similar interactions'* and to be consistent with other work on the development of the C H A R M M Z Z force field.16 To decrease the size of the calculation, C, symmetry was imposed for DHP, the mirror plane being perpendicular to the ring plane and through atoms N1 and C4. The structures of DHP and water were obtained by full geometry optimization of the isolated molecule and were not varied in the dimer interaction. Optimization of DHP began from the crystal coordinates of an N-substituted dihydr~nicotinamide.'~Mini~~
(16) MacKerrell, A . D., Jr.; Wiorkiewicz-Kuczera, J.; Karplus, M., private communication. (17) Frisch. M.; Head-Gordon, M.; Schlegel, H.; Raghavachari, K.; Binkley, J.; Gonzalez, C.; Defrees. D.; Fox, D.; Whiteside, R. A,; Seeger. R.; Melius. C.; Baker. J.; Martin, R. L.: K a h n , L. R.; Stewart, J.; Fluder, E.; Topiol, S . ; Pople, J . Goussian 88. Carnegie-Mellon University, Pittsburgh, PA, 1982. . (18) Duffv, E. M.; Severance, D. L.; Jorgensen, W. L. J . Am. Chem. SOC.
Figure 2. Diagram of the dihedral angles, &Jc4K5K:3x:6 and & used to define the reaction coordinate S for ring pucker.
Jc~~+c~-~~,
mization of the intermolecular ab initio energy for the DHP-water dimer was done for 7 of 11 selected orientations of the water relative to the geometry of DHP. (Four of these orientations are redundant due to symmetry.) The orientations chosen corresponded to the strongest intermolecular interactions. The intermolecular distance along a direction of approach and, in some cases, the angular orientation of the water molecule were allowed to vary in the ab initio optimization. The intermolecular empirical energy was minimized as a function of the DHP-water distance using the simplex method. The minimum interaction energy values from the empirical potential were fit to the ab initio interaction energies by varying 4,. Of the nonbonded energy terms, only q, was varied to reach agreement, while E,,, and R,,, are from the CHARMMZZ parameters.I6 The resulting charges are listed in Table I. Listed in Table I1 are the energies for the seven interactions from the 6-31G* calculation and from the nonbonded terms of the empirical force field. The force constants for the dihedral angles about Nl-C2, Nl-C6, C3-C4, and C4-C5 were varied to obtain an energy minimum for a near-planar structure of DHP in agreement with the optimized a b initio geometry and with other results. A near planar conformation of DHP is obtained by ab initio full geometry optimization by this work and others.7~x~20*21 Furthermore, the dihydropyridine ring in the crystallographic structure of N-substituted dihydr~nicotinamides'~ is nearly planar, although crystal forces can be significant to determining the conformation observed in the crystal state. The values for the pseudodihedral angles &--5
