Intrinsic Torsional Potential Parameters for Conformational Analysis of

three-term Fourier series expansion is used to represent the intrinsic torsional energy. ... truncated Fourier expansions,7,8 while the latter are rep...
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15588

J. Phys. Chem. 1996, 100, 15588-15598

Intrinsic Torsional Potential Parameters for Conformational Analysis of Peptides and Proteins Young Kee Kang,*,†,‡ Kyoung Tai No,‡,§,| and Harold A. Scheraga*,‡ Department of Chemistry, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, Korea, Department of Chemistry, Soong Sil UniVersity, Sang Do 5 Dong 1-1, Dong Jak Gu, Seoul 156-743, Korea, and Baker Laboratory of Chemistry, Cornell UniVersity, Ithaca, New York 14853-1301 ReceiVed: April 18, 1996X

New sets of intrinsic torsional parameters, obtained by fitting to experimental and/or theoretical values of torsional barriers and relative conformational energies of various uncharged model organic compounds, are presented. They are intended for use in conformational energy computations on peptides and proteins. A three-term Fourier series expansion is used to represent the intrinsic torsional energy. Each set of intrinsic torsional parameters, obtained from a single model compound, reproduces experimental torsional barriers, relative conformational energies, and torsion angles of related molecules not used for the parametrization. The sets of parameters of a new potential function, including electrostatic interactions based on partial atomic charges, and nonbonded, hydrogen-bond, and intrinsic torsional energies, are tested in conformational energy calculations on a model peptide N-acetyl-N′-methylalanineamide. The electrostatic energy component plays a significant role in the total conformational energy and leads to a high relative energy of the RR (A) conformation compared to the C7eq (C) conformation, although the latter is still the global minimum. These results differ from those with ECEPP/3, CHARMM, and AMBER, but are reasonably consistent with those from recent ab initio studies.

Introduction Studies of the changes of conformation and energy of a molecule associated with internal rotation about its single bonds have long been of considerable interest.1-3 The torsions about the bonds of the backbones and side chains of peptides and proteins have been found to be important in determining their three-dimensional structures.4-6 The energy associated with internal rotations is represented by a sum of terms that depend on torsion angles and interatomic distances.4 The former terms are sometimes expressed as truncated Fourier expansions,7,8 while the latter are represented by electrostatic and nonbonded potentials. Some molecular force fields include potentials for deformation of the geometry in the latter terms.9-12 The ECEPP algorithm (empirical conformational energy program for peptides), developed in this laboratory,13-16 has been used for conformational energy computations on peptides and proteins, allowing only their torsion angles to be varied. Since the ECEPP parameters are derived from experimental data, new experimental or theoretical information that was not available in 1975 for torsional barriers and conformational energy differences of molecules with various functional groups has enabled us to develop the new sets of intrinsic torsional parameters for incorporation into the ECEPP force field. Taking advantage of the need for updating and/or modifying the parameters used in the computation of the conformational energies of peptides and proteins, we have developed a method to calculate partial atomic charges17-20 based on the concept of modified partial equalization of orbital electronegativity (MPEOE). In addition, the parameters for the nonbonded and hydrogen* Authors to whom correspondence should be addressed. † Chungbuk National University. ‡ Cornell University. § Soong Sil University. | Member of the Center for Molecular Science, Korea. X Abstract published in AdVance ACS Abstracts, September 1, 1996.

S0022-3654(96)01143-4 CCC: $12.00

bond interactions were recently derived from crystal data and ab initio calculations on organic compounds and amino acids.21-24 The aim of the present work is to report the new sets of intrinsic torsional parameters utilizing the recently obtained partial atomic charges and nonbonded parameters. These new sets can reproduce experimental and theoretical values of torsional barriers and conformational energy differences for various uncharged organic compounds and can be used for conformational energy computations on peptides and proteins. In the second part of the Results and Discussion section, the influence of the new potential parameters on the low-energy conformations of N-acetyl-N′-methylalanineamide (Ac-Ala-NHMe) is discussed. Procedure A. Potential Functions. The total conformational energy ETOT is calculated as the sum of the electrostatic energy EES, the nonbonded energy ENB, and the intrinsic torsional energy ETOR. The hydrogen-bond energy EHB is included in the nonbonded energy components.13 The forms of the electrostatic and nonbonded potentials were taken as those of ECEPP.13 The partial atomic charges for each molecule were calculated by the MPEOE method of No et al.17-20 The effective dielectric constant was taken as unity17-24 instead of 2 (effectively 4) as in ECEPP. The recently derived values of dispersion coefficients21 were used for the attractive term of the nonbonded Lennard-Jones potential ENB,24 and the repulsive coefficients were obtained from crystal data on organic compounds and amino acids.24 The hydrogen-bond energy EHB was calculated by using 6-12 type potential functions, whose parameters were optimized with 6-31G** ab initio potential energy surfaces of several hydrogen-bonded molecular pairs;23 this replaces the 10-12 type EHB of ECEPP. Differing from the procedure in ECEPP, a three-term Fourier series expansion is used to represent the intrinsic torsional energy ETOR for a general torsion angle θ. © 1996 American Chemical Society

Conformational Analysis of Peptides and Proteins

J. Phys. Chem., Vol. 100, No. 38, 1996 15589

ETOR(θ) ) (V1/2)(1 + cos θ) + (V2/2)(1 - cos 2θ) + (V3/2)(1 + cos 3θ) (1) where θ designates φ, ψ, ω, and χ’s of the polypeptide chain. Because the electrostatic and nonbonded energies also depend on the torsion angle θ, the total conformational energy, not only the intrinsic torsional energy given by eq 1, is used to derive the intrinsic torsional parameters V1, V2, and V3. However, in deriving the intrinsic torsional parameters, the hydrogen-bond energy EHB was omitted from the total energy because the reference molecules used to obtain the parameters do not have any atom pairs that are capable of forming hydrogen bonds. Each set of parameters was obtained by fitting the computed torsional barriers and/or relative conformational energies of only one compound of the set to the corresponding experimental (or theoretical) values. The important role of the V1 and V2 terms, in addition to the V3 term, for describing the intrinsic torsional properties of alkanes has been reported previously.8,25 In the nonbonded 6-12 component of ECEPP, an empirical factor for 1-4 interactions was introduced to scale the empirical r-12 repulsive coefficients determined from crystal data.13 A value of 0.5 was chosen for this factor because it produced force-constant curves that fit those from Hartree-Fock or Thomas-Fermi-Dirac calculations well in the range of 1-4 contacts found in polypeptides. However, in the present work, to account for the reduction of repulsions at such short distances, each equilibrium distance (r0) between two interacting atoms is replaced by its collision diameter (σ, the value of r at which ENB ) 0), i.e., reduced by a factor of 21/6. Therefore, the nonbonded energy ENB for the 1-4 interaction of two atoms i and j is calculated by using the expression

ENB ) (σ/rij)12 - 2(σ/rij)6 ) (r0/rij)6{(1/4)(r0/rij)6 - 1}

(2a) (2b)

where  is the depth of the energy well of the nonbonded potential and r0 ) 21/6σ. A factor of 21/6 was necessary because a constant factor of 0.5 does not reproduce experimental torsional barriers, relative conformational energies, and conformations. For example, using the factor 0.5, a set of intrinsic torsional parameters for the C-C torsion of aliphatic chains was fitted to experimental data of n-butane, but it failed to reproduce the torsional barriers and the gauche conformation of the aliphatic portion of n-propylamine; however, the factor of 21/6 did provide good agreement between the calculated and experimental values. Each set of intrinsic torsional parameters was obtained from the procedure described below. First, based on the experimental (or ab initio) data and symmetry, a decision was initially made as to whether one, two, or three of the Vi’s were required. For example, for the central C-C intrinsic torsion of n-butane, all three are required. In cases where one or two of V1, V2, or V3 were judged to be zero, such a zero value was preassigned before using the following procedure. Second, from experimental (or ab initio) torsional barriers and relative conformational energies, the relative total conformational energies (∆ETOT) were assigned at the torsion angles θ ) 0°(cis), 60°(gauche), 120°(a barrier for the trans-to-gauche or gauche-to-trans conformational change), and 180°(trans) for a 3-fold type of torsion, and at θ ) 0°(cis), 90°(a barrier for the trans-to-cis or cis-to-trans conformational change), and 180°(trans) for a 2-fold type of torsion. At each of these values of θ, the initial intrinsic torsional energy (ETOR) was calculated by subtracting the sum of the electrostatic energy (∆EES) and the nonbonded energy

(∆ENB) from the relative total conformational energy (∆ETOT). By using the values of ETOR(0°), ETOR(60°), ETOR(120°), and ETOR(180°) for a 3-fold type of torsion and the values of ETOR(0°), ETOR(90°), and ETOR(180°) for a 2-fold type of torsion, the initial values of the Vi’s were calculated. The relationships between the Vi’s and ETOR’s are shown in Appendix 2. Third, with these initial values of the Vi’s, the total energy ETOT was minimized with respect to the torsion angle θ, whose starting values were 0°, (60°, (120°, and (180° for a 3-fold type of torsion, and 0°, (90°, and (180° for a 2-fold type of torsion. From these new total conformational energies at the new torsion angle θ’s, the torsional barriers for gauche-to-trans and onegauche-to-another-gauche conformational change, and the energy of the gauche conformation relative to the trans conformation, were computed. Then, the three parameters V1, V2, and V3 were varied one by one, and the minimization of ETOT with respect to θ at each of θ ) 0°, 60°, 120°, and 180° was followed for each set of the Vi’s. This procedure for assigning the Vi’s and minimizing ETOT was repeated until the deviations between the calculated barriers and the relative energies and the corresponding experimental (or ab initio) data converged within a criterion of less than 0.001 kcal/mol. In each energy minimization, the SUMSL (secant-type unconstrained minimization problem solver) algorithm26 was used. B. Molecular Geometry and Experimental Data. The geometry used for the organic compounds is in general that given in the structural literature27,28 for each molecule. References to the structures not contained in refs 27 and 28 are listed in Appendix 1. Only structures obtained from electron diffraction, microwave, infrared, and Raman experiments in the gas phase were selected. In the case of molecules for which no information about bond lengths and bond angles was available, the geometry was taken to be the same as that of similar molecules with known structure. In conformational energy calculations, bond lengths and bond angles were fixed (as in ECEPP), and only the torsion angles for internal rotation were taken as the variables. Because the aim of this work is to obtain the sets of intrinsic torsional parameters that can be used for conformational energy calculations on peptides and proteins, as mentioned above, the use of rigid geometry here is valid, provided that the set of bond lengths and bond angles is chosen properly.5 The experimental torsional barriers and/or relative conformational energies used for parametrization were, in principle, obtained from microwave, electron diffraction, Raman, farinfrared, NMR, and ultrasonic experiments in the gas phase. However, if the gas-phase experimental data are not available, some data in the liquid state or organic solvents were used. For example, the data obtained from NMR experiments in both the gas phase and organic solvents were used for amides. When sufficient experimental data were not available, especially for 2-butanone, ethylmethylamine, methylguanidine, ethyl methyl ether, acetic acid, and dimethyl disulfide, the results of ab initio calculations were used for parametrization. C. Intrinsic Torsional Parameters. To describe torsions properly, atom types are defined and listed in Table 1. For each type of torsion, experimental data for only one compound (listed in the fifth column of Table 2) were used to derive a set of intrinsic torsional parameters for the molecules in the same set of related compounds. The procedures used to obtain each of these adjustable parameters are described in detail below for each class of torsions. The best fitted values of the intrinsic torsional parameters V1, V2, and V3 for internal rotations are listed in Table 2. a. C-C Torsions. First, the intrinsic torsional parameters

15590 J. Phys. Chem., Vol. 100, No. 38, 1996 TABLE 1: List of Atom Types Used for Intrinsic Torsional Parameters atom type a

this work

ECEPP

C CM CR CB CA CF N1 N2 NA NH

C6 (C9) C6 (C9) C8 (C10) C7 (C11) C7 (C11) C8 (C10) N13 (N14, N15) N13 (N14, N15) N13 (N14, N15) N13 (N14, N15)

NC NE NG1 NG2 O OH OA OS S SH

N13 (N14, N15) N13 (N14, N15) N13 (N14, N15) N13 (N14, N15) O18 (O19) O18 (O19) O18 (O19) O18 (O19) S20 (S21) S20 (S21)

a

descriptiona aliphatic CH2, CH, or C aliphatic CH3 aromatic C ketone, acid, or ester carbonyl C amide carbonyl or peptide bond C Cζ of Arg side chain primary amine N secondary amine N amide N N-methylated amide or peptide bond N N,N-dimethylated amide N N of Arg side chain Nη1 of Arg side chain Nη2 of Arg side chain ether O alcohol O acid O ester O sulfide and disulfide S thiol S

These are the definitions given in refs 13-16.

for the C-C bond were fitted to the experimental barriers of n-butane for the trans-to-gauche (3.4 ( 0.4 kcal/mol, from ultrasonic relaxation measurements in the liquid phase)29 and one-gauche-to-another-gauche (4.54 kcal/mol, from Raman experiments)30 conformational change, and to the energy of the gauche conformation relative to the trans conformation (0.89 ( 0.03 kcal/mol, from Raman experiments).30 The corresponding calculated values are 3.40, 4.54, and 0.89 kcal/mol, respectively. The computed gauche torsion angle (the same for g+ and g-) is 64.2°, which is consistent with experimental values 62 ( 1°,30 65 ( 6°,31 and 72 ( 5°.32 However, for the symmetric 3-fold potential for CM-C bonds, another set of parameters was required and obtained by using the barrier of 3.17 kcal/mol of propane from microwave experiments.33 For the C-CR torsion, a 2-fold intrinsic torsional parameter was obtained, using the experimental barrier34 of ethylbenzene and evidence that the ethyl group is perpendicular to the benzene ring in its stable conformation.35 The intrinsic torsional parameters for the C-CB bond in ketones, acids, and esters were best fitted to ab initio results with a 6-31G* basis set on torsional barriers and relative energies of 2-butanone,36 because of insufficient experimental data. The computed energy of the g+ ()g-) conformation relative to that of the trans conformation of CH3CH2-CO in 2-butanone, i.e., for C-CB, is 1.79 kcal/ mol, which is in agreement with a value (2.1 ( 0.4 kcal/mol) from an electron diffraction study.37 However, since this torsion is not relevant to the symmetric 3-fold CM-CB torsions, the value of V3 ) 0.666 kcal/mol was obtained by using the barrier of 0.78 kcal/mol of acetone from microwave experiments.38 The intrinsic torsional parameters for the C-CA or CMCA bond, of which the former corresponds to the NCR-C′N (ψ) bond of the peptide backbone, were fitted to the CH3-C′N barrier of N-methylacetamide, 1.92 kcal/mol, obtained from neutron inelastic scattering experiments in the gas phase.39 In the case of the symmetric 3-fold CM-CA torsion in acetamide, however, the value of V3 was obtained after fitting the CH3C′N barrier to the experimental value of 0.07 kcal/mol,40 because the barrier in acetamide is significantly lower than that in N-methylacetamide. b. C-N Torsions. A set of intrinsic torsional parameters for the C-N1 bond were fitted to the experimental barrier (1.97

Kang et al. TABLE 2: Potential Parameters (kcal/mol) for Internal Rotationsa typeb

V1

C-C CM-C C-CR C-CB CM-CB C-CA CM-CA C-N1 CM-N1 C-N2 CM-N2 CA-NA CA-NH CA-NC NH-C NH-CM NE-CF CF-NG1 CF-NG2 C-O CM-O C-OH CM-OH CR-OH CB-OA CB-OS

0.091 0 0 1.849 0 -0.018 0 0.317 0 -0.660 0.275 0 4.109 0 0 0 0 0 0 -9.138 0.412 -0.495 0 0 -1.531 -0.977 0.219 0 0 -0.504 -0.114 -0.263 0 2.338

OS-C OS-CM C-S CM-S C-SH CM-SH S-S

V2

V3

ref compdc

0.695 2.372 n-butane 0 2.848 propane 2.102 0 ethylbenzene 0.950 0.840 2-butanone 0 0.666 acetone 0.047 1.663 N-methylacetamide (ψ)d 0 -0.100 acetamide -0.019 1.738 ethylamine 0 1.912 methylamine 1.399 1.264 ethylmethylamine -0.189 2.798 dimethylamine 17.961 0 acetamide 22.109 0 N-methylacetamide (ω)d 17.944 0 N,N-dimethylacetamide 0 1.498 N-methylacetamide (φ)d 0 1.498 N-methylacetamide 11.335 0 methylguanidine (Arg, χ5)e 24.960 0 methylguanidine (Arg, χ6,1)e 8.553 0 methylguanidine (Arg, χ6,2)e 6.157 -0.320 ethyl methyl ether -0.289 1.787 dimethyl ether 0.547 0.801 ethanol 0 0.997 methanol 4.085 0 phenol 10.013 0 acetic acid 13.583 0 methyl acetate 10.416 0 methyl formate 0 0.526 methyl formate 0 0.526 methyl formate -0.049 1.660 ethyl methyl sulfide 0.093 1.918 dimethyl sulfide -0.279 1.166 ethanethiol 0 1.229 methanethiol -7.546 0 dimethyl disulfide

a Parameters V1, V2, and V3 are those appearing in the intrinsic torsional potential of eq 1. Zero values of V1, V2, or V3 were preassigned on the basis of the experimental symmetry of the total potential function. b Atom types are defined in Table 1. c Reference compound used in the determination of the adjustable parameters of a given set of related compounds; see text. d Torsion angles for peptide backbone. e Side chain of Arg residue.

kcal/mol) and the energy of the g+ ()g-) conformation relative to the trans conformation (0.31 kcal/mol) of ethylamine.41 A different set of parameters for the methyl torsion (CM-N1) of methylamine was obtained as a 3-fold type (V3) by fitting to the experimental barrier (1.96 kcal/mol).42 For the intrinsic torsion C-N2 of secondary amines, the results of ab initio calculations on ethylmethylamine with a 4-31G basis set by Allinger et al.43 were used to derive the intrinsic torsional parameters. The resulting calculated barriers for the trans-to-gauche and one-gauche-to-another-gauche conformational change are 2.87 and 5.62 kcal/mol, respectively, which are in good agreement with the ab initio results43 (2.87 and 5.62 kcal/mol, respectively). The computed energy of the g+ ()g-) conformation relative to the trans conformation is 1.44 kcal/mol, which is also in accord with the ab initio value43 (1.44 kcal/mol). However, another set of intrinsic parameters for the symmetric 3-fold CM-N2 torsion was obtained to reproduce the experimental barrier in dimethylamine.44 The intrinsic torsional parameters for the CA-NA bond of amides were fitted to a barrier of acetamide (18.2 kcal/mol) obtained from NMR experiments on this compound in acetone,45 and a 2-fold parameter V2 was obtained. For the torsion of the CA-NH bond, which corresponds to that of the CRC′-NCR (ω) bond of the peptide backbone, the parameters were fitted to the barrier (22.6 kcal/mol) for the conformation with the amide N-H bond of N-methylacetamide perpendicular to the

Conformational Analysis of Peptides and Proteins plane of the CO-N group relative to the planar trans conformation, and to the energy (2.8 kcal/mol) of the cis conformation relative to the trans conformation of N-methylacetamide based on NMR experiments on this compound in C2H4Cl2.46 For the CA-NC torsion of N,N-dimethylamides, a barrier of N,Ndimethylacetamide (15.8 ( 1.1 kcal/mol) obtained from 1H NMR experiments in the gas phase47 was used to obtain a 2-fold parameter V2. For the intrinsic torsion of the NH-C or NH-CM bond, of which the former corresponds to the C′N-CRC′(φ) bond of the peptide backbone, the potential parameters were fitted to the barrier (1.69 kcal/mol) for rotation of the N-methyl group of N-methylacetamide obtained from neutron inelastic scattering experiments in the gas phase.39 A 3-fold parameter V3 was found to be sufficient to represent this torsion. The intrinsic torsional parameters for the NE-CF and CFNG bonds, which correspond to the N-Cζ (χ5) and Cζ-Nη (χ6) of the side chain of the neutral Arg residue, were obtained by using ab initio results with a 6-31G basis set on methylguanidine.48 The ab initio barrier for the trans-to-cis conformational change of the NE-CF torsion used for the parametrization is 11.90 kcal/mol. In the case of the CF-NG torsions for methylguanidine, two different 2-fold parameters were also obtained by fitting to ab initio barriers of 24.10 and 7.50 kcal/ mol, which correspond to those for χ6,1 and χ6,2 of the Arg side chain. c. C-O Torsions. The intrinsic torsional parameters for C-O bonds were fitted to the barriers of ethyl methyl ether for the trans-to-gauche (2.67 kcal/mol) and one-gauche-to-anothergauche (5.63 kcal/mol) conformational change (for rotation about the CH3O-CH2CH3 bond) obtained from ab initio calculations at the HF/6-31G* level,49 and to the energy of the gauche conformer relative to the trans conformer (1.5 ( 0.2 kcal/mol) from an infrared spectral analysis.50 The calculated gauche torsion angle is 77.3°, which is consistent with a value of 84 ( 6° from electron diffraction.51 For the symmetric 3-fold CM-O torsion of dimethyl ether, another set of parameters was obtained from the barrier from infrared experiments (2.63 ( 0.02 kcal/mol).44 For the intrinsic torsion about the C-OH bond of alcohols, a set of parameters was obtained by fitting to barriers for the trans-to-gauche and one-gauche-to-another-gauche conformational change (1.17 kcal/mol), and to the energy of the g+ ()g-) conformation relative to the trans conformation (0.12 kcal/mol) of ethanol based on microwave experiments.52 The calculated gauche torsion angle is 58°, which is well in accord with the result of a microwave study (54 ( 6°).53 The intrinsic torsional parameters of the symmetric CM-OH bond of methanol was found to be a 3-fold one, by using the barrier from a microwave experiment (1.07 ( 0.02 kcal/mol).54 A 2-fold parameter for the CR-OH bond of phenol was obtained by fitting to the barrier (3.36 kcal/mol) obtained from a microwave experiment.55 For the intrinsic torsion about the CB-OA bond of acids, a set of parameters was derived from the barrier for the cis-to-trans conformational change (12.55 kcal/mol) and the energy of the trans conformer relative to the cis conformer (5.85 kcal/mol) from ab initio results with the MP3/6-311+G** basis set using the geometry obtained by optimization with the 6-31G* basis set on acetic acid.56 The intrinsic torsional parameters for the CB-OS bond of esters were fitted to the barrier for the cis-to-trans conformational energy change (5.9 kcal/mol) and to the energy of the cis conformer relative to the trans conformer (8.5 ( 1.0 kcal/mol) in methyl acetate, which were obtained from ultrasonic measurements on the liquid compound57 and infrared experiments

J. Phys. Chem., Vol. 100, No. 38, 1996 15591 in an Ar matrix,58 respectively. However, the parameters obtained for methyl acetate do not reproduce well the corresponding experimental values for methyl formate and ethyl formate. Therefore, another set of parameters for the CB-OS bond of methyl formate was obtained from the energy of the cis conformer relative to the trans conformer (3.85 ( 0.20 kcal/ mol) in a gas-phase infrared experiment59 and the barrier for the cis-to-trans conformational change (7.8 kcal/mol) measured by ultrasonic techniques on the liquid compound.57 In addition, the parameters for the symmetric 3-fold OS-CM torsion were obtained from gas-phase microwave experiments on methyl formate,60 and the intrinsic torsional parameters of the OS-C bond were taken as those of the OS-CM bond. d. C-S and S-S Torsions. For the C-S intrinsic torsion of sulfides, the parameters were fitted to experimental barriers for the gauche-to-trans (1.98 kcal/mol, from microwave experiments)61 and for one-gauche-to-another-gauche (3.43 kcal/mol, from infrared and Raman experiments)62 conformational change, and to the energy of the trans conformer relative to the gauche conformer (0.27 kcal/mol, from microwave experiments) in ethyl methyl sulfide.61 The intrinsic parameters of the symmetric 3-fold CM-S torsion of dimethyl sulfide were obtained from the barrier from microwave experiments (2.15 ( 0.02 kcal/ mol).63 A set of intrinsic torsional parameters for the C-SH bond of thiols was obtained by fitting to barriers for the gauche-totrans (1.37 kcal/mol) and one-gauche-to-another-gauche (1.51 kcal/mol) conformational change, and to the energy of the trans conformer relative to the gauche conformer (0.43 kcal/mol) from microwave experiments on ethanethiol.64 A different parameter, V3, was assigned for the symmetric 3-fold CM-SH bond of methanethiol from the barrier (1.27 ( 0.03 kcal/mol) from a microwave experiment.65 Because of the importance of the S-S bond in influencing protein structure, considerable attention has been devoted to determine the structures and the conformational preferences of simple alkyl disulfides by Raman,66-69 infrared,70 and electron diffraction71 experiments. However, the cis and trans barriers, which correspond to one-gauche-to-another-gauche conformational changes through the cis and trans conformations, respectively, for the S-S bond were not identified, and only the barrier has been estimated to be 7-10 kcal/mol for dimethyl sulfide.66,70 Hence, the intrinsic torsional parameters for the S-S bond of disulfides were fitted to recent ab initio barriers and relative conformational energies of dimethyl disulfide calculated at the MP2/6-31G** level,72 in which the cis and trans barriers are 11.48 and 6.19 kcal/mol, respectively. The calculated most stable conformation of dimethyl disulfide is gauche with a torsion angle of 84.5°, which is in excellent agreement with that from an electron diffraction study (85.3 ( 3.7°)71 and ab initio calculations (84.8°).72 Results and Discussion A. Torsional Barriers and Relative Conformational Energies. The experimental and computed torsional barriers and relative conformational energies for the four classes of organic compounds considered here are compared in Tables 3-6. The tables also include those compounds (marked by asterisks) that were used to determine the intrinsic torsional parameters in each set. The average difference between the observed and calculated values for each class of molecules, which were not included in the parametrization, is used for analyzing the results below. The results on the C-C torsions are shown in Table 3. The average difference in the barriers does not exceed (0.5 kcal/

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Kang et al.

TABLE 3: Calculated and Experimental Torsional Barriers and Relative Conformational Energies (kcal/mol) for C-C Bonds torsional barrierb moleculea propane* ethane n-butane 2-methylpropane 2,2-dimethylpropane ethylbenzene ethylamine tert-butylamine ethylmethylamine ethyl methyl ether tert-butyl methyl ether ethanol 1-propanol 2-methyl-2-propanol propionic acid ethyl formate ethanethiol 2-propanethiol 2-methyl-2-propanethiol ethyl methyl sulfide diethyl sulfide isopropyl methyl sulfide

calcdd 3.17 2.98 3.16 3.49 3.72 3.22 3.00 (t) 3.00 (g) 3.60 3.08 (t) 2.95 (g) 3.03 3.89 3.14 (t) 3.17 (g) 3.21 (tt) 3.21 (tg) 3.21 (gg) 3.53 3.23 3.04 3.14 3.62 3.89 3.00 3.23 3.52

rel conf energyc exptle

calcdd

exptle

0.89 (g/t) 0.97 (tg/tt) 0.65 (g/t) 0.91 (t/g) 0.58 (g/t)

0.89 ( 0.03jj 0.8kk 0.81 ( 0.05ll 0.95 ( 0.1mm 0.32,nn 0.37oo

1.79 (g/t) 2.14 (g/t) 2.01 (g/t)

2.1 ( 0.4VV 1.5 ( 0.6ww

a. CM-C Type 3.17f 2.88 ( 1g 3.4h 3.9 ( 0.75,i 3.62j 4.2-4.8k 2.70,l 4.10m 3.74n 3.56,n 3.71 ( 0.05o 3.88p 3.30 ( 0.01q 3.84 ( 0.02q 3.08,r 3.30 ( 0.03s 3.75p 3.31t 3.81t 3.08 ( 0.05u 2.87 ( 0.05u 2.62 ( 0.05V 3.80w 2.34 ( 0.03x >3y 3.26 ( 0.03,z 3.31 ( 0.09,aa 3.77bb 3.95,cc 3.73dd 5.10ee 3.33ff 3.55gg 3.95hh b. C-C Type 3.4 ( 0.4ii/3.65 ( 0.03jj 4.2 ( 0.4ii

n-butane* n-pentane 2-methylbutane 2,3-dimethylbutane n-propylamine

3.40/3.65 3.42 (ttftg) 3.15 (tfg) 6.30 (gft) 3.18/2.77 (t) 3.20/2.61 (g)

ethylbenzene*

1.30 (pfc)

c. C-CR Type 1.30,l 1.16m

acetone* acetic acid methyl acetate

0.78 0.72 0.71

d. CM-CB Type 0.78,pp 0.76qq 0.48,rr 0.64ss 0.31 ( 0.05tt

2-butanone* 3-methyl-2-butanone propionic acid

1.73/1.00 1.67/0.93 1.99/1.01

acetamide* N-methylacetamide*

0.07 1.92

4.12/5.17,nn 4.06/5.09oo 3.82/5.29,nn 3.92/4.59oo

e. C-CB Type 1.73/1.00uu

f. CM-CA Type 0.07xx 1.92yy

a The starred molecules were used to obtain the numerical values of the intrinsic torsional parameters. In cases where several stable conformations are known to exist for a single compound, each conformation is denoted by conformational letters in parentheses. b The designation of barriers t, g, c, and p stand for trans, gauche, cis, and perpendicular (i.e., torsion angles at ∼90°) conformations, respectively. When the difference between the barriers for tfg+ and g+fg- conformational changes is less than 0.1 kcal/mol, their average value is listed. Otherwise, the designation b1/b2 stands for the barriers b1 and b2 for tfg+ and g+fg- conformational changes, respectively. c Designations of relative conformational energies: (g/t) for conformational energy of g relative to that of t, etc. d Calculated from the total conformational energy. e The experimental methods are designated as ED, MW, IR, R, NS, and T for electron diffraction, microwave, infrared, and Raman spectroscopies, neutron scattering, and thermal methods, respectively, in each reference shown below. In addition, the ab initio method is denoted as AB. f Reference 33. g Hirota, E.; Endo, Y.; Saito, S.; Duncan, J. L. J. Mol. Spectrosc. 1981, 89, 285 (MW). h Pitzer, K. S. J. Chem. Phys. 1937, 5, 473 (T). i Lide, Jr., D. R.; Mann, D. E. J. Chem. Phys. 1958, 29, 914 (MW). j Pitzer, K. S.; Kilpatrick, J. E. Chem. ReV. 1946, 39, 435 (T). k Durig, J. R.; Craven, S. M.; Harris, W. C. Vibrational Spectra and Structure; Marcel Dekker: New York, 1972; Vol. 1. (IR). l Reference 34. m Miller, A.; Scott, D. W. J. Chem. Phys. 1978, 68, 1317 (T). n Tsuboi, M.; Tamagake, K.; Hirakawa, A. Y.; Yamaguchi, J.; Nakagawa, H.; Manocha, A. S.; Tuazon, E. C.; Fateley, W. G. J. Chem. Phys. 1975, 63, 5177 (IR). o Durig, J. R.; Li, Y. S. J. Chem. Phys. 1975, 63, 4110 (R). p Durig, J. R.; Craven, S. M.; Mulligan, J. H.; Hawley, C. W.; Bragin, J. J. Chem. Phys. 1973, 58, 1281 (IR). q Durig, J. R.; Compton, D. A. C. J. Phys. Chem. 1979, 83, 2873 (IR, R). r Durig, J. R.; Compton, D. A. C. J. Chem. Phys. 1978, 69, 4713 (IR). s Hayashi, M.; Kuwada, K. J. Mol. Struct. 1975, 28, 147 (MW). t Reference 52. u Abdurakhmanov, A. A.; Ragimova, R. A.; Imanov, L. M. Phys. Lett. 1970, 32A, 123 (MW). V Abdurakhmanov, A. A.; Veliyulin, E. I.; Ragimova, R. A.; Imanov, L. M. J. Struct. Chem. 1981, 22, 28 (MW). w Berynon, E. T., Jr.; McKetta, J. J. J. Phys. Chem. 1963, 67, 2761 (T). x Reference 80. y Demaison, J.; Boucher, D.; Burie, J.; Dubrulle, A. Z. Naturforsch. 1984, 39A, 560 (MW). z Nakagawa, J.; Kuwada, K.; Hayashi, M. Bull. Chem. Soc. Jpn. 1976, 49, 3420 (MW). aa Reference 64. bb Durig, J. R.; Bucy, W. E.; Wurrey, C. J.; Carreira, L. A. J. Phys. Chem. 1975, 79, 988 (R). cc McCullough, J. P.; Finke, H. L.; Scott, D. W.; Gross, M. E.; Messerly, J. F.; Pennington, R. E.; Waddington, G. J. Am. Chem. Soc. 1954, 76, 4796 (T). dd Crowder, G. A.; Scott, D. W. J. Mol. Spectrosc. 1965, 16, 122 (IR). ee McCullough, J. P.; Scott, D. W.; Finke, H. L.; Hubbard, W. N.; Gross, M. E.; Katz, C.; Pennington, R. E.; Messerly, J. F.; Waddington, G. J. Am. Chem. Soc. 1953, 75, 1818 (T). ff Reference 62. gg Scott, D. W.;

Conformational Analysis of Peptides and Proteins mol, except for ethylamine, n-propylamine, ethylmethylamine, propionic acid, 2-methyl-2-propanethiol, and n-pentane. Our intrinsic torsional parameters produce somewhat lower barriers for the methyl torsions of ethylamine, ethylmethylamine, and 2-methyl-2-propanethiol, and for the C-C torsions of n-pentane and n-propylamine than the corresponding experimental values. On the other hand, the higher barrier for the methyl torsion of propionic acid was obtained. The electron diffraction experiment73 on ethylamine and ab initio calculations on n-propylamine74,75 and ethylamine75 showed that the C-C-N bond angles for the gauche conformers are about 5° smaller than those in the trans conformers. However, the same bond lengths obtained for the trans conformer were used in computing conformational energies of the corresponding gauche conformers in this work. That may be why the calculated barriers for the one-gauche-to-anothergauche conformational changes of these amines appear to be a little low. In general, as seen in Table 3, experimental barriers for the CM-C and C-C bonds of aliphatic hydrocarbons increase slightly as the chains become longer and branched. This could be ascribed to the effects of the steric deformations associated with steric strain in gauche conformations and with the deformation of a trans conformation by an adjacent gauche conformation.76,77 These effects were suggested to result in the increase in average C-C bond lengths and C-C-C bond angles of higher alkanes.76-78 Thus, the intrinsic torsional parameters obtained from propane and n-butane yield somewhat lower barriers than experimental values for longer or branched alkyl groups, e.g., the methyl torsion of 2-methyl-2-propanethiol and the C-C torsion of n-pentane. Microwave experiments on propionaldehyde79 and propionic acid80 showed that the 3-fold barriers for the methyl torsions of these molecules are untypically low (about 2.4 kcal/mol). A structural comparison of propionic acid and propane based on microwave experiments81 has shown that bond distances in the CH3-CH2- fragments of the two molecules are unaffected by the replacement of a methyl group by a carboxylic group. However, there occurs a noticeable deviation (4.9°) of the H-C-H plane of the methylene group from the external bisector of the skeletal C-C-C bond angle toward the hydroxyl oxygen in propionic acid,81 although the CH3CH2-C bond length is shorter by 0.023 Å in propionic acid than propane.82 For this reason, the intrinsic torsional parameters obtained from propane may overestimate slightly the barrier for the methyl torsion of propionic acid. Table 4 shows the calculated results for the C-N torsions. Although the number of molecules used in testing the torsion of the C-N bonds is limited, the average differences in barriers and relative conformational energies are quite similar to those for the molecules with C-C torsions. In particular, there is a large discrepancy between the calculated barrier (1.98 kcal/mol) and the corresponding ab initio value (3.27 kcal/mol)75 for the trans-to-gauche conformational change in n-propylamine. This ab initio value was computed at the 3-21G(N*) level, which gave the corresponding barrier in ethylamine that was too high

J. Phys. Chem., Vol. 100, No. 38, 1996 15593 by about 1.3 kcal/mol75 compared with the experimental value (1.97 kcal/mol).41 Thus, the calculated barrier 1.98 kcal/mol in n-propylamine seems to be quite reasonable. For the C-O torsions, the calculated results are shown in Table 5. The overall agreement between the computed and experimental values is better than those for the C-C and C-N torsions. In the case of ethyl formate, there are some differences in the calculated and observed barriers for the cis-to-trans and one-gauche-to-another-gauche conformational changes of the CB-OS and OS-C bonds, respectively. However, the calculated results seem to be reasonable if the inaccuracy involved in the experiments57,83 is taken into account. In Table 6, the calculated and experimental (or ab initio) barriers and relative conformational energies for the C-S and S-S torsions are shown. All the experimental data, except those for tert-butyl methyl sulfide and ethyl methyl disulfide, are reproduced well with a small average deviation between the calculated and experimental values. In addition, the torsion angles of the calculated low-energy conformations of the molecules considered here are consistent with the corresponding observed or ab initio values. A somewhat high estimated barrier for the C-S bond in tertbutyl methyl sulfide can be ascribed to the same reason proposed for the C-C torsions of branched hydrocarbons above. The intrinsic torsional parameters for the C-S bond fitted to experimental barriers and relative conformational energy of ethyl methyl sulfide61,62 reproduce satisfactorily experimental barriers for the C-S torsions of sulfides and ab initio barriers for ethyl methyl disulfide84 computed at the HF/3-21G+d(C,S) level. The conformational preference about the CC-SS bond is calculated here to be gauche+ > trans > gauche-, which is comparable with the results of a Raman spectral analysis67 and an electron diffraction study71 as well as those of ab initio calculations.84 A recent ab initio study on dimethyl disulfide at the MP2/631G** level72 reveals that electron correlation effects increase the barriers of the S-S bond by 0.6-1.0 kcal/mol. Therefore, the cis barrier (6.22 kcal/mol) in ethyl methyl disulfide, calculated by using intrinsic torsional parameters fitted to ab initio barriers of dimethyl disulfide at the MP2/6-31G** level, seems to be reasonable, although it is larger than the ab initio value (3.5-4.0 kcal/mol) calculated at the HF/3-21G+d(C,S).84 The intrinsic torsional parameters of a three-term Fourier expansion function, obtained by fitting the experimental or ab initio barriers and relative conformational energies of each reference compound, can be used to represent the torsional properties of uncharged organic molecules containing various functional groups satisfactorily. The overall average difference between the calculated and observed values of the tested molecules does not exceed (0.4 kcal/mol for the four classes of torsions, viz., C-C, C-N, C-O, and C-S/S-S. This indicates that the method presented here can provide the barriers and conformational energies associated with the internal rotations for the backbones and side chains of peptides and proteins reliably. In ECEPP,13 no intrinsic torsional energy contributions to rotation about the C′N-CRC′ (φ) and NCR-C′N (ψ) bonds of

TABLE 3: (Continued) Finke, H. L.; Hubbard, W. N.; McCullough, J. P.; Oliver, G. D.; Gross, M. E.; Katz, C.; Williamson, K. D.; Waddington, G.; Huffman, H. M. J. Am. Chem. Soc. 1952, 74, 4656 (T). hh McCullough, J. P.; Finke, H. L.; Messerly, J. F.; Pennington, R. E.; Hossenlopp, I. A.; Waddington, G. J. Am. Chem. Soc. 1955, 77, 6119 (T). ii Reference 29. jj Reference 30. kk Ito, K. J. Am. Chem. Soc. 1953, 75, 2430 (T). ll Verma, A. L.; Murphy, W. F.; Bernstein, H. J. J. Chem. Phys. 1974, 60, 1540 (R). mm Chen, J. A.; Petrauskas, A. A. J. Chem. Phys. 1959, 30, 304 (sound absorption). nn Reference 74. oo Reference 75. pp Reference 38. qq Vacherand, J. M.; van Eijck, B. P.; Burie, J.; Demaison, J. J. Mol. Spectrosc. 1986, 118, 355 (MW). rr van Eijck, B. P.; van Opheusden, J.; van Schaik, M. M. M.; van Zoeren, E. J. Mol. Spectrosc. 1981, 86, 465 (MW). ss Derissen, J. L. J. Mol. Struct. 1971, 7, 67 (ED). tt Williams, G.; Owen, N. L.; Sheridan, J. Trans. Faraday Soc. 1971, 67, 922 (MW). uu Reference 36. VV Reference 37. ww Sakurai, T.; Ishiyama, M.; Takeuchi, H.; Takeshita, K.; Fukushi, K.; Konaka, S. J. Mol. Struct. 1989, 213, 245 (ED). xx Reference 40. yy Reference 39.

15594 J. Phys. Chem., Vol. 100, No. 38, 1996

Kang et al.

TABLE 4: Calculated and Experimental Torsional Barriers and Relative Conformational Energies (kcal/mol) for C-N Bonds torsional barrierb moleculea

calcdd

rel conf energyc exptle

1.96

ethylamine* n-propylamine tert-butylamine

1.97 1.98/1.98 2.34

dimethylamine* ethylmethylamine

3.28 3.20 (t) 3.01 (g)

ethylmethylamine*

2.87/5.62

d. C-N2 Type 2.87/5.62o

acetamide*

18.20 (tfc)

e. CA-NA Type 18.2,o 20.1p

N-methylformamide N-methylacetamide*

22.52 (tfc) 22.60 (tfc)

f. CA-NH Type 22.1,q 22.4r 22.6-23.2r

N,N-dimethylformamide N,N-dimethylacetamide*

18.24 (tfc) 15.80 (tfc)

g. CA-NC Type 19.7 ( 0.3,t 19.6-20.5u 15.8 ( 1.1,V 17.4-20.7w

methylguanidine*

24.10 (χ6,1, tfc) 7.50 (χ6,2, tfc)

h. CF-NG Type 24.10x 7.50x

a-e

b. C-N1 Type 1.97g 3.27/2.12h 2.49j

0.31g 0.40,h 0.30i

1.44 (g/t)

1.44o

0.92 (c/t) 2.80 (c/t)

1.5,q 4.9,r 1.6s 2.8-3.4r

0.08 (c/t) 0.00 (c/t)

i. NH-CM Type 1.69y

11.90 (tfc) f

0.31 (g/t) 0.33 (g/t)

c. CM-N2 Type 3.28,k 3.01,l 3.62 ( 0.05m 3.12 ( 0.02n 3.27 ( 0.03n

1.69

methylguanidine*

exptle

a. CM-N1 Type 1.96f

methylamine*

N-methylacetamide*

calcdd

g

j. NE-CF Type 11.90x h

2.94 (c/t) i

j

See footnotes a-e of Table 3. Reference 42. Reference 41. Reference 75. Reference 74. Gilchrist, J. Chem. Phys. 1982, 65, 1 (dielectric relaxation). k Reference 44. l Durig, J. R.; Griffin, M. G.; Groner, P. J. Phys. Chem. 1977, 81, 554 (R). m Mo¨ller, K. D.; De Meo, A. R.; Smith, D. R.; London, L. H. J. Chem. Phys. 1967, 47, 2609 (IR). n Footnote q of Table 3. o Reference 43. p Reference 45. q Anet, F. A. L.; Squillacote, M. J. Am. Chem. Soc. 1975, 97, 3243 (NMR). r Reference 46. s Miyazawa, T. J. Mol. Spectrosc. 1960, 4, 155 (IR). t Ross, B. D.; True, N. S. J. Am. Chem. Soc. 1984, 106, 2451 (NMR). u Drakenberg, T.; Dahlqvist, K.-I.; Forse´n, S. J. Phys. Chem. 1972, 76, 2178 (NMR). V Reference 47. w Neuman, R. C.; Jones, V. J. Org. Chem. 1974, 39, 929 (NMR). x Reference 48. y Reference 39.

peptides were introduced, because the barriers to internal rotation of the methyl groups (representing the equivalents of variations of φ and ψ) of N-methylformamide and N-methylacetamide were found to be very low from EHT and CNDO/2 calculations,85 and because no sufficiently accurate experimental data were available in 1975. However, the barriers for the two methyl groups of N-methylacetamide obtained from neutron inelastic scattering experiments in the gas phase39 have enabled us to derive new sets of intrinsic torsional parameters for these C′N-CRC′ (φ) and NCR-C′N (ψ) bonds. B. Minimum-Energy Conformation of Ac-Ala-NHMe. To investigate the effects of the new potential parameters on the conformations of peptides, conformational energy calculations were carried out on a model peptide N-acetyl-N′methylalanineamide (Ac-Ala-NHMe). Each conformation is denoted in terms of the conformational letter code for the backbone torsion angles φ and ψ, defined by Zimmerman et al.86 A conformational energy φ-ψ contour map for the terminally blocked Ala residue is shown in Figure 1. Energies were calculated at 10° intervals of φ and ψ with adiabatic relaxation; that is, the energy was minimized with respect to all other torsion angles at each given value of φ and ψ. The steep boundaries of the low-energy regions on the map of Figure 1 coincide with those on the map of ECEPP/316,87,88 (see Figure 10B in ref 89). However, inside the low-energy regions, slight shifts of local minima occur, and the barriers between local minima become higher, in the map of Figure 1 compared to those of the map of ECEPP/3. In addition, the flat potential

surface of the F (PII) region in the ECEPP/3 calculations disappeared in the present map, as it did in computations with an earlier version of ECEPP.86 The computed minimum-energy conformations (MEC), their relative energies, and normalized Boltzmann factors90 are listed in Table 7. The relative energies of the first three MECs, C (C7eq), E (C5), and D (β2), are similar to those from the ECEPP/3 calculations.87,88 However, the energy of the MEC A (RR) is now even higher than that of the MEC D and G because of unfavorable electrostatic energy contributions, as seen in ∆EES of Table 7. The large difference in ∆E between MEC C and A is caused mainly by electrostatic interactions between the carbonyl oxygen of the acetyl group and the amido hydrogen of the methylamide group. In MEC C, there is a hydrogen bond between these two groups with an N‚‚‚O distance of 2.24 Å. On the other hand, in MEC A the corresponding distance r(N‚‚‚O) is 3.77 Å, and the longer distance gives rise to the increase in the electrostatic energy of MEC A by 8.17 kcal/ mol than MEC C, which contributes dominantly to ∆ETOT between MEC C and A. Also, the total conformational energy, -17.80 kcal/mol of MEC C, lower than that of the ECEPP/3 calculations, results from the lower electrostatic energy, -16.34 kcal/mol. As discussed in the previous paragraph, a conformation F is no longer a local minimum, and its energy is higher by ca. 6 kcal/mol than the global MEC C. The analysis of conformational energies, shown in Table 7, indicates that the electrostatic energy components contribute significantly to the conformational energies. This may be caused by the use of a small value, unity, for the dielectric constant

Conformational Analysis of Peptides and Proteins

J. Phys. Chem., Vol. 100, No. 38, 1996 15595

TABLE 5: Calculated and Experimental Torsional Barriers and Relative Conformational Energies (kcal/mol) for C-O Bonds torsional barrierb moleculea

calcdd

dimethyl ether* ethyl methyl ether tert-butyl methyl ether

2.63 2.64 2.12/2.48

ethyl methyl ether* diethyl ether

2.67/5.63 2.64 (ttftg)

methanol*

1.07

ethanol* 1-propanol 2-propanol 2-methyl-2-propanol

1.17/1.17 1.42 (ttftg) 1.76/1.14 1.51/0.71

phenol*

3.36 (cft)

acetic acid* propionic acid

12.55 (cft) 12.52 (cft)

methyl formate*

methyl acetate*

11.65 (tfc) 7.80 (cft) 10.94 (tfc) 8.47 (cft) 14.40 (tfc)

methyl formate* ethyl formate methyl acetate

1.19 0.74/2.79 1.20

rel conf energyc exptle

calcdd

a. CM-O Type 2.63 ( 0.02,f 2.72 ( 0.14g 2.61,h 2.70 ( 0.01i 2.10j b. C-O Type 2.67/5.63k

1.50 (g/t) 1.28 (tg/tt)

1.5 ( 0.2,l 1.23 ( 0.27m 1.37 ( 0.10,n 1.1o

1.27,V 0.90w

0.12 (g/t) 0.25 (tg/tt) 0.04 (t/g) 0.06 (t/g)

0.12q 0.4,r -0.29 ( 0.15s 0.45 ( 0.21,t