JOURNAL
`OF THE AMERICAN CHEMICAL SOCIETY
`©Copyright 1988 by the American Chemical Society
`
`VOLUME 110, NUMBER 6
`
`MARCH 16, 1988
`
`The OPLS Potential Functions for Proteins. Energy
`Minimizations for Crystals of Cyclic Peptides and Crambin
`
`William L. Jorgensen* and Julian Tirado-Rives
`
`Contribution from the Department of Chemistry, Purdue University,
`West Lafayette, Indiana 47907. Received January 26, 1987
`
`Abstract: A complete set of intermolecular potential functions has been developed for use in computer simulations of proteins
`in their native environment. Parameters are reported for 25 peptide residues as well as the common neutral and charged terminal
`groups. The potential functions have the simple Coulomb plus Lennard-Janes form and are compatible with the widely used
`models for water, TIP4P, TIP3P, and SPC. The parameters were obtained and tested primarily in conjunction with Monte
`Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aqueous solutions of organic ions representative
`of subunits in the side chains and backbones of proteins. Bond stretch, angle bend, and torsional terms have been adopted
`from the AMBER united-atom force field. As reported here, further testing has involved studies of conformational energy
`surfaces and optimizations of the crystal structures for four cyclic hexapeptides and a cyclic pentapeptide. The average
`root-mean-square deviation from the X-ray structures of the crystals is only 0.17 A for the atomic positions and 3% for the
`unit cell volumes. A more critical test was then provided by performing energy minimizations for the complete crystal of the
`protein crambin, including 182 water molecules that were initially placed via a Monte Carlo simulation. The resultant
`root-mean-square deviation for the non-hydrogen atoms is still ca. 0.2 A and the variation in the errors for charged, polar,
`and nonpolar residues is small. Improvement is apparent over the AMBER united-atom force field which has previously been
`demonstrated to be superior to many alternatives.
`
`Computer simulations are undoubtedly destined to become an
`increasingly important means for investigating the structures and
`dynamics of biomo1ecular systems.' At the heart of such theo(cid:173)
`retical calculations are the force fields that describe the interatomic
`interactions and the mechanics of deformations of the molecules. 2
`There is also little doubt that there will be a continual evolution
`in force fields with added complexity and improved performance
`paralleling the availability of computer resources. Our own efforts
`in this area over the last few years have resulted in the OPLS
`potential functions for proteins whose development and perform(cid:173)
`ance are summarized here. These potential functions have a simple
`form and they have been parametrized directly to reproduce
`experimental thermodynamic and structural data on fluids.
`Consequently, they are computationally efficient and their de(cid:173)
`scription of proteins in solution or crystalline environments should
`be superior to many alterantives that have been developed with
`limited condensed-phase data. The latter point is pursued here
`primarily through calculations on the crystal structures for four
`cyclic hexapeptides, a cyclic pentapeptide, and the protein cram bin.
`Improvements are apparent in comparison to the AMBER un(cid:173)
`ited-atom force field 3 which has previously been shown to be
`superior to many alternatives.4
`
`(I) Beveridge, D. L., Jorgensen, W. L., Eds. Ann. N.Y. Acad. Sci. 1986,
`482.
`(2) For reviews, see; (a) Levitt, M. Annu. Rev. Biophys. Bioeng. 1982,
`11, 251. (b) McCammon, J. A. Rep. Prog. Phys. 1984, 47, I.
`(3) Weiner, S. J.; Kollman, P. A.; Case, D. A.; Singh, U. C.; Ghio, C.;
`Alagona, G.; Profeta, S.; Weiner, P. J. Am. Chern. Soc. 1984, 106, 765.
`
`Parametrization
`The peptide residues of proteins contain readily identifiable
`organic subunits such as amides, hydrocarbons, alcohols, thio(cid:173)
`ethers, etc. In view of this and since data are available on the
`corresponding pure organic liquids, our approach to developing
`a force field for proteins was to build it up from parameters
`demonstrated to yield good descriptions of organic liquids. Ul(cid:173)
`timately, the force field would need to treat both intramolecular
`terms for bond stretches, angle bends, and torsions, as well as the
`intermolecular and intramolecular nonbonded interactions. The
`latter are generally accepted to be the most difficult part of the
`problem and have been our focus. 3 A simple, computationally
`efficient form was chosen to represent the non bonded interactions
`through Coulomb and Lennard-Janes terms interacting between
`sites centered on nuclei (eq I). Thus, the intermolecular inter-
`
`action energy between molecules a and b is given by the sum of
`interactions between the sites on the two molecules. The non(cid:173)
`bonded contribution to the intramolecular energy is evaluated with
`the same expression for all pairs of sites separated by more than
`three bonds. In the OPLS (optimized potentials for liquid sim(cid:173)
`ulations) model, each atomic nucleus has an interaction site, except
`CHn groups are treated as united atoms centered on the carbon.
`It is important to note that in this model no special functions were
`
`(4) Hall, D.; Pavitt, N.J. Comput. Chern. 1984, 5, 411.
`
`0002-7863/88/1510-1657$01.50/0
`
`© 1988 American Chemical Society
`
`

`
`1658 J. Am. Chern. Soc., Vol. 110, No.6, 1988
`
`Jorgensen and Tirado- Rives
`
`Table I. Liquids Simulated with the OPLS Potential Functions
`ref
`liquid
`ref
`liquid
`T (OC)
`T (OC)
`9
`25
`25
`5
`HCONH2
`9
`25
`25, 100 5
`HCON(CHlh
`10
`-161
`CH3CONHCH3 100
`5
`10
`-89
`25
`6
`CH30H
`10
`-42, 25
`25
`6
`C2HsOH
`-o.5, 25 10
`25
`6
`n-C 3H10H
`25
`10
`25
`6
`i-C3H10H
`25
`10
`25
`6
`t-C4H90H
`25
`10
`7
`6
`CH3SH
`25
`10
`7
`25
`C2HsSH
`25
`10
`7
`25
`(CHlhS
`25
`10
`7
`25
`C2HsSCH3
`25
`10
`25
`7
`(C2HshS
`10
`7
`25
`25
`CH3SSCH3
`25
`10
`-25
`8
`(CHlhO
`25
`10
`25
`C2HsOCHl
`8
`25
`10
`25
`8
`(C2HshO
`25
`8
`25
`8
`THF
`
`pyrrole
`pyridine
`CH4
`C2H6
`C3Hs
`n-C4H10
`i-C4H10
`n-CsH12
`i-CsH12
`neo-CsH12
`c-CsHIO
`n-C6Hl4
`CH3CH2CH=CH2
`t-CH3CH=CHCH3
`C-CH3CH=CHCH3
`(CH3hC=CH2
`benzene
`CH3C02CH3
`
`c
`
`c
`
`230 MOLECULAR VOLUMES
`
`195
`
`160
`
`90
`
`55
`
`55
`
`160
`125
`90
`EXPERIMENTAL
`Figure 1. Comparison of computed and experimental volumes per
`molecule in A3 for the liquids in Table I and TIP4P water.
`
`195
`
`230
`
`II JJ
`
`12
`
`6
`
`found to be needed to describe hydrogen bonding and. there are
`no additional interaction sites for lone pairs. Another Important
`point is that standard combining rules are used for the Len(cid:173)
`nard-Jones interactions such that Aij = (A 11AjYI2 and Cij =
`(c . .c..) 112• The A and C parameters may also be expressed in
`terms of Lennard-Jones u's and E's as A11 = 4E1u1 and C11 = 4Et<Tt •
`The OPLS parameters for the 20 neutral peptide residues
`reported here were obtained primarily via Monte Carlo simulations
`for the 36 organic liquids listed in Table J.S-10 Standard geom(cid:173)
`etries were used for the molecules with fixed bond lengths and
`bond angles, though torsional motion was included, as described
`in detail elsewhere.s-I 0 Particular emphasis was placed on re(cid:173)
`producing the experimental densities and heats of vaporization
`for the liquids. In view of the simplicity of the functional form
`(eq 1 ), the accord with the experimental data is remarkable as
`illustrated in Figures 1 and 2; the average deviation between the
`experimental data and the theoretical results is less than 3%. The
`structural results for the liquids were also shown to be in accord
`with available experimental data including vibrational spectroscopy
`and diffraction data for formamide, dimethylformamide (DMF),
`methanol, ethanol, !-propanol, 2-methyl-2-propanol, methane,
`ethane, neopentane, and benzene. The hydrogen bonding in the
`alcohols, thiols, and amides is well-represented by the OPLS
`potential functions. It should be noted that the number of unique
`parameters has been kept to a minimum. 5- 10 Thus, only 12
`different CH. groups are used to describe all alkanes, alkenes,
`
`(5) Jorgensen, W. L.; Swenson, C. J. J. Am. Chern. Soc. 1985, 107, 569.
`(6) Jorgensen, W. L. J. Phys. Chern. 1986, 90, 1276.
`(7) Jorgensen, W. L. J. Phys. Chern. 1986, 90, 6379.
`(8) Jorgensen, W. L.; Briggs, J. M., to be published.
`(9) Jorgensen, W. L.; Contreras, L., to be published.
`(10) Jorgensen, W. L.; Madura, M.D.; Swenson, C. J. J. Am. Chern. Soc.
`1984, 106, 6638.
`
`18 ~H=E7RT~S~O~F~V~R~P=07R~It~R=T7!0~N~--~
`
`15
`
`12
`
`6
`
`3
`
`0 0
`
`3
`
`12
`9
`6
`EXPERIMENTAL
`Figure 2. Comparison of computed and experimental heats of vapori(cid:173)
`zation in kcalfmol for the liquids in Table I and TIP4P water.
`
`15
`
`18
`
`and benzene, 10 and, for example, the parameters for the OH groups
`in all alcohols6 and the carbonyl groups in all arnides are the same.5
`The parametrization for the neutral residues also entailed
`careful consideration of the interactions between the organic
`fragments and a water molecule. The water model used in con(cid:173)
`junction with the OPLS potentials was TIP4P, 11 •12 though the
`TIP3P 11 or SPC 13 models yield very similar results. For most
`purposes, these three alternatives may be considered to be in(cid:173)
`terchangeable, though the slightly more complicated TIP4P model
`gives a better description of the angular variation of hydrogen bond
`energies. Complexes of a water molecule with amides, ethers,
`esters, alcohols, thiols, sulfides, azoles, and azines were studied
`with the OPLS potentials as well as ab initio molecular orbital
`calculations primarily with the 6-31G(d) basis set. 14 The trends
`in the ab initio findings for the hydrogen bond strengths and
`9
`geometries are well reproduced by the OPLS results. 5-
`•15
`Furthermore, Monte Carlo simulations were carried out for dilute
`aqueous solutions of formamide, 15 N-methylacetamide (NMA), 15
`DMF, 15 methanol, 16 and seven alkanesY For the amides, ex(cid:173)
`perimental structural data are limited; however, the computed
`numbers of amide-water hydrogen bonds are reasonable and the
`computed heats of hydration, ca. -20 kcaljmol, are in the correct
`range. 15 Similarly, the hydration of methanol appears reasonable
`and the computed difference in free energies of hydration for
`methanol and ethane, 6.75 ± 0.2 kcaljmol, is in excellent accord
`with the experimental value, 6.93 kcaljmol. 16 The free energy
`calculations are a powerful diagnostic tool, but very demanding
`on computer resources. 16 The results for the hydrophobic hy(cid:173)
`dration of the alkanes also revealed no aberrations and yielded
`pleasing correlations between numbers of water molecules in the
`first hydration shells and experimental enthalpies and entropies
`of hydrationP
`The parametrization for the five charged protein residues, Asp,
`Glu, Hip (protonated His), Lys, and Arg, and terminal ammonium
`and carboxylate groups required a somewhat different approach.
`Since corresponding pure organic liquids cannot be construed in
`these cases, the emphasis was placed on comparisons with ab initio
`results for ion-molecule complexes and on Monte Carlo simula(cid:173)
`tions for hydrated ions. Specifically, parameters for Lys, Glu,
`Asp and the charged terminal groups were developed through a
`
`(II) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J.D.; Impey, R. W.;
`Klein, M. L. J. Chern. Phys. 1983, 79, 926.
`(12) Jorgensen, W. L.; Madura, J.D. Mol. Phys. 1985, 56, 1381.
`(13) Berendsen, H. J. C.; Postma, J.P. M.; von Gunst~ren, W. F.; Her(cid:173)
`mans, J. In Intermolecular Forces; Pullman, B., Ed.; Re1del: Dordrecht,
`Holland, 1981; p 331.
`(14) Franc!, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon,
`M.S.; DeFrees, D. J.; Pople, J. A. J. Chern. Phys. 1983, 77, 3054.
`(15) Jorgensen, W. L.; Swenson, C. J. J. Am. Chern. Soc. 1985, 107, 1489.
`(16) Jorgensen, W. L.; Ravimohan, C. J. Chern. Phys. 1985, 83, 3050.
`(17) Jorgensen, W. L.; Gao, J.; Ravimohan, C. J. Phys. Chern. 1985,89,
`3470.
`
`

`
`The OPIS Potential Functions for Proteins
`
`J. Am. Chern. Soc., Vol. 110, No.6, 1988 1659
`
`24~----~~---=-=~~~----~
`
`INTERRCTI~N ENERGIES
`(KCRL/M~Ll
`
`c
`
`c c
`c
`c c
`c
`
`c
`
`21
`
`18
`
`Cfl a: 15
`
`El
`
`12
`
`9
`
`c
`
`c
`
`6 6
`
`9
`
`12
`
`15
`6-31Gidl
`Figure 3. Comparison of interaction energies (kcaljmol) for ion-water
`complexes obtained with the OPLS potential functions and ab initio
`6-31 G( d) calculations.
`
`18
`
`21
`
`24
`
`general study of the hydration of ammonium and carboxylate
`ions. 18 Ab initio calculations were carried out with the 6-31G(d)
`basis set for low-energy forms of complexes between water and
`NH/, CH3NH/, and HC00-.18•19 The OPLS parameters were
`chosen to reproduce the resultant optimal geometries and inter(cid:173)
`action energies, which are also in good accord with gas-phase
`experimental data. 18•19 In addition, the OPLS parameters were
`required to yield good agreement with experimental heats of
`hydration for NH/, CH3NH 3+, (CH3) 4N+, HCoo-, and
`CH 3Coo-. 18 This was demonstrated through Monte Carlo sim(cid:173)
`ulations for the five ions in dilute aqueous solution. 18 The
`structural results were also shown to mirror experimental estimates
`of hydration numbers for the ammonium and carboxylate groups
`in Lys, Glu, and Asp from NMR studies of frozen polypeptide
`solutions. 18•20
`Recently, the OPLS parameters for Arg and Hip have been
`obtained by fitting to ab initio 6-31G(d) results for complexes
`of water with guanidinium ion and protonated imidazole. 21 The
`principal concern was the charge distributions for the ions since
`the Lennard-Jones parameters were adopted from standard values
`for nitrogen and carbons (all explicit hydrogens have cr = e = 0
`in the OPLS potentials). The accord between the OPLS and
`6-31G(d) results for low-energy geometries is uniformly good. For
`example, the OPLS optimal interaction energy and CO distance
`for 1 are 16.1 kcaljmol and 3.33 A, whereas the 6-31G(d) values
`with fixed water and guanidinium geometries are 18.2 kcaljmol
`and 3.41 A. And, for 2, the OPLS predictions for the interaction
`energy and NO distance are 16.0 kca1jmol and 2.72 A versus the
`H
`H
`\
`I
`C=C
`I
`I
`_...N;;_.+.;;N......._
`H
`H"'
`C
`I
`"'-o/
`I
`H
`H
`
`H
`I
`
`H
`
`2
`6-31G(d) values of 16.1 kcaljmol and 2.85 A. In general, the
`accord between the OPLS and 6-31G(d) results is good as il(cid:173)
`lustrated in Figures 3 and 4 for 14low-energy geometries of water
`with NH/, CH3NH/, Hcoo-, guanidinium ion, and protonated
`imidazole. The OPLS interaction energies are deliberately de(cid:173)
`signed to be less than the 6-31G(d) results, since the latter are
`typically somewhat greater than the limited experimental data. 18•19
`At this time, fluid simulations have not been executed for guan(cid:173)
`idinium ion or protonated imidazole in water. Experimental
`
`(18) Jorgensen, W. L.; Gao, J. J. Phys. Chern. 1986, 90, 2174.
`(19) Gao, J.; Garner, D. S.; Jorgensen, W. L. J. Am. Chern. Soc. 1986,
`108,4784.
`(20) Kuntz, I. D. J. Am. Chern. Soc. 1971, 93, 514.
`(21) Jorgensen, W. L.; Gao, J., unpublished results.
`
`Table II. OPLS Atom and Group Assignments for Proteins•
`atom
`atom
`or group
`or group
`
`residue
`
`type
`residue
`Main Chains
`Ala
`3
`4
`5
`I
`2
`3
`14
`I
`2
`
`Aib
`
`Leu
`
`Side Chains
`7
`Val
`65
`9
`9
`15
`8
`9
`7
`10
`
`Phe
`
`Cys
`
`Met
`
`Cystine
`
`Hyp
`(Pro-OH)
`
`Gin
`
`Glu
`
`Hip
`(His-W)
`
`22
`23
`24
`25
`23
`24
`7
`9
`II
`II
`II
`26
`23
`24
`9
`I
`2
`12
`13
`
`16
`17
`18
`
`9
`45
`40
`41
`44
`43
`42
`
`Arg
`
`Hyl
`(Lys-OH)
`
`type
`
`3
`4
`6
`I
`2
`3
`4
`64
`1
`2
`
`8
`7
`9
`8
`7
`9
`II
`11
`11
`II
`31
`32
`33
`9
`34
`35
`36
`37
`38
`9
`25
`15
`23
`24
`9
`9
`1
`2
`12
`13
`9
`16
`17
`18
`9
`49
`46
`47
`49
`48
`46
`47
`9
`57
`56
`54
`55
`53
`51
`52
`9
`9
`25
`23
`24
`19
`20
`21
`
`N
`H(N)
`CH•
`c
`0
`N
`H(N)
`c·
`c
`0
`
`CH~
`CH3 ~
`CHl
`CH~
`CH31
`CH/
`c~
`CH1
`CH'
`CHi
`CHl
`s~
`H~
`CH/
`CH 2
`1
`sa
`CH 3'
`CHl
`s~
`CHl
`CH~
`CH/
`oa
`H 1(0)
`CHl
`CH2~
`ca
`o·
`N'
`H'(N)
`CHl
`CH2~
`ca
`o·
`CHl
`c~
`Na
`H'(N)
`CH1
`CH'
`N'
`H'(N)
`CHl
`CH2~
`1
`CH2
`N'
`H'(N)
`c>
`N•
`H•(N)
`CHl
`CH2~
`CH1
`0'
`H'(O)
`CH2'
`N'
`H'(N)
`
`Gly
`
`Pro
`
`Ala
`Aib
`Pro
`
`lie
`
`Ser
`
`Thr
`
`Tyr
`
`Asn
`
`Asp
`
`His
`
`N
`H(N)
`CH2•
`c
`0
`N
`CH•
`c
`0
`
`CHl
`CHl
`CHl
`CH2~
`CH/
`CH~
`CH2~
`CHJ'
`1
`CH3
`
`CH/
`o~
`H~
`CHP
`o~
`H'(O)
`CH3 ~
`CHl
`c~
`CH1
`CH'
`cr
`0"
`H•
`CH/
`C'
`O'
`Na
`H 1(N)
`
`CHl
`c~
`Na
`H 1(N)
`CH1
`CH'
`N•
`
`CHl
`c~
`CH1
`ca
`N'
`H'(N)
`c·
`CH' cw
`
`Trp
`
`Lys
`
`9
`50
`45
`50
`40
`41
`45
`II
`11
`CH•
`11
`CH/
`9
`9
`CH2'
`CH21
`9
`CH 2'
`19
`N'
`20
`H'(N)
`21
`• Nomenclature for atoms: ref 22.
`
`thermodynamic data do not appear to be available in these cases.
`The OPLS parameters obtained in this way for 25 common
`peptide residues and both neutral and charged terminal residues
`
`

`
`1660 J. Am. Chern. Soc., Vol. 110, No. 6, 1988
`
`Jorgensen and Tirado- Rives
`
`3.4
`
`3.2
`
`(f) 0:3 .o
`
`0
`
`2.8
`
`2.6
`
`c
`
`c
`
`c
`
`c
`
`cc
`c
`
`c cc
`
`c
`
`c
`
`Table IV. OPLS Parameters for Proteins
`u, A
`q
`type
`I
`0.500
`3.750
`-o.soo
`2
`2.960
`3
`-o.570
`3.250
`4
`0.370
`0.0
`0.200
`3.800
`5
`6
`0.200
`3.800
`7
`0.0
`3.910
`8
`0.0
`3.850
`9
`0.0
`3.905
`10
`0.0
`3.905
`11
`0.0
`3.750
`12
`-o.s5o
`3.250
`0.425
`0.0
`13
`14
`0.285
`3.800
`15
`0.285
`3.800
`16
`-Q.lOO
`3.905
`17
`0.700
`3.750
`18
`-o.soo
`2.960
`19
`0.310
`3.905
`20
`-Q.300
`3.250
`21
`0.330
`0.0
`22
`0.265
`3.905
`23
`-o.700
`3.070
`24
`0.435
`0.0
`25
`0.265
`3.850
`26
`0.265
`3.750
`27
`0.310
`3.800
`28
`0.100
`3.800
`29
`0.310
`3.800
`30
`0.100
`3.800
`31
`0.180
`3.905
`32
`-Q.450
`3.550
`33
`0.270
`0.0
`34
`0.235
`3.800
`35
`-Q.470
`3.550
`36
`0.235
`3.800
`37
`0.300
`3.800
`38
`-o.300
`3.550
`39
`0.200
`3.800
`40
`-Q.570
`3.250
`41
`0.420
`0.0
`42
`-Q.490
`3.250
`43
`0.410
`3.750
`44
`0.100
`3.750
`45
`0.130
`3.750
`46
`-o.540
`3.250
`47
`0.460
`0.0
`48
`0.500
`3.750
`49
`0.330
`3.750
`50
`-o.055
`3.750
`51
`-o.soo
`3.250
`52
`0.460
`0.0
`53
`0.640
`2.250
`54
`-Q.700
`3.250
`55
`0.440
`0.0
`56
`0.310
`3.905
`57
`0.070
`3.905
`58
`0.550
`3.750
`59
`-Q.450
`2.960
`60
`0.250
`3.800
`61
`0.250
`3.800
`62
`-Q.400
`3.000
`63
`0.250
`3.800
`64
`0.200
`3.800
`65
`0.0
`3.960
`
`E, kcaljmol
`0.105
`0.210
`0.170
`0.0
`0.118
`0.080
`0.160
`0.080
`0.118
`0.175
`0.110
`0.170
`0.0
`0.080
`0.118
`0.118
`0.105
`0.210
`0.118
`0.170
`0.0
`0.118
`0.170
`0.0
`0.080
`0.110
`0.118
`0.118
`0.080
`0.080
`0.118
`0.250
`0.0
`0.118
`0.250
`0.170
`0.118
`0.250
`0.170
`0.170
`0.0
`0.170
`0.145
`0.145
`0.145
`0.170
`0.0
`0.145
`0.145
`0.145
`0.170
`0.0
`0.050
`0.170
`0.0
`0.118
`0.118
`0.105
`0.210
`0.080
`0.118
`0.170
`0.170
`0.050
`0.145
`
`need to be included. Since substantial work has been done on the
`former items by others,2•3 merger of the OPLS nonbonded potential
`functions and the local vibration and torsional functions from
`another force field could be considered. AMBER3 was chosen
`because it is widely used and because of its documented success
`in comparison to 15 other force fields for calculations of the crystal
`structures of 3 cyclic hexapeptides, though we recognize that the
`test was limited since only Gly and Ala residues were represented.4
`The bond stretch and angle bend terms in AMBER are
`quadratic, while the torsional potentials consist of a cosine term
`
`2.6
`
`3.0
`2.8
`6-31G(dl
`Figure 4. Comparison of optimal separations in A for ion-water com(cid:173)
`plexes obtained with the OPLS potential functions and ab initio 6-31G(d)
`calculations.
`
`3.2
`
`3.4
`
`3.6
`
`Table III. OPLS Atom and Group Assignments for Terminal
`Residues
`
`residue
`
`H 3N+CHRC=O
`
`NHCHRC02-
`
`atom or group
`Charged Termini
`N
`H(N)
`CHa
`CHt (R=H)
`c
`0
`N
`H(N)
`CHa
`CH2a (R=H)
`c
`0
`
`Neutral Termini
`N
`NHCHRC(O)OCH3
`H(N)
`CHa
`CHt (R=H)
`c
`0
`O(CH3)
`CH3
`CH 3
`c
`0
`N
`H(N)
`CH3
`
`CH3C(O)(NHCHRC(O))
`
`(NHCHRC(O))NHCH3
`
`type
`
`20
`21
`29
`27
`1
`2
`3
`4
`30
`28
`17
`18
`
`3
`4
`60
`61
`58
`59
`62
`63
`7
`1
`2
`3
`4
`39
`
`are summarized in Tables 11-IV. The atom and CHn group type
`assignments are given in Tables II and III with use of standard
`notation,22 while the actual charges and Lennard-Janes parameters
`are in Table IV. In all, 65 unique atom and group types are
`designated, though the number of unique sets of Lennard-Janes
`parameters is only 19. For reference, the parameters for the
`TIP4P, TIP3P, and SPC models for water are provided in Table
`V with use of consistent units. It should be noted that the side
`chains are each charge balanced to a net charge of 0, + 1 or -1.
`The only charged side chains are for Asp, Glu, Hip, Lys, and Arg.
`Also, all residues use the Ala backbone except Gly, Pro, and Aib.
`Further testing of the OPLS potentials then ensued after in(cid:173)
`corporation into the AMBER program. 3
`
`Merger with AMBER
`In order to provide a complete energetic description of biom(cid:173)
`olecular systems, the intramolecular terms for bond length and
`bond angle variations as well as the torsions and non bonded terms
`
`(22) IUPAC-IUB Commission on Biochemical Nomenclature: Biochem(cid:173)
`istry 1970, 9, 3471.
`
`

`
`The OPLS Potential Functions for Proteins
`
`Table V. Parameters for Water Models
`
`model
`TIP4P"
`0
`
`site
`geometry
`r(OH) = 0.9572 A 0
`r(OM) = 0.1500 A H
`H/1'-..H LHOH = 104.52° M
`M
`r(OH) = 0.9572 A 0
`TIP3P"
`LHOH = 104.52°
`H
`r(OH) = 1.0000 A 0
`LHOH = 109.47°
`H
`• Reference I I. b Reference 13.
`
`spcb
`
`u,A
`q
`3.15365
`0.0
`0.520 0.0
`-1.040 0.0
`--Q.834 3.15061
`0.417 0.0
`--o.820 3.16557
`0.410 0.0
`
`E,
`kcaljmol
`0.1550
`0.0
`0.0
`0.1521
`0.0
`0.1554
`0.0
`
`J. Am. Chern. Soc., Vol. 110, No.6, 1988 1661
`
`Table VII. Relative Energies for Conformations of Methyl Ethyl
`Ether•
`
`gauche
`method
`1.5
`AMBER/OPLS
`1.6
`AMBER-normal
`1.6
`AMBER-big
`1.4
`AMBER-all atom
`1.8
`MM2
`2.0
`4-31G
`1.5
`IR, gas phase
`1.2
`ED, gas phase
`• Energies relative to the trans conformer in kcalfmol.
`
`cis
`8.7
`9.4
`8.9
`5.3
`4.5
`7.3
`
`ref
`this work
`this work
`this work
`24
`31
`32
`33
`34
`
`Table VI. Relative Energies for Conformations of Butane•
`ref
`cis
`gauche
`method
`this work
`7.08
`1.03
`AMBER/OPLS
`this work
`6.97
`0.89
`AMBER-normal
`this work
`5.56
`0.37
`AMBER-big
`24
`4.57
`0.58
`AMBER-all atom
`4.73
`0.88
`25
`MM2
`26
`6.0
`0.7
`MP3/6-311G**+ZPE
`27
`4.52
`0.89
`Raman, gas phase
`28
`0.97
`IR, gas phase
`29
`3.6
`0.65
`ED, gas phase
`• Energies relative to the trans conformer in kcaljmol.
`
`plus the 1 ,4-nonbonded interaction, both Coulombic and Len(cid:173)
`nard-lones. Thus, the torsional potentials are affected by the
`choice of nonbonded parameters. Furthermore, the 1,4-nonbonded
`interactions are scaled in AMBER by dividing by factors SCNB
`and SCEE for the Lennard-Jones and Coulombic terms, re(cid:173)
`spectively. The default value for SCEE is 2.0 and has been used
`in all calculations reported here. The default value for SCNB
`is also 2.0 when the "normal" AMBER nonbonded parameters
`are used.3 However, in the note added in proof in ref 3, an
`alternative set of "big" parameters was proposed for CH, CH2,
`and CH3 united atoms adopted from the TIPS potentials.23
`In
`this case, the recommended SCNB is 8.0.3 For the purpose of
`merging the OPLS and AMBER force fields in an uncomplicated
`manner, it was necessary to readdress the best choices for SCNB
`and SCEE. This was done by choosing values that gave reasonable
`agreement between results for conformational surfaces with
`AMBER/OPLS and "normal" AMBER. These tests are sum(cid:173)
`marized in the next section, followed by more significant tests of
`the two force fields on crystal structures.
`The calculations were executed by using a modified version of
`AMBER 2.0 on a Microvax II computer in our laboratory.
`Complete geometry optimizations were carried out with the
`conjugate gradients procedure. 3 All of the calculations employed
`a dielectric constant of 1 for evaluating the electrostatic energy.
`This is the proper choice since the OPLS parameters have been
`derived in this way and are intended for use on condensed-phase
`systems.
`Conformational Results
`Conformational energy surfaces were computed for butane,
`methyl ethyl ether, and two dipeptides. These calculations in(cid:173)
`dicated that for AMBER/OPLS acceptable choices for SCEE
`and SCNB are 2.0 and 8.0, i.e., the same as for "big" AMBER.3
`All results for AMBER/OPLS reported here use these values.
`For butane, the energies of the gauche and cis conformers
`relative to trans are listed in Table VI. The AMBERfOPLS
`and normal AMBER results are similar; the gauche - trans energy
`difference is on the high side of the range of experimental val(cid:173)
`ues27-30 and of the best available ab initio result.26
`
`(23) Jorgensen, W. L. J. Am. Chem. Soc. 1981, 103, 335.
`(24) Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Comput.
`Chem. 1986, 7, 230.
`(25) (a) Jorgensen, W. L. J. Chem. Phys. 1982, 77, 5757. (b) Allinger,
`N. L. J. Am. Chem. Soc. 1977, 99, 8127.
`(26) Ragavachari, K. J. Chem. Phys. 1984, 81, 1383.
`(27) Compton, D. A. C.; Montero, S.; Murphy, W. F. J. Phys. Chem.
`1980, 84, 3587.
`
`Table VIII. Relative Energies and Torsional Angles ( .P, it) for
`Conformations of N-Acetylglycine N-Methylamide
`
`ref
`this work
`0.0 (82, -67) 1.7
`AMBER/OPLS
`0.0 (77, -64) 3.2
`AMBER-normal
`3
`3
`AMBER-all atom 0.0 (75, -65) 3.3
`0.0 (83, -76) 0.9
`35
`UNICEPP
`36
`0.0 (79, -73) 1.2
`ECEPP/2
`37
`0.0 (83, -71) 0.8
`4-21G
`0.0 (80, -40) 2.0
`38
`PCILO
`(75, -50)
`39
`IR, NMR (CC14)
`40
`(109, -21)
`X-ray (crystal)
`•Energies in kcaljmol, angles (.P and it) in deg. bThe C5 confor(cid:173)
`mation has .P = it = 180°.
`
`4.1 (66, 35)
`4.1 (60, 39)
`1.2 (71, 52)
`1.2 (73, 74)
`
`The corresponding results for methyl ethyl ether are summa(cid:173)
`rized in Table VII. The AMBER/OPLS and normal AMBER
`results are again similar; the predicted gauche - trans energy
`differences are also close to the experimental findings. 33·34
`The two standard dipeptides that were studied are N-acetyl(cid:173)
`glycine N-methylarnide (GA) and N-acetylalanine N-methylamide
`(AA). Rough energy maps were constructed by varying <I? and
`if; in 30° intervals between -180° and 180°. The local energy
`
`H
`I
`R H
`0
`)(• ~ '__,N
`N'l 'If '-...CH3
`CHa
`I o
`H
`
`GA:R=H
`AA: R•CH3
`
`(28) Verma, A.; Murphy, W.; Bernstein, H. J. Chem. Phys. 1974, 60,
`1540.
`(29) Kuchitsu, K. Bull. Chem. Soc. Jpn. 1959, 32, 748.
`(30) Kanesaka, 1.; Snyder, R. G.; Strauss, H. L. J. Chem. Phys. 1986, 84,
`395.
`(31) Burkert, U. J. Comput. Chem. 1980, /, 285.
`(32) Jorgensen, W. L.; Ibrahim, M. J. Am. Chem. Soc. 1981, 103, 3976.
`(33) Kitagawa, T.; Miyazawa, T. Bull. Chem. Soc. Jpn. 1968, 41, 1976.
`(34) Oyanagi, K.; Kuchitsu, K. Bull. Chem. Soc. Jpn. 1978, 5/, 2237.
`(35) Dunfield, L. G.; Burgess, A. W.; Scheraga, H. A. J. Phys. Chem.
`1978, 82, 2609.
`(36) Vazquez, M.; Nemethy, G.; Scheraga, H. A. Macromolecules 1983,
`16, 1043.
`(37) (a) Schafer, L.; Van Alsenoy, C.; Scarsdale, J. N.J. Chem. Phys.
`1982, 76, 1439. (b) Klimkowski, V. J.; Schafer, L.; Momany, F. A.; Van
`Alsenoy, C. J. Molec. Str. (THEOCHEM) 1985, 124, 143.
`(38) Maigret, B.; Pullman, B.; Dreyfus, J. J. Theor. Bioi. 1970, 26, 231.
`(39) Cung, M. T.; Marraud, M.; Nee!, J. Ann. Chim. (Paris) 1972, 7, 183.
`(40) Iwasaki, F. Acta Crystallogr., Sect. B 1974, B30, 2503.
`(41) Schafer, L.; Klimkowski, V. J.; Momany, F. A.; Chuman, H.; Van
`Alsenoy, C. Biopolymers 1984, 23, 2335. Scarsdale, J. N.; Van A1senoy, C.;
`Klimkowski, V. J.; Schafer, L.; Momany, F. A. J. Am. Chem. Soc. 1983, 105,
`3438.
`(42) Hossain, M. B.; van der Helm, D. J. Am. Chem. Soc. 1978, 100, 5191.
`(43) Karle, I. L.; Gibson, J. W.; Karle, J. J. Am. Chem. Soc. 1970, 92,
`3755.
`(44) Kostansek, E. C.; Thiessen, W. E.; Schomburg, D.; Lipscomb, W. N.
`J. Am. Chem. Soc. 1979, 101, 5811.
`(45) Karle, I. L. J. Am. Chem. Soc. 1978, 100, 1286.
`
`

`
`1662 J. Am. Chem. Soc., Vol. 110, No.6, 1988
`
`Jorgensen and Tirado- Rives
`
`Table IX. Relative Energies and Torsional Angles (.P, 'lit) for Conformations of N-Acetylalanine N-Methylamide
`
`0.0 (-84, 70)
`AMBER/OPLS
`0.0 (-79, 69)
`AMBER-normal
`0.0 (-76, 66)
`AMBER-all atom
`0.0 (-83, 81)
`UNICEPP
`0.0 (-80, 76)
`ECEPP/2
`0.0 (-85, 73)
`4-210
`0.3 (-78, 40)
`PCILO
`(-75, 50)
`IR, NMR (CCI4)
`a Energies in kcalfmol, angles ( .P, if) in deg.
`
`1.5 (-150, 162)
`2.3 (-150, 154)
`3.2 (-161, 169)
`0.7 (-152, 147)
`0.7 (-155, 157)
`1.4 (-166, 167)
`1.7 (-171, 164)
`(-160, 170)
`
`3.0 (-69, -29)
`3.6 (-61, -41)
`1.2 (-72, -44)
`0.8 (-74, -35)
`6.0 ( -78, -26)
`2.4 ( -29, -59)
`
`4.6 (55, 35)
`4.3 (54, 42)
`3.5 (55, 57)
`2.3 (54, 46)
`6.7 (61, 41)
`
`2.5 (67, -56)
`0.8 (68, -58)
`0.6 (69, -64)
`
`7.3 (76, -65)
`2.6 (75, -62)
`0.0 (75, -40)
`
`ref
`this work
`3
`3
`35
`36
`41
`38
`39
`
`Table X. Experimental Data on Cyclic Peptide Crystals
`no. of water•
`space group
`peptide
`abbrev
`1
`cyclo-(Ala-Ala-Gly-Giy-Aia-Giy)
`CPI
`P21
`cyclo-(Aia-Aia-Giy-Aia·Giy-Giy)
`2
`CP2
`P212121
`cyclo-(Gly-Gly-o-Aia-o-Ala-Gly-Giy)
`3
`CP3
`P2t2t2t
`4
`cyclo-(Gly-Pro-Giy-Giy-Pro-Giy)
`CP4
`P2l
`P2 12121
`cyclo-(Giy-Pro-Gly-o-Ala-Pro)
`0
`CPS
`a Number of water molecules per peptide in the crystal. bNumber of peptide molecules in the unit cell.
`
`zb
`2
`4
`4
`2
`4
`
`ref
`42
`42
`43
`44
`45
`
`minima were then located in unconstrained optimizations starting
`from conformations in the low energy regions. The results are
`summarized in Tables VIII and IX where the relative energies
`of the C7 (1-7 H-bonded), C5 (extended), and a-helical forms
`are reported along with the if> and Y, values for the minima.
`For GA, there is agreement that the C 7 conformer is lowest
`in energy with if> and Y, near 80° and -70°. There is scatter in
`the predicted energies for the C5 form with the AMBER/OPLS
`value in the middle of the range. The a-helical conformer is at
`still higher energy with AMBER. A minimum could not be found
`in this case with AMBER/OPLS; all attempts at optimization
`collapsed to the c7 conformer.
`The reduced symmetry in AA leads to more possibilities for
`distinct energy minima (Table IX). There is now general accord
`that the equatorial C7 form is lowest in energy with if> and Y, near
`-80° and 70°. The energy for the extended Cs conformation from
`AMBER/OPLS is in the middle of the tabulated range. The a
`helical conformers are again not found as energy minima by several
`computational methods including AMBER/OPLS. Their ex(cid:173)
`istence as minima was previously found to be sensitive to the
`scaling of the 1 ,4-interactions in AMBER. 3 In the absence of more
`definitive experimental data, the main conclusion from these
`comparisons is that the AMBER/OPLS predictions for confor(cid:173)
`mational energies are reasonable.
`
`Polypeptide Crystals
`The structures for the five cyclic polypeptide crystals listed in
`Table X were also calculated with the normal AMBER and
`AMBER/OPLS force fields to obtain a stringent test of the
`representation of the intermolecular interactions. Similar com(cid:173)
`putations were the basis of the recent evaluation of force fields
`by Hall and Pavitt that proved very favorable for AMBER.4 They
`used the first three polypeptides in Table X.
`Version 2.0 of AMBER did not include the code necessary for
`the crystal calculations. Thus, additions were made to allow energy
`minimizations for a realistic representation of the crystalline
`environment. In our modified version of the minimization pro(cid:173)
`cedure, the intramolecular interactions are calculated in the
`standard fashion over all atoms in one asymmetric unit. For
`evaluating the intermolecular interactions, the unit cell is first
`completed by generating coordinates for all remaining atoms. This
`entails reflection and/or translation of the original asymmetric
`unit. The full crystalline environment is then provided by periodic
`boundary conditions using translated images of the unit cell in
`all directions, i.e., the unit cell is effectively surrounded by 26
`images of itself. These spatial transformations were made relative
`to the current dimensions of the unit cell at each cycle of the
`minimization. Two types of calculations were performed. In one,
`the unit cell dimensions were fixed at the experimental values,
`while in the other, they were optimized with use of the simplex
`method.46 The latter calculations were relatively time-consuming
`
`since complete energy minimization for the contents of the
`asymmetric unit was performed with the AMBER program be(cid:173)
`tween each simplex cycle.
`The energy and forces were calculated for an asymmetric unit
`by including the interactions with all image atoms within the cutoff
`range. Specif