JOURNAL
`OF 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
`
`\VilUam L. Jorgensen• and JuUan Tirado-Rhes
`
`Contribution from the Department of Chetnistry. Purdue U11illersity,
`JVeJ't Lafayette, Indiana ./7907. Received January 26, 1987
`
`Abstract: A complete set of intermolocular 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 comfTIQn neutral and charged terminal
`groups. The potential functions have the simple Coulomb plus Lennard-Jones form and arc compatible with the widely used
`models for water, TIP4P, TIPJP, and SPC. The parameters were obtained and tested primarily in conjunction with r-+i:onte
`Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aquoous 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 A~fBER 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 romp!ete crystal of the
`protein crambin, including 182 water molecules that were initially placed via a r-+fonte Carlo simulation. The resultant
`root-me.an-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 Al\fBER united-atom forc.e field which has previously been
`demonstrated to be ~uperior to many alternatives.
`
`Computer simulations are undoubtedly destined to beo:ime an
`increasingly important means for investigating the structures and
`dynamics of biomolecular systems. 1 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 mo\ecu\cs. 2
`There is also little doubt that there will be a continual evolution
`in force fields with added c-0mplexity 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·
`ance are summariz.cd here. These potential functions have a simple
`form and they have been parametrized dire<:tly to reproduce
`experimental thermodynamic and structural data on fluids.
`Consequently, they are computationally efficient and their de·
`scription of proteins in solution or crystalline environments should
`be superior to many altcrantives 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 hexapeptidcs, a cyclic pentap:ptide, and the protein crambin.
`Improvements are apparent in comparison to the At-.fBER un·
`ited-atom force field 1 which has previously been shown to be
`superior to many alternatives.4
`
`(I) lk...cridge, D. L., Jorgensen, W. L., Eds. A11n. N.Y. A(od, Sd. 1986,
`481.
`(2) For revie.,,,s, !ee: (a) Le~·itt, M_. Anm.1. Rtl). BiopliyJ. Bioeng. 1982,
`lJ, 251. (b) MtCammon, J. A. Rep. Prog. PliyJ. 1984, f7, I.
`(J) Weiner, S. J.: Kollman, P.A.; Case, D, A.; Singh, U. C.; Ghio, C.;
`Alagona, G.: Profeta, S.: Weiner, P. /. Am. Chtm. Soc. 1984, UM, 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.J A simple, computationally
`efficient form was chosen to represent the nonbonded interactions
`through Coulomb and Lennard-Jones terms interacting between
`sites centered on nuclei (eq I). Thus, the intermolecular inter-
`°"'.<'II b
`AE1b = L E (q,qjl /rlJ + A1J/r1/1 - C11-/r1/)
`'
`I
`action energy between molecules a and bis given by the sum of
`interactions between the sites on the two molecules. The non·
`bonded oontribution to the intramo\ecular 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·
`ulations) model, e<ich atomic nucleus has an interaction site, except
`CH,. groups arc treated as united atoms centered on the carbon.
`It is important to note that in this model 110 sptcialfimctions were
`
`(1)
`
`(4) Hall, D.; Pavitt, N. J. Compui. Chnn. 1984, j, 411.
`
`0002-7863/88/1510·1657SOJ.50/0 © 1988 An1erican Chemical Society
`
`Roxane Labs., Inc.
`Exhibit 1025
`Page 001
`
`

`
`1658 J. Am. Chem. Soc., Vol. 110, No. 6, 1988
`
`Jorgensen and Tirado- Rives
`
`Tablt I. tlquid1 Simu\attd with the OPLS Potential Function1
`liquid
`liquid
`2S
`HCONHi
`25, 100
`HCON(CH,)i
`CH1CONHCH1 100
`CH10H
`C1H,OH
`n-C1H70H
`l·C1H10H
`t·C,H10H
`CH,SH
`C1H1SH
`(CH1hS
`C1H1SCH1
`(CiH1hS
`CH,SSCH1
`(CH,)iO
`CiH,OCHi
`(C1H1hO
`THF
`
`T (°C) "'
`'
`'
`'
`'
`'
`'
`'
`'
`
`2S
`2S
`2S
`
`2S
`
`7
`7
`7
`7
`7
`7
`
`8
`
`2S
`-25
`
`pyrrole
`pyridine
`CH,
`CiH,
`c,n,
`n-C,H10
`i-C,H10
`n-C1Hu
`l·CiHn
`nto-C1H11
`c·C1H10
`n·CiHu
`CH,CH1CH-CH1
`
`(CH1hC=CHi
`benzene
`CH,COiCHi
`
`"
`"
`"
`"
`t·CH1CH-CHCH1 "
`C-CH1CH=CllCH1 "
`"
`
`T(°C) "'
`'
`'
`
`2S
`2S
`-161
`10
`-89
`10
`-42, 25
`10
`-o.s, 25 10
`2S
`10
`2S
`10
`2S
`10
`10
`10
`10
`10
`10
`10
`10
`10
`8
`
`2S
`2S
`
`18 °"H~EA~T~S~DF~V~R~PO~R~l~Z~R~Tl~D~N~~~
`
`12
`
`"l
`13 9
`
`6
`
`'
`
`O D
`
`'
`
`!2
`9
`6
`EXPERIHENTRL
`Fii\Jre 2. Comparison of computed and experimental heats of vapori·
`talion in kcal/mo! for the liquids in Table I and TIP4P water.
`
`15
`
`"
`
`"
`"
`'
`"
`"
`"
`'
`"
`"
`'
`"
`'
`2lD MOLECULAR VOLUMES
`
`195
`
`160
`
`~
`
`~125
`
`90
`
`55
`
`55
`
`160
`125
`90
`EXFERIHEl/TRL
`Figure I. Comparison of computed and experimental YOlumcs per
`molecule in Al for the liquids in Tt.ble I and TIP4P water.
`
`195
`
`230
`
`found to be needed to describe hydrogen bonding and there are
`M additional interaction sites/or lone pairs. Another important
`point is that standard combining rules are used for the Len·
`nard-Jones interactions such that A11 = (A11A11)1l 1 and c,1 ""
`(C11CJJ) 111• The A and C parameters may also be e:-:pressed in
`11 and Cu= 4Eifri6.
`terms of Lennard-Jones 11's and t's as Aa = 4t'j<11
`The OPLS parameters for the 20 neutral peptide residues
`reported here were obtained primarily via ~iontc Carlosimulation.s
`for the 36 organic liquids listed in Table J.5-lO Standard geom·
`etries were used for the molecules with fixed bond lengths and
`bond angles, though torsional motion was included, as described
`in detail elsewhere.s-10 Particular emphasis was placed on re·
`producing the e:tperimcntal densities and heats of vaporization
`for the liquids. In view of the simplicity of the functional form
`(eq I), the accord with the experimental data is remarkable as
`illustrated in Figures l and 2; the average deviation between the
`e:tperimental 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 (D~1F),
`methanol, ethanol, 1-propanol, 2-mcthy!·2-propanol, methane,
`ethane, neopcntane, 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.5·1° Thus, only 12
`different CH~ groups are used to describe all alkanes, alkenes,
`
`(5) Jorgen1en, \V. L.; Swen.on, C, J. J. A!"f. Clum. S0<. 1985, 101, 569.
`(6) Jorgen5en, W. L. /. Phys. Chtm. 1986, 9(), 1276.
`(7) Jorgen1en, W. L. /. Phys. Chtm. 1986, 90, 6379.
`(8) Jorg~nsen, W. L.; Brigg5, J. M., to be published.
`(9) Jorgen1en, \V, L.; Contreras, L., to be pub\hbc<l.
`(10) Jorgenltn, \V. L.; Madura, M. D.; SwenJOO, C. 1.1. Am. Chan. SIX.
`1984, 106, 6638.
`
`and benzene, 10 and, for example, the parameters for the OH groups
`in all a!oohols6 and the carbonyl groups in all amides 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·
`junction with the OPLS potentials was TIP4P, ll,ll though the
`TIPJP 11 or SPCD 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 OOnd
`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 6-3 IG(d) basis set.1' The trends
`in the ab initio findings for the hydrogen bond strengths and
`geometries are well reproduced by the OPLS re-sults.s--9,IS
`Furthermore, Monte Carlo simulations were carried out for dilute
`aqueous solutions of formamide,1 5 1V-methylacetamide (NMA),15
`D~iF,1s methano!,16 and seven alkane.s.11 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 kcal/mo!, are in the correct
`range. 15 Similarly, the hydration of 1nethanol appears reasonable
`and the computed difference in free energies of hydration for
`methanol and ethane, 6.75 ± 0.2 kcal/mo!, is in excellent accord
`with the experimental value, 6.93 kcal/mol. 15 The free energy
`calculations are a powerful diagnostic too!, but very demanding
`on computer resources. 16 The results for the hydrophobic hy·
`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 hydration.n
`The parametri1.ation 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 con~trued 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
`
`(JI) Jorgenien, W. L.; Cha.rnlruel:.hu, J.; Madura, 1. D.; lmpey, R. \\'.;
`Klein, M. L. /. Chtm. Phys. 1983, 19, 926.
`(l2) Jorgens-cn. W. L.; Madura, J. D. Aloi. Phys. 1985, 56, IJ8L
`(IJ) Berendsen, H.J. C.; Ponma, J.P. M.; \'On Gunste1en, W. F.; Her·
`mans, J. In /nlermoluu/ar Forus; Pullman, B., Ed.; Reidel: Dordrecht,
`Holland, 1981; p 331.
`(14) Francl, M. M.; Pieuo, W. J.; Hehre, W. J.; Bink.Icy. J. S.; Gordon,
`J\f. S.; DeFrc~s. D. J.; Pople, J. A. I. Chtm. PhyJ. 1983, 77, 3054.
`(15) Jorgtns-co, W. L.; Sweruon, C. J. /.Am. Chtm. Soc. 1985, 107, 1489.
`(16) Jorgcnien, W. L.; RaYimohan, C. J, Chtm. Phys. 1985, 83, 3050.
`(17) Jorgen5eo, W. L.; Gao, J.; RaYimohan, C. J. P~ys. Chtm. 1985, 89,
`3470.
`
`Roxane Labs., Inc.
`Exhibit 1025
`Page 002
`
`

`
`The OPLS Potential Functions for Proteins
`
`J. An1. Chen1. Soc., Vol. 110, No. 6, 1988 1659
`
`Table 11. OPLS Atom and Group Assignments for Proteins•
`atom
`atom
`or group
`or group
`
`residue
`
`24 ~I~N~TE~R~R~C~T~IO~Nc-oE~N~E~RG~IE~Sc----,,
`IKCRL/MOLJ
`
`21
`
`~
`
`5:'. IS
`D
`
`12
`
`9
`
`' ' '
`"
`' '
`
`6 6
`
`9
`
`12
`
`15
`6-3\Gldl
`Figure 3. Comparison of interaction energies (keal/mol) for ion-water
`comple~es obtained with the OPLS potential functions and ab initio
`6·31G(d) calculations.
`
`18
`
`21
`
`24
`
`general study of the hydration of ammonium and carboxy!ate
`ions. 18 Ab initio calculations were carried out with the 6-3 lG(d)
`basis set for low-energy forms of complexes between water and
`NH/, CH3NH3+, and Hcoo-."·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. 13•19 In addition, the OPLS parameters were
`required to yield good agreement with experimental heats of
`hydration for NH4+, CH3NH1+, (CH1)4N+, Hcoo-, and
`CH1Coo-. 1s This was demonstrated through Monte Carlo sim(cid:173)
`ulations for the five ions in dilute aqueous solution. 1g The
`structural results were also shown to mirror experimental estimates
`of hydration numbers for the ammonium and carboxylate groups
`in Lys, Qiu, 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-JlG(d) results for complexes
`of water with guanidiniu1n ion and protonated imidazole.n 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 u = t = 0
`in the OPLS potentials), The accord between the OPLS and
`6·3 IG(d) results for low-energy geometries is uniformly good. For
`example, the OPLS optimal interaction energy and CO distance
`for 1are16.1 kcal/mo! and 3.33 A, whereas the 6-31G(d) values
`with fixed water and guanidinium geometries are 18.2 kcal/mo!
`and 3.41 A. And, for 2, the OPLS predictions for the interaction
`energy and NO distance are 16,0 kcal/mo! and 2.72 A versus the
`H
`H
`\
`I
`c=c
`I
`I
`H
`H/N;;,.6-;:N......._H
`I
`'-a···
`I
`H
`
`H
`
`1
`2
`6·31G(d) values of 16.1 kcal/mo! and 2.85 A. In general, the
`accord between the OPLS and 6·31G(d) results is good as ii·
`lu.strated in Figures 3 and 4 for 14 low-energy geometries of water
`with NH.+, CH3NH3 +, Hcoo-, guanidinium ion, and protonated
`imidazole. The OPLS interaction energies are deliberately de(cid:173)
`signed to be less than the 6-JIG(d) results, since the latter are
`typically somewhat greater than the limited experimental data.1*·19
`At this time, fluid simulations have not been executed for guan·
`idinium ion or protonated imidazole in water. Experimental
`
`(18) Jorgemcn, \V. L.; Gao, J. J. Phys. Chem. 1986, 90, 2174.
`(19) Gao, J.; Garner, D. S,; Jorgensen, \V. L. J, Arn. Chem. Sor. 1986,
`108, 4784.
`(20) Kuntz. I. D. J. Am. Chem. Soc. 1971, 93, 514.
`(21) Jorgemen, \V. L.; Gao, J., unpublishe-0 resu!U,
`
`Gly
`
`Pw
`
`Ah
`Aib
`Pw
`
`llo
`
`Ser
`
`Tyr
`
`N
`ll(N}
`CH!"
`c
`0
`N
`CH'
`c
`0
`
`CHl
`CHl
`CH18
`CH11
`6
`CH1
`CH'
`CH1
`.,.
`CHJ.,.
`3
`CH3
`
`CH1e
`0'
`IP
`CH'
`0'
`IP(O)
`CH)1
`CHl
`C'
`CH'
`CH•
`er
`o•
`H•
`CH18
`C>
`O'
`N'
`H 1(N)
`
`CH/
`
`C' o•
`CH/
`c•
`N'
`H1(N)
`CH'
`CH'
`N'
`
`residue
`type
`.\fain Chains
`3
`Ala
`4
`5
`I
`2
`3
`14
`I
`2
`
`Aib
`
`Leu
`
`Side Chains
`7
`Val
`65
`9
`9
`15
`8
`9
`7
`10
`
`Phe
`
`Cys
`
`~fet
`
`Cystine
`
`Hyp
`(Pro-OH)
`
`Gin
`
`Glu
`
`Hip
`(His-H+)
`
`22
`23
`24
`25
`23
`24
`7
`9
`II
`II
`11
`26
`23
`24
`9
`I
`2
`12
`13
`
`16
`17
`18
`
`9
`45
`40
`41
`44
`43
`42
`
`Arg
`
`type
`
`3
`4
`6
`I
`2
`3
`4
`64
`I
`2
`
`' 2
`
`8
`7
`9
`8
`7
`9
`II
`II
`II
`II
`31
`32
`JJ
`9
`34
`J5
`36
`37
`38
`9
`25
`15
`23
`24
`9
`9
`
`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(NJ
`CH'
`c
`0
`N
`H{N)
`C'
`c
`0
`
`CH'
`CH3.,.
`CH/
`CH'
`CH1'
`CHl
`C'
`CH'
`CH'
`CH'
`CH 2J
`S•
`H'
`CH18
`CH11
`s•
`CH3•
`CHl
`S•
`CHl
`CH'
`CH23
`o•
`H'(O)
`CHl
`Cl-11.,.
`c•
`o·
`N'
`H'(N}
`CHl
`CH1 1
`c•
`o•
`CHl
`C'
`N'
`H1(N)
`CH'
`CH'
`N'
`H'(N)
`CHl
`CH11
`CH11
`N'
`H'(N}
`er
`N•
`H~(N)
`CH28
`CH11
`CH'
`o·
`H'(O)
`CH1'
`N'
`Hf(:'-.')
`
`CH28
`9
`C'
`50
`45
`CH'
`C'
`50
`N'
`40
`41
`H'(N)
`c·
`45
`II
`CH'
`CH<
`11
`CH•
`11
`CH18
`9
`CH11
`9
`CH/
`9
`CH 1'
`19
`N'
`20
`21
`Hf(N)
`•Nomenclature for atoms: ref 22.
`
`Lys
`
`Hy!
`(Lys-OH)
`
`thermodynamic data do not appear to be available in these cases.
`The OPLS parameters obtained in this way for 25 con1mon
`peptide residues and both neutral and charged terminal residues
`
`Roxane Labs., Inc.
`Exhibit 1025
`Page 003
`
`

`
`1660 J. Am. Chem. Soc .. Vol. 110, No. 6, 1988
`
`Jorgensen and Tirado-Rives
`
`Table lV, OPLS Parameters for Proteins
`type
`q
`'·A
`I
`0.500
`3.750
`2
`2.960
`--0.500
`J
`3.250
`--0.570
`0.0
`0.370
`4
`0.200
`3.800
`3.800
`0.200
`0.0
`3.910
`0.0
`3.850
`0.0
`3.905
`0.0
`3.905
`0.0
`3.750
`--0.850
`3.250
`0.0
`0.425
`0.285
`3.800
`0.285
`3.800
`3.905
`--0.100
`3.750
`0.700
`--0.800
`2.960
`0.310
`3.905
`3.250
`--0.JOO
`0.0
`0.330
`0.265
`3.905
`3.070
`--0.700
`0.0
`0.435
`0.265
`3.850
`0.265
`3.750
`0.310
`3.800
`0.100
`3.800
`3.800
`0.310
`0.100
`3.800
`3.905
`0.180
`--0.450
`3.550
`0.0
`0.270
`0.235
`3.800
`--0.470
`3.550
`0.235
`3.800
`0.300
`3.800
`3.550
`--0.300
`0.200
`3.800
`--0.570
`3.250
`o.o
`0.420
`--0.490
`3.250
`0.410
`3.750
`0.100
`3.750
`3.750
`0.130
`3.250
`--0.540
`o.o
`0.460
`o.soo
`3.750
`3.750
`0.330
`3.750
`--0.055
`3.250
`--0.800
`0.0
`0.460
`0.640
`2.250
`--0.700
`3.250
`o.o
`0.440
`3.905
`0.310
`0.070
`3.905
`0.550
`3.750
`--0.450
`2.960
`0.250
`3.800
`3.800
`0.250
`J.000
`--0.400
`0.250
`3.800
`3,800
`0.200
`0.0
`J.960
`
`61
`62
`6J
`
`" "
`
`3·6 QPT!MAL SEPARAHONS
`
`3 ,q
`
`3"
`
`"'
`
`2.6
`
`0
`
`0
`
`2.6
`
`3.0
`2-B
`6-31G!dl
`Figure 4. Comparison of optimal se()arations In A for ion-water com·
`pl exes. obtained with the OPLS potential functions and ab initio 6-31 G(d)
`calculations.
`
`3.2
`
`3,4
`
`3.6
`
`Tab!t Ill. OPLS Atom and Group Assignmcnli for Terminal
`Residues
`
`residue
`
`H1N .. CHRC=O
`
`NHCHRC0 2-
`
`atom or group
`Charged Termini
`N
`H(N)
`CH"
`CH1• (R=H)
`C
`0
`N
`H(N)
`CH"
`CH1" (R=H)
`c
`0
`
`Neutral Termini
`NHCHRC(O}OCH1
`N
`H(N)
`CH'"
`CH1" (R=H)
`c
`0
`O(CHJ)
`CH1
`CHi
`C
`0
`N
`H(N)
`CH1
`
`CHJC(O)(NHCHRC(O))
`
`(NHCHRC(O))NHCHi
`
`type
`
`20
`21
`29
`27
`I
`2
`3
`4
`30
`28
`11
`18
`
`3
`4
`60
`61
`58
`59
`62
`63
`7
`I
`2
`3
`4
`39
`
`are summari1..ed in Tables II-IV. The atom and CHA group type
`assignments are given in Tables II and III with use of standard
`nol.3.tion,22 white the actual charges and Unnard-Jones parameters
`are in Table IV. In all, 65 unique atom and group types are
`designated, though the number of unique sets of Lennard-Jones
`parameters is only 19. For reference, the parameters for the
`TIP4P, TIP3P, and SPC models for water arc 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, +I or -l.
`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
`~1erger with A~IDER
`In order to provide a wmplete energetic description of biom(cid:173)
`olecular systems, the intramolecular terms for bond length and
`OOnd angle variations as well as the torsions and nonOOnded terms
`
`(22) IUPAC-IUB Commis.si-On on Blochemieal Nomcndtture: Bfod1tm·
`lsuy 1970, 9, 3471.
`
`' 6
`
`1
`8
`9
`10
`II
`12
`13
`14
`ll
`16
`17
`18
`19
`20
`21
`22
`2l
`
`" 25
`
`26
`27
`28
`29
`JO
`JI
`J2
`J3
`J4
`JS
`J6
`31
`J8
`J9
`40
`41
`42
`
`" " '5
`" " " 49
`" " " 56
`" 60
`
`50
`51
`52
`
`57
`58
`
`f, kc-al/mol
`0.105
`0.210
`0.l70
`0.0
`0.118
`0.080
`0.160
`0.080
`0.ll8
`0.175
`0.110
`0.170
`0.0
`0.080
`0.118
`0.118
`0.105
`0.210
`0.118
`0.l 70
`0.0
`0.118
`0.l70
`0.0
`0.080
`O.llO
`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.\70
`0.0
`0.050
`0.170
`0.0
`0.ll8
`O.! !8
`0.!05
`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
`fonner item.'> by others,1..l merger of the OPLS non bonded potential
`functions and the local vibration and torsional functions from
`another force field wuld be considered. AMBERl was chosen
`be<:ause it is widely used and because of its documented success
`in wn1parison to 15 other force fields for calculation.<; of the crystal
`structures of 3 cyclic hexapeptides, though we recognize that the
`test was limited since only Gly and Ala residues were represented.~
`The bond stretch and angle bend terms in AMBER are
`quadratic, while the torsional potentials consist of a cosine term
`
`Roxane Labs., Inc.
`Exhibit 1025
`Page 004
`
`

`
`The OPLS Potential Funcliom for Proteins
`
`J, Am. Chen1. Soc., Vol. 110, No. 6, 1988 1661
`
`Table v, Parameters for Water l\{odeh
`
`mode!
`
`TIP4P"
`
`K/l'-,K
`"
`TIP JP'
`
`geometry
`site
`,(QH) = 0.9572 A
`0
`r(OM) = 0.1500 A H
`LHOH = 104.52° M
`r(OH) = 0.9572 A
`0
`LHOH = 104.52°
`H
`r(OH) :i 1.0000 A
`0
`LHOH = 109.47°
`H
`•Reference 11. h Reference JJ.
`
`SPC'
`
`,,A
`q
`0.0
`J.15365
`0.520 o.o
`-l.040 o.o
`---0.834 3.15061
`0.417 0.0
`---0.820
`J.16557
`0.410 0.0
`
`,,
`
`kcal/mo\
`
`0.1550
`o.o
`0.0
`0.1521
`0.0
`0.1554
`0.0
`
`T111ble VII, Relative Energies for Conformations of Methyl Eth)'l
`Ether•
`
`method
`
`A?lfBER/OPLS
`AMBER-normal
`AMBER-big
`AMBER-all atom
`~fM2
`4-310
`JR, gas phase
`ED, gas phase
`
`gauche
`l.S
`1.6
`1.6
`1.4
`1.8
`2.0
`I 5
`1.2
`
`cis
`8.7
`9.4
`8.9
`5.J
`4.5
`7J
`
`this work
`this work
`this work
`24
`JI
`32
`33
`34
`
`•Energies rtlative to the trans conforn1er in kcal/mol.
`
`T1ble VJ. Relative Ener8ie.s for Conformations of Butane•
`cis
`method
`gauche
`
`a
`
`Table VIII. Relative Energies and Torsional Angles (4', 'V) for
`Conformations of N-Acetylglycine iV-Methylamide
`C1
`ref
`C/
`method
`this work
`0.0 (82, -67) 1.7
`AMBER/OPLS
`3
`0.0 (77, -64) 3.2 4.1 {66, JS)
`AMBER-normal
`AMBER-all atom 0.0 (75, -65) 3.3 4.1 (60, J9)
`3
`JS
`UNICEPP
`0.0 (83, -76) 0.9 1.2 (71, 52)
`36
`ECEPP/2
`0.0 (79, -7J) 1.2 1.2 (73, 74)
`J7
`4-210
`0.0 (BJ, -71) 0.8
`0.0 (80, -40) 2.0
`38
`PCJLO
`39
`IR, NMR (CCI,)
`(75, -50)
`X-ray (crystal)
`40
`(109, -21)
`"Energies in kcal/mo!, angle.s (ol> and~) in deg. hThe Cs confor(cid:173)
`mation has. 4' "" ii' = 180".
`
`The corresponding results for methyl ethyl ether are summa(cid:173)
`rized in Table VII. The A1fBER/OPLS and normal AMBER
`results are again similar; the predicted gauche - trans energy
`differences are also close to the experimental findings.ll.H
`The two standard dipeptides that were studied arc 1V-acetyl(cid:173)
`glycine N-methylamide (GA) and N-acetyla!anine N-methylamide
`(AA). Rough energy maps were constructed by varying <I> and
`If in 30" intervals between -180° and 180°. The local energy
`
`CH3
`
`H
`I
`0
`R H
`)!.._• ~ '/"
`N .... I 'If '-...CH3
`I o
`H
`GA:R•H
`AA: R•CH3
`
`(28) Verma, A.: Murphy, \\'.; Bernstein, H. J. Chem. PhyJ. 1974, 60,
`1540.
`(29) Kuchit~u. K. Bui/. Chem. Soc. Jpn. 1959, 31, 148.
`(30) Kanwika, I.; Snyder, R. G.; Stra1,1n, H. L. J. Chem. PhyJ. 1986, 84,
`395.
`(ll) Burkert, U. J. Compur. Chem. 1980, /, 285.
`(32) Jorgensen, \V, L.; Ibrahim, M. J. Am. Chtm. Soc. 1981, 101. 3976.
`(33) Kitagawa, T.; Miya:uwa, T. Bull. Cltem. Srx. Jpn. 1968, 41. 1916.
`(34) OyaMgi, K.; Kuchitsu, K. Bu//. Chem. Srx. Jpn. 1978, 51, 2237.
`(35) Dunficld, L. G.; Burge.u, A. W.; Scheraga. H. A. J. Phys. Chem.
`1978, 81, 2609.
`(l6) Vaz.q1.1c2, M.; Ncmethy, G.: Schciaga, H. A. J.faaomoltcules 1983,
`16, 1043.
`(37) (a) Schafer, L.; Van Alicnoy, C.: Se.audale, J. N. J. Chem. Phys.
`1982, 76, 1439. (b) Klimi::owski, V. J.: Schafer, L.; Momany. f. A.: Van
`Ahenoy, C. J. J.foltc. Str. (THEOCHEM) 1985, 11<1, 143.
`(38) Maigret, B.: Pullman, B.; OreyfuJ, J. J. Thtor. Bio/. 1970, 16, 23\.
`(l9) 0.rng, M. T.; Marraud, M.; Nod, J. An11. Chim. (PariJ) 1972, 7, 183.
`(40) Iwasa'a'.i, F. A'la CryJ/a/logr., Sui. B 1974, 830, 2503.
`(41) &:hafcr, L; Klimkowski, V. J.; Moman)', F. A.: Ch1.1man, H.; Van
`Alun11y, C, Biopo/ymeu 198~, 11, 2335. Scandal~. J. N.; Van Al;cnoy, C.:
`Klimko.,..1ki, V, J.; Schafer, L.; Momany, f. A. J. Am. Chun. So.:. 1983, 105,
`3438.
`(42) Howin, M. B.; ~·an dcr Helm, D. J. Am. Chem. Soc. 1978, JOO, 5191.
`(43) Karle, I. L.; Gi'ooson, J. W.; Karle. J. J. Am. Chtm. Stx. 1970, 91,
`3755.
`(44) Kostan~k. E. C.; Thiessen, \V. E.; &:homburg, D.: Lipscomb, W. N.
`J. Am. Chem. Soc. 1979, IOI, 5811.
`(45) Karle, I. L. J. Am. Chem. Stx. 1978, JOO, 1286.
`
`"'
`
`I.OJ
`AMBER/OPLS
`0.89
`AMBER-normal
`O.J7
`AMBER-big
`0.58
`AMBER-all atom
`0.88
`~[M2
`hf P3/6-3 l 1Gu + ZPE
`0.7
`0.89
`Raman, gas phase
`IR, gas phase
`0.97
`ED, gu phase
`0.65
`~Energies relative to the trans conformer in kcal/mo!.
`
`7.08
`6.97
`5.S6
`4,57
`4.73
`6.0
`4.52
`
`3.6
`
`this work
`this work
`thi! work
`24
`25
`26
`27
`28
`29
`
`plus the 1,4-nonbonded interaction, both Coulombic and Len(cid:173)
`nard-Jones. Thus, the torsional potentials are affected by the
`choice of non bonded parameters. Furthermore, the l,4-nonbonded
`interactions are scaled in AMBER by dividing by factors SCND
`and SCEE for the Lennard-Jones and Coulombic terms, re·
`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 "normalB AMBER nonbonded parameters
`are used.J 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 SCND is 8.0.3 For the purpose of
`merging the OPLS and Al\fBER force fields in an uncomplicated
`manner, it was necessary to readdress the best choices for SCNB
`and SCEE. This was done by choosing value5 that gave reasonable
`agreement between results for conformational surfaces with
`AMBER/OPLS and "normat• AMBER. These tests are sum(cid:173)
`marizc-0 in the next section, fo\lowed 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.1 All of the calculations employed
`a dielectric C>.Jnstant of l for evaluating the electrostatic energy.
`This is the proper choice since the OPLS parameters have bun
`derive.cl 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 A?\iBER/OPLS acceptable choices for SCEE
`and SCND are 2.0 and 8.0, i.e., the same as for "big" A~iDER. 1
`All results for A?\1BER/OPLS reported here use these values.
`For butane, the energies of the gauche and cis conformers
`relative to trans are listed in Table VI. Tb.e AhfBER/OPLS
`and normal AMBER re.suits are similar; the gauche- trans energy
`difference is on the high side of the range of experimental val(cid:173)
`ues11-JO and of the best available ab initio rcsult,26
`
`(2J) Jorgcn1en, W. L. J. Am. Chtm. Soc. 1981, 103, 335.
`(24) Weincr.S. J.; Kollman. P, A.; Nguyen, 0. T.; Case, 0. A. J. Ccmput.
`Chtm. 1986, 7, 230.
`(25) (a) Jorgensen, W. L. J. Chnn. Phys. 1981, 71, 5751. (b) AIHngcr,
`N. L. J. Am. Chtm. Stx. 1977, 99, 8127.
`(26) Ragavachari, K. J. Chtm. Phys. 198,, 81, 1383.
`(27) Compton, 0. A. C.; Montero, S.; Murphy, W. F. J. PhyJ. Chtm.
`1980, 84, 3587.
`
`Roxane Labs., Inc.
`Exhibit 1025
`Page 005
`
`

`
`1662 J. Am. Chen1. Soc., Vol. J 10, No. 6, 1988
`
`Jo1gensen and Tl!ado-Rives
`
`Table IX. Relative Energies and Torsional Angles (4', 'I') for Conformations of N·A..:etylalanine N-~{ethylam!de
`
`0.0 (-84, 70)
`AMBER/OPLS
`AMBER-normal
`0.0 (-79, 69)
`Al'.fBER-all atom
`0.0 (-76, 66)
`UNICEPP
`0.0 (-83, SI)
`ECEPP/2
`0.0 (-80, 76)
`0.0 (-85, 73)
`4-210
`0.) (-78, 40)
`PCILO
`(-75, 50)
`IR, N~iR (CCI•)
`• Energie1 in kcal/mol, angles (<I>, 'i') in deg.
`
`LS (-150, 162)
`2.J (-150, 154)
`J,2 (-161, 169)
`0.7 (-152, 147)
`0.7 (-155, 157)
`1.4 (-166, 167)
`1.7 (-171. 164}
`(-160, 170)
`
`).0 (-69, -29)
`J.6 (-61, -41)
`1.2 (-72, -44)
`0.8 (-74, -JS)
`6.0 (-78, -26)
`2.4 (-29, -59)
`
`4.6 (55, 35)
`4.3 (54, 42)
`3.S (55. 57)
`2.J (54. 46)
`6.7 (61, 41)
`
`2.S (67, -56)
`0.8 (68. -58)
`0.6 (69, -64)
`
`7.3 (76, -65)
`2.6 (75, -62)
`0.0 (75, -40)
`
`"'
`
`this worlc
`3
`3
`35
`36
`41
`
`'' 39
`
`Table X. Experimental Data on Cyclic Peptide Cr}>tals
`space group
`no. or water•
`abbrev
`peptide
`n1
`eyclo-(Ala-Ala·Gly·Gly·Ala·Gly)
`I
`CPI
`cyclo-{Ala-Ala-Gly-Ala·Gly·Gly)
`P2 12121
`2
`CP2
`cyclo-(Gly·Gly·D·Ala·o--Ala·Gly.Qly)
`P2 12121
`3
`CP)
`n 1
`cyc!o-(Gly·Pro·Gly-Gly-Pro-Gly)
`4
`CP4
`CPS
`cyc!o-(Gl>··Pro-Gly-o-Ala·Pro)
`P2 12 121
`0
`•Number of water molecules per peptide in the crystal. !Numhtr of peptide moleculci in the unit cell.
`
`z•
`2
`4
`4
`2
`4
`
`42
`42
`43
`44
`45
`
`minima were then located in unconstrained optimizations starting
`from conformations in the low energy regions. The results arc
`summarized in Tables VIII and IX where the relative energies
`of the C7 (1-7 JI-bonded}, C 5 (extended), and a-helical forms
`are reported along with the 4> and 1" values for the minima.
`For GA, there is agr~ment that the C7 conformer is lowest
`in energy with 4> and Vi near 80° and - 70°, There is scatter in
`the predicted energies for the C 5 form with the AMDER/OPLS
`value in the middle of the range. The a·helica\ conformer is at
`still higher energy with AMBER. A minimum could not be found
`in this case with A~iBER/OPLS; all attempts at optimization
`collapsed to the C 7 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 fonn is lowest in energy with 4> and .,P near
`-80° and 70°. The energy for the extended C1 conformation from
`Al\iBER/OPLS is in the middle of the tabulated range. The a
`helical confonners are again not found as energy minima by several
`computational methods including AMBBR/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 A;\iBER/OPLS predictions for confor·
`matlonal energies are reasonable.
`Polypeptide Crystals
`The structures. for the five cyclic polypeptide crystals listed in
`Table X were also calculated with the normal A~fBER 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.' They
`used the first three polypeptides in Table X.
`Version 2.0 of A1'.fBER did not include the code ne.c-cnary for
`the Cf)"$la] calculations. Thus, additions were made to allow energy
`minimizations for a realistic representation of the Cr)'Stalline
`environment. In our modified version of the minimization pro·
`cedure, the intramo\ecular 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 reO~tion 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 c.ell is effectively surrounded by 26
`images of itself. These spatial transformations were made relative
`to the current dimensions of the unit c.ell 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.4"5 The latter calculations were relatively time-consuming
`
`since complete energy minimization for the contents of the
`as)·mmetric unit was performed with the AMBER program b