Peptide Bond Vibrational Coupling

Transcription

1 J. Phys. Chem. B 2007, 111, Peptide Bond Vibrtionl Coupling Ntliy S. Myshkin nd Snford A. Asher* Deprtment of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVni ReceiVed: August 14, 2006; In Finl Form: Jnury 3, 2007 Neutrl trilnine (Al 3 ), which is geometriclly constrined to hve its peptide bond t Φ nd Ψ ngles of R-helix nd PPII-like conformers, re studied t the B3LYP/6-31+G(d,p) level of theory to exmine vibrtionl interctions between djcent peptide units. Delocliztion of the mide I, mide II, nd mide III 3 vibrtions re nlyzed by clculting their potentil energy distributions (PED). The vibrtionl coupling strengths re estimted from the frequency shifts between the mide vibrtions of Al 3 nd the locl mide bond vibrtions of isotopiclly substituted Al 3 derivtives. Our clcultions show the bsence of vibrtionl coupling of the mide I nd mide II bnds in the PPII conformtions. In contrst, the R-helicl conformtion shows strong coupling between the mide I vibrtions due to the fvorble orienttion of the CdO bonds nd the strong trnsitionl dipole coupling. The mide III 3 vibrtion shows wek coupling in both the R-helix nd PPII conformtions; this bnd cn be treted s locl independent vibrtion. Our clculted results in generl gree with our previous experimentl UV Rmn studies of 21-residue minly lnine-bsed peptide (AP). * Corresponding uthor. E-mil: [email protected]. Telephone: (412) Fx: (412) Introduction Vibrtionl spectroscopy is powerful method for determining moleculr structure nd dynmics, s evident from the numerous IR nd Rmn studies tht hve exmined the conformtions nd dynmics of peptides nd proteins These studies interpret spectrl chnges in terms of ltertions in equilibrium conformtions. Most often, the underlying ssumption is tht the systems re liner nd tht the mesured spectr derive from weighted liner sum of the spectrl contributions of the individul conformtions. In the cse of peptide secondry structure studies, it is ssumed tht the spectr re the liner sum of the spectr of the individul peptide bonds nd tht the individul peptide bond spectr re uniquely chrcteristic of the conformtion bout ech peptide bond. This presumption ssumes tht there is negligible coupling between the tomic motions of djcent peptide bonds. If significnt coupling occurs between djcent peptide bonds, the individul peptide bond spectr would depend upon their context. In this cse, simple liner interprettion of the resultnt observed spectr becomes impossible. It would, thus, become necessry to understnd the dependence of the peptide bond spectr on coupling of tomic motions between djcent peptide bonds. This coupling cn be studied theoreticlly by clculting the norml modes of peptides. Previous studies, which hve exmined vibrtionl coupling between the sme peptide bond vibrtions between peptide bond units, hve minly focused on the mide I vibrtion, which is primrily CdO stretching mode mixed with minor contributions from C-N stretching nd C R -C-N deformtion. 2,4,5,16-27 It hs been demonstrted tht the mide I vibrtions of polypeptides show significnt coupling nd re deloclized cross mny peptide bonds. The coupling between the mide I vibrtions is enbled by its lrge trnsition dipole moment s shown by Krimm nd co-workers Very few studies hve exmined vibrtionl coupling between the mide II (C-N stretching nd N-H bending coupled outof-phse) vibrtions of djcent peptide units nd the coupling between mide III vibrtions (C-N stretching nd N-H bending coupled in-phse) of djcent peptide units. 32 These couplings should be smller thn tht of the mide I vibrtions becuse the trnsition dipoles re smller. Understnding the extent of coupling of the mide III vibrtions is importnt becuse the mide III Rmn bnds re the most sensitive to peptide conformtion. In fct, the lowest frequency mide III bnd component, which is denoted s the mide III 3 vibrtion, is sensitive probe of the peptide bond Ψ ngle It is importnt to understnd whether the mide III 3 vibrtion is locl mode or if it involves collective peptide unit motion; is its frequency determined solely by the conformtion of the vibrting peptide unit, or is its frequency lso determined by the conformtion of djcent peptide units? To exmine the extent of coupling of mide I, mide II, nd mide III 3 vibrtions between peptide units, we previously experimentlly studied this coupling by exmining the UV resonnce Rmn spectr (UVRS) of two linked mides in mixed H 2 O/D 2 O solutions. 36 We lso exmined the 21-residue minly poly Al peptide (AP), which is 50% R-helix t 0 C nd melts to polyproline II (PPII) conformtion t higher tempertures. 36,37 Our hypothesis ws tht if the peptide vibrtions were coupled, then prtil deutertion of the mide nitrogens would lter the mide bond vibrtions drmticlly, becuse deutertion of the N-H decouples N-H bending from C-N stretching. This lrge mss chnge would drmticlly chnge the specific peptide bond mide vibrtions. Thus, the prtilly deuterted spectrum would not simply be the sum of the spectr of the fully deuterted nd non-deuterted peptides. These studies 36,37 suggested essentil vibrtionl independence of the mide III 3 nd mide II bnds for linked peptide bonds in both the R-helix nd PPII conformtions of AP. In ddition, the mide I nd mide I vibrtions showed no evidence for coupling in the cse of the AP PPII conformtion, nd the mide I bnd of the R-helix conformtion showed significnt interpeptide bond coupling /jp065247i CCC: $ Americn Chemicl Society Published on Web 03/30/2007

2 4272 J. Phys. Chem. B, Vol. 111, No. 16, 2007 Myshkin et l. The wekness of our experimentl study ws tht we did not know the mgnitude expected for the bnd frequency perturbtion due to coupling of djcent peptide bonds. In the work here, we further clrify the extent of interpeptide coupling using vibrtionl nlysis clculted by using electronic structure methods. We exmined trilnine (Al 3 ) s model peptide to study vibrtionl interctions between djcent peptide units nd studied the norml mode compositions of the mide I, mide II, nd mide III 3 vibrtions for geometries constrined to occur in the PPII nd R-helicl conformtions. We lso clculted the norml modes for severl Al 3 isotopomers where we reduce coupling between djcent substituents nd peptide bonds by ltering the tomic msses. We used these clculted locl mode frequencies to estimte the mgnitude of the mide bnd frequency shifts due to vibrtionl coupling. Computtionl Detils Figure 1. Lbeling of peptide toms indicting definitions of peptide unit nd Ψ nd φ ngles. All clcultions were performed t the density functionl theory (DFT) level by using the Gussin 03 clcultion pckge. 41 Geometry optimiztion nd vibrtionl frequency nlysis were crried out by using B3LYP functionl nd 6-31+G(d,p) bsis set. Prtil geometry optimiztion ws performed for trilnine (Al 3 ) in vcuum with ech specified pir of fixed vlues of φ nd ψ ngles corresponding to R-helicl (φ )-76 ; ψ )-44 ) nd PPII-like (φ )-67 ; ψ ) 132 ) secondry structures. The vlues of the φ- nd ψ-ngles were tken from the moleculr dynmics study performed by Mu et l. 45 The uthors showed tht conformtions with these prticulr vlues of ψ nd φ ngles re the most populted by short peptides. To tke into ccount frequency shifts tht occur in the PPII conformtion due to peptide-wter hydrogen-bonding, we prtilly optimized the geometry nd clculted frequencies for Al 3 in PPII conformtion surrounded by wter molecules. We clculted the norml modes of Al 3 in both the R-helicl nd PPII conformtions for the nturl bundnce nd the following isotopomers: 13 Cd 18 O substituted t the N-terminus peptide unit, 13 Cd 18 O substituted t the C-terminus peptide unit, N-D substituted t the N-terminus peptide unit, N-D substituted t the C-terminus peptide unit, ND 2 substituted t the N-terminus mide group, simultneous ND 2 substitution nd N-D substitution t the N-terminus peptide unit, nd simultneous ND 2 substitution nd N-D substitution t the C-terminus peptide unit. The hrmonic vibrtionl frequencies were corrected by the previously suggested scling fctor of ,47 We clculted the potentil energy distribution (PED) by using the GAR2PED Gussin output processing progrm written by J. M. L. Mrtin nd C. Vn Alsenoy. 48 To distinguish contributions of the nucler motions of different peptide units to the clculted norml mode composition, we lbeled the internl vibrtionl coordintes (bonds, vlence nd torsion ngles corresponding to stretching, bending nd torsionl vibrtions, respectively, Figure 1). Results nd Discussion Norml Mode Composition Anlysis. Amide I. Our previous experimentl study of the UVRS of the 21-residue AP peptide in pure wter, pure D 2 O, nd H 2 O/D 2 O mixtures concluded tht the mide I vibrtions re coupled in R-helicl AP nd uncoupled in the PPII conformtion. 37 This conclusion is consistent with the results of Hochstrsser s group. 5,24 Our R-helicl Al 3 vibrtionl nlysis demonstrtes two mide I modes, high frequency A symmetry vibrtion (1716 cm -1 ), nd lower frequency E 1 symmetry vibrtion (1702 cm -1 ) (Tble 1). Ech mode contins CO stretching contributions from both peptide units. In contrst, the two mide I modes clculted for the PPII conformtion of Al 3 re essentilly locl vibrtions of the individul CO stretches. These results gree with our experimentl dt, which indicted coupled mide I modes in the R-helicl conformtion but locl mide I modes in the PPII conformtion. Amide II.InD 2 O, N-H deutertion cuses the complex mide II vibrtion to become n lmost pure C-N stretch (mide II ) due to decoupling of N-H bending from C-N stretching. 49,50 The mide II ppers s doublet in N-methylcetmide (NMA) nd AP becuse of Fermi resonnce between the mide II vibrtion nd combintion of the low frequency mide IV (632 cm -1 ) nd skeletl deformtion vibrtion ( 873 cm -1 ). 50 Our theoreticl results for the mide II of R-helicl Al 3 indicte more coupling thn our experimentl studies do. Experimentlly, we did not observe cler frequency shift for the mide II nd mide II bnds in the PPII nd R-helix conformtions of AP upon djcent peptide bond deutertion/ protontion. Unfortuntely, we were unble to completely exclude smll frequency shifts for the mide II bnds due to TABLE 1: Amide I Frequencies nd Norml Mode Compositions of Al 3 in r-helix nd PPII Conformtions conformer ν,cm -1 PED, % R-helix 1702 N-term PU: CO s (51), NC RC b (4), -CN s (4), -C RC s (2), NH inp b (1), -CN pc R b (1) C-term PU: -C O s (27), C R N C b (2), C N s (2), C R CN b (1), C C R s (1), -C C Rb N b (1) 1716 C-term PU: C O s (52), C R N C b (4), -C N s (3), -C C R s (2), -N H inp b (2), C C Rb N b (1), -C NC R b (1) N-term PU: CO s (27), NC RC b (2), -CN s (2), -C RC s (1), -NH inp b (1), C R CN b (1) PPII 1695 N-term PU: CO s (70), NC RC b (6), -CN s (5), -NH 2 scs (4), -C RC s (3), -C O s (3), -NH inp b (2), CN pc R b (2), C R CN b (2), -CC βc R b (1) 1698 C-term PU: C O s (75), -C N s (7), C R N C b (6), CO s (3), -C C R s (3), -N H inp b (2), C C Rb N b (2), C NC R b (1) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch; b, bending; inp b, in-plne bending; scs, scissoring.

3 Peptide Bond Vibrtionl Coupling J. Phys. Chem. B, Vol. 111, No. 16, TABLE 2: Clculted Amide II Frequencies nd Norml Mode Compositions (PED) for Al 3 in r-helicl nd PPII Conformtions conformer ν,cm -1 PED, % R-helix 1480 N-term PU: NH inp b (19), -CN s (10), -CH Rb inp b (5), CH 3b sym def (4), -CO inp b (2), -CH 3 sym def (2), C RC s (1), CO s (1) C-term PU: N H inp b (26), -C N s (12), N C Rb s (4), -C H R inp b (2), NC R s (3), -C O inp b (2), C C R s (1), -CH 3b sym def (1), CH 3b rocking (1) 1495 N-term PU: NH inp b (28), -CN s (15), CO inp b (3), C RC s (2), -CH 3 sym def (1) C-term PU: N H inp b (20), C N s (8), NC R s (4), CH R inp b (4), -N C Rb s (3), CH 3 sym def (2), -CH R inp b (2), C O inp b (1), -C C R s (1), -CH 3b sym def (1), -C O s (1) PPII 1491 N-term PU: NH inp b (39), -CN s (23), C RC s (4), -CO inp b (4), -CH 3 sym def (2), CH R inp b (1), CO s (1), -NH 2 rocking (1) C-term PU: N H inp b (5), NC R s (5), -CH R inp b (4), -C N s (3), CH 3 sym def (2), NC β C R b (1), N C Rb s(1) 1495 C-term PU: N H inp b (44), -C N s (25), N C Rb s (6), -N C Rb s (4), C C R s (4), -CH 3 sym def (2), C R H R inp b (2), -C Rb H Rb inp b (1), -NC R s (1), N C βb C Rb b (1), CH 3b sym def (1), C Rb H Rb outp b (1), -N C pc Rb b (1) N-term PU: -NH inp b (3), CN s (2) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch; b, bending; inp b, in-plne bending; outp b, out-of-plne bending; scs, scissoring. TABLE 3: Clculted AmIII 3 Frequencies nd Norml Mode Compositions of Trilnine conformer ν,cm -1 PED, % R-helix 1222 C-term PU: C N s (18), N H inp b (17), -C C R s (16), C O inp b (7), -CH Rb outp b (6), -N C Rb s (6), C Rb H Rb inp b (4), NC R s (3), CH 3b rocking (2), -NC β C R b (2), CH 3 rocking (2), C NC R b (2), -CH 3 rocking (1), C C β C R b (1), -CH 3 sym def (1), CH 3b rocking (1), CH 3b sym def (1), N C pc Rb b (1), -C R H R outp b (1), N C βb C Rb b (1), C R C β s (1) N-term PU: -NH 2 rocking (2), C RH R outp b (1), -CO p inp b (1) 1247 N-term PU: NH inp b (17), CN s (10), -NH 2 rocking (12), CH R outp b (10), -C RC s (8), CO inp b (4), -CH 3 rocking (2), -C βn pc R b (2), CO s (2), CH 3 rocking (1), CN pc R b (1), C RC β s (1), CH R inp b (1), -CH 3 sym def (1) C-term PU: -C R H R outp b (12), C R H R inp b (6), C Rb H Rb outp b (2), -NC R s (1), -N H inp b (1), CH 3 rocking (1), -C N s (1), -CH Rb inp b (1), CH 3 sym def (1) PPII 1205 C-term PU: C N s (21), N H inp b (16), -N C Rb s (14), N C Rb s (6), OH p* inp b (6), C R H R outp b (6), C R H R inp b (5), CH 3b rocking (4), -C Rb H Rb outp b (4), -C C R s (2), N C βb C Rb b (1), -CH 3 rocking (1), -C NC R b (1), -CN pc R b (1), N C pc Rb b (1), -COp inp b (1), CN s (1), C C Rb N b (1), C Rb C p s (1) N-term PU: -NH 2 rocking (3), NH inp b (1), N pc R s (1) 1227 N-term PU: NH 2 rocking (18), -CN s (16), -NH inp b (13), -CO inp b (7), CN pc R b (6), -N pc R s (3), -C RH R outp b (3), C RC s (2), -CC βc R b (2), -CO s (1), CH 3 rocking (1), CH 3 rocking (1), C βn pc R b (1), CH 3 sym def (1) C-term PU: C R H R outp b (10), N R C R s (5), -C R H R inp b (2), -CH 3 rocking (2), -CH 3 rocking (1), -CH 3 sym def (1), N C Rb s (1), -C NC R b (1), N H inp b (1) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch; b, bending; inp b, in-plne bending; outp b, out-of-plne bending; scs, scissoring. -NH 2 rocking is penultimte group vibrtion contribution. overlp of HOD bending nd rginine side-chin bnds nd the moleculr O 2 stretching vibrtions, which shows spectrl intensity vritions. 37 Tble 2 indictes two different mide II modes for the R-helicl Al 3 conformtion (1480 nd 1495 cm -1 ), which derive from the in- nd out-of-phse coupled vibrtions of both peptide units. These mide II vibrtions contin similr contributions of C-N stretching nd N-H bending of both peptide units. For exmple, the 1495 cm -1 mide II vibrtion contins 28% N-H bending of the N-terminl peptide units nd 20% N-H bending of the C-terminl peptide unit. In contrst, the two mide II vibrtions of Al 3 in the PPII conformtion occur much closer in frequency nd re lmost locl modes (Tble 2). Amide III 3. The mide III spectrl region shows severl bnds tht originte from vibrtions involving C-N, N-C R,C R -C, nd C-C R stretching nd N-H nd C R -Η bending motions. 51 The clssic mide III bnd (specificlly the mide III 3 ) involves CN stretching with in-phse N-H bending, which couples to C R H in-phse bending in the PPII conformtion. This conformtion-dependent coupling mkes this mide III 3 bnd extremely sensitive to peptide secondry structure. 35 In the R-helicl AP, this bnd occurs t 1261 cm -1, nd in the PPII conformtion, the mide III 3 bnd occurs t 1245 cm -1. The D 2 O decoupling of ND bending from CN stretching nd C R H bending upon deutertion results in the disppernce of the mide III 3 bnd, s well s the other mide III region bnds. 49,51,52 Our UVRS comprison between the R-helicl nd PPII bnds of AP spectr in H 2 O/D 2 O mixtures indicted tht the spectr could be modeled s the sum of the deuterted nd protonted species in both the R-helicl nd PPII conformtions. We concluded tht there ws insignificnt coupling between the mide III 3 vibrtions of djcent peptide units. 37 The conclusions from our theoreticl studies re confounded by the fct tht the two mide III 3 vibrtions in Al 3 differ significntly becuse the N-terminl peptide unit mide III 3 vibrtion selectively couples to the penultimte NH 2 rocking motion (Tble 3). The mide III 3 vibrtion is very complicted. In ddition to the tomic motions listed bove, the mide III 3 vibrtion lso hs contributions from C R -C stretching, CH 3 rocking (from the Al methyl side-chin), nd CdO in-plne bending. However, the min contributions re still from C-N

4 4274 J. Phys. Chem. B, Vol. 111, No. 16, 2007 Myshkin et l. TABLE 4: Clculted Amide III 3 Frequencies nd Norml Mode Compositions of ND 2 -Substituted Al 3 conformer ν,cm -1 PED, % R-helix 1218 C-term PU: C N s (14), N H inp b (12), -C C R s (11), C O inp b (6), -N C Rb s (4), -C Rb H Rb outp b (4), -C R H R outp b (4), C Rb H Rb inp b (3), CH 3 rock (3), C NC R b (2), CH 3b rock (1), C C β C R b (1), -NC β C R b (1), -CH 3 sym def (1), CH 3b rock (1), NC R s (1), CH 3b sym def (1), C R H R inp b (1) N-term PU: NH inp b (8), CN s (5), -C RC s (5), -NH 2 scs (3), CO inp b (2), CO s (1), CN pc R b (1) 1232 N-term PU: NH inp b (15), CN s (13), -C RC s (10), CO inp b (5), CN pc R b (2), -NH 2 scs (1), CH 3 rock (1), -NH 2 rock (1), -C βn pc R b (1), CO s (1), -CH 3 rock (1), C RC β s (1), CC βc R b (1), -CH 3 sym def (1) C-term PU: -N H inp b (6), -C N s (5), C C R s (5), -C R H R outp b (5), -NC R s (4), C R H R inp b (4), C Rb H Rb outp b (4), CH 3 rock (2), N C Rb s (2), -C Rb H Rb inp b (2), -C O inp b (2), NC β C R b (1), -CH 3b rock (1), -CH 3b rock (1) PPII 1201 C-term PU: N C R.b s (13), -C N s (13), -N H inp b (8), NC R s (6), -O ph p* inp b (5), -CH 3b rock (3), -CH Rb inp b (3), -C O inp b (2), -CH 3 rock (2), C Rb H Rb outp b (2), -N C βb C Rb b (1), -NC β C R b (1), -C R N C b (1), -C Rb C p s (1), -C C Rb Ν b (1), -N C pc R.b b (1), C p.c βb C Rb b (1) N-terminl PU: -CN s (11), -NH inp b (8), -C RH R inp b (4), -CO inp b (4), -C RH R outp b (1), CN pc R b (1), -NH 2 scs (1), C RC s (1), NH 2 rock (1), CH 3 rock (1) 1212 N-terminl PU: -CN s (12), -NH inp b (7), -CO inp b (4), -C RH R inp b (4), -C RH R outp b (2), CN pc R b (1), -CH 3 sym def (1), CH 3 rock (1), C RC s (1), NH 2 rock (1) C-terminl PU: C N s (9), N H inp b (9), CH R outp b (13), NC R s (9), C O inp b (4), -CH 3 rock (3), -N C Rb s (3), -C Rb H Rb outp b (3), -C NC R b (2), -CH 3 rock (2), -C C R s (2), OH p* inp b (2), CH 3b rock (1), -NC β C R b (1) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch; b, bending; inp b, in-plne; outp b, out-of-plne bending; scs, scissoring. stretching nd N-H bending. The mide III 3 norml modes in both the R-helix nd PPII conformtions of Al 3 ct s locl modes in terms of contributions from C-N stretching nd N-H bending from individul peptide units (Tble 3). The two mide III 3 bnds in the R-helicl conformtion were clculted to occur t 1222 nd 1247 cm -1, with the 25 cm -1 higher frequency bnd corresponding to the vibrtion of the N-terminus peptide unit with contributions from the terminl NH 2 group rocking bending. A similr gp between two mide III 3 frequencies ws clculted for the PPII conformtion where the N-terminl peptide unit vibrtion lso hs contribution from NH 2 rocking. Becuse these two mide III 3 vibrtions differ due to the unique NH 2 rocking contribution from the N-terminl group, it is likely tht this clcultion my not be relevnt to the mide III 3 bonds of the internl peptide unit of peptides, which cnnot include NH 2 rocking. Thus, we ttempted to exmine mide III 3 norml modes in Al 3 isotopomers, which were uncoupled to the terminl NH 2 group motions; we exmined the ND 2 - deuterted derivtive of Al 3. ND 2 -deutertion decreses the frequency difference between the two mide III 3 bnds to 14 cm -1 in the R-helicl conformtion nd to 11 cm -1 in the PPII conformtion (Tble 4). In the ND 2 R-helicl Al 3 derivtive, the higher frequency mide III 3 vibrtion is dominted by the N-terminus peptide unit but lso contins smller contribution of motion from the other peptide unit. The low frequency mide III 3 bnd corresponds minly to C-terminus mide III 3 vibrtion with significnt but smller N-H bending nd C-N stretching contributions from the other peptide unit. The mide III 3 vibrtions (1201 nd 1212 cm -1 ) in the PPII conformtion of ND 2 Al 3 re evidently coupled; both mide III 3 vibrtions involve comprble contributions of CN stretching nd NH bending from ech peptide unit (Tble 4). Our experimentl results concluded little coupling evidenced by insignificnt spectrl frequency shifts upon deutertion of djcent peptide units. Frequency Shifts of the Amide Bnds Due to Coupling. The coupling between locl motions is monitored by the vlue of the coupling force constnts, i.e., the off-digonl elements of the Hessin mtrix. For system with two peptide bonds, the Hessin mtrix is F (φ,φ) ) [ K 1 (φ,φ) C 12 (φ,φ) C 12 (φ,φ) K 2 (φ,φ) ] where K 1 nd K 2 re force constnts of the locl modes nd C 12 is the coupling force constnt between locl modes. Due to the nonzero coupling force constnts, interction between two locl modes results in formtion of two coupled deloclized modes with perturbed frequencies. In the cse of mide I locl mode coupling, two coupled mide I modes of symmetry A nd E 1 re formed. The frequencies of the A nd E 1 modes will occur t higher nd lower frequencies reltive to tht of the unperturbed locl CdO stretches. The A component refers to the symmetricl, in-phse stretching of CdO bonds. The E 1 component origintes from symmetric or out-of-phse stretching motions of CdO bonds. When the trnsition dipole moments of the CdO stretch re perpendiculr to the xis of the peptide bckbone (s in the PPII or β-strnd-like conformtions), the E 1 component will show strong IR bsorbnce nd the A component will be ctive in Rmn but vnish in IR mesurements. For these conformtions, there is difference between the mide I frequency observble in IR nd the mide I frequency observble in Rmn. This frequency difference corresponds to the A-E 1 splitting, which origintes from coupling of the locl CdO stretches. By contrst, in the R-helix conformtion, where the trnsition dipole moment of ech peptide group is lmost prllel to the helix xis, the A component cquires strong IR bsorbnce in ddition to Rmn intensity. Therefore, R-helicl peptides show n mide I bnd of A symmetry, which is observble in both the IR nd Rmn spectr; there will be no frequency difference between the IR nd Rmn observed mide I bnds in this cse. There re few published studies dedicted to the peptide secondry structure determintion from experimentlly mesured A-E 1 splitting between the mide I Rmn nd IR frequencies. 25,53,54 The frequency difference between coupled vibrtions depends upon the mgnitude of the vibrtionl coupling constnt. The lrger the coupling constnt, the stronger the coupling nd the

5 Peptide Bond Vibrtionl Coupling J. Phys. Chem. B, Vol. 111, No. 16, TABLE 5: Clculted Amide I Frequencies (cm -1 ) of Norml Abundnce Al 3 nd Al 3 Isotopomers in r-helicl nd PPII Conformtions R-helix PPII C 13 O 18 -Al l(cdo) ) Å 1699 l(cdo) ) Å C 13 O 18 -Al l(cdo) ) Å 1695 l(cdo) ) Å Al (A) 1698 (C term. PB) 1702 (E 1) 1695 (N term. PB) Frequencies nd CdO bond lengths correspond to indicted PB. TABLE 6: Norml Mode Compositions of Amide I Vibrtions of D 2 N, ND-Isotopomers of Al 3 PU deuterted ν,cm -1 PED, % R-helix N-terminus 1715 C-term PU: C O s (60), C R N C b (5), -C N s (4), -C C R s (2), -N H inp b (2), C C Rb N b b (1), -C NC R b (1) N-term PU: CO s (19), -CN s (2), NC RC b (2), -C RC s (1) 1699 N-term PU: CO s (60), -CN s (5), NC RC b (5), -C RC s (2), -CN pc R b (1) C-term PU: -C O s (19), -C R N C b (2), C N s (2), C R CN b (1), C C R s (1) C-terminus 1713 C-term PU: C O s (43), C R N C b (3), -C N s (3), -C C R. s (2) N-term PU: CO s (37), NC RC b (3), -CN s (3), C RC s (2) 1701 N-term PU: CO s (41), NC RC b (4), -CN s (3), -C RC s (2), -NH inp b (1), -CN pc R b (1) C-term PU: -C O s (37), C N s (3), -C R N C b (3), C C R s (1), -C C Rb N b (1), C NC R b (1), C R CN b (1) PPII N-terminus 1695 C-term PU: C O s (76), -C N s (8), C R N C b (6), -C C R s (2), N C C Rb b (2), C NC R b (1) N-term PU: CO s (3) 1690 N-term PU: CO s (75), NC RC b (7), -CN s (6), -C RC s (3), -ND inp b (2), CN pc R b (1) C-term PU: -C O s (3), C R CN b (2) C-terminus 1699 C-term PU: C O s (78), -C N s (7), C R N C b (7), -C C R s (3), -N D inp b (2), C C Rb N b (2), C NC R b (1) 1685 N-term PU: CO s (79), -CN s (7), NC RC b (7), -C RC s (3), CN pc R b (1), -NH inp b (1) C-term PU: C R CN b (2) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch; b, bending; inp b, in-plne; outp b, out-of-plne bending; scs, scissoring. more the frequencies of coupled bnds re perturbed compred to the frequencies of the locl uncoupled bnds. Therefore, we cn estimte the strength of the mide bnd coupling by monitoring the frequency differences between clculted mide bnds compred to the frequencies of the originl uncoupled locl vibrtions. To obtin these uncoupled frequencies, we clculted the norml modes of vrious Al 3 isotopomers. Amide I. The PED of the R-helicl nturl bundnce Al 3 norml modes shows tht the two clculted mide I bnds (1702 nd 1716 cm -1 ) re coupled modes of A nd E 1 symmetry. We singly substituted C 13 -O 18 t ech of the two Al 3 peptide bonds nd clculted the frequency of the other nturl bundnce peptide bond. In this cse, the locl mide I vibrtions t the crboxyl end occurred t 1712 cm -1 nd t the mine end occurred t 1708 cm -1. The frequencies differ becuse their optimized structures hve slightly different CdO bond lengths (Tble 5). If we ssume reference frequency for the uncoupled locl CdO stretching mode of Al 3 s simple verge (1710 cm -1 ) of the locl mide I frequencies clculted for two Al 3 isotopomers, we conclude tht the coupling interctions in nturl bundnce Al 3 up-shift the high frequency A component by 6 cm -1 nd down-shifts the E 1 component by 8 cm -1 (Tbles 5 nd 10). In contrst, the PPII Al 3 PED shows tht two clculted mide I modes re uncoupled nd their frequencies re lmost equl to the uncoupled mide I frequencies of Al 3 isotopomers. These results re fully consistent with our experimentl dt. Our results re lso consistent with Torii nd Tsumi 17 who theoreticlly showed tht the coupling constnts between djcent mide I vibrtions in the R-helix conformtion re lrger thn those in the β-region (close to tht of PPII conformtion). There re two min mechnisms of vibrtionl coupling: through bond coupling (or mechnicl coupling) nd through spce coupling (or electrosttic coupling). Mechnicl coupling results from the impct of locl tomic motion on the structure of djcent moleculr bonds; electrosttic coupling results from the motion of locl dipolr bonds. The lrge dipole moment of the C-O bond gives rise to significnt electrosttic coupling for the mide I modes in ddition to significnt mechnicl coupling. In contrst, mechnicl coupling domintes the coupling between the mide II nd mide III 3 vibrtions due to the smller dipole moments of the vibrting bonds. Amide I coupling in the R-helix conformtion nd the lck of it in the PPII conformtion result from the different reltive sptil orienttions of the CdO bonds in the R-helix nd PPII conformtions. In the R-helix, the CdO bonds re lmost co-prllel; in the PPII conformtion, they project out t ngles of 120 from one nother. The more they project upon one nother, the lrger

6 4276 J. Phys. Chem. B, Vol. 111, No. 16, 2007 Myshkin et l. TABLE 7: Clculted Amide I, Amide II, nd Amide III 3 Frequencies of Norml Abundnce Al 3 nd Al 3 Isotopomers in PPII nd r-helicl Conformtions mide I mide II mide III 3 deutertion conform N-term. C-term. N-term. C-term. N-term. C-term. none R-helix 1702 out-of-phse 1480 in-phse in-phse 1495 out-of-phse PPII ND 2 R-helix 1702 out-of-phse 1480 in-phse in-phse 1496 out-of-phse PPII in-phse 1212 out-of-phse ND-N term R-helix 1699 out-of-phse ND 1487 ND in-phse PPII ND 1495 ND 1206 ND-C term R-helix 1701 out-of-phse 1489 ND 1245 ND 1713 in phse PPII ND 1226 ND ND 2,ND-N term R-helix 1699 out-of-phse ND 1487 ND in-phse PPII ND 1495 ND 1206 ND 2,ND-C term R-helix 1701 out-of-phse 1489 ND 1227 ND 1713 in-phse PPII ND 1207 ND TABLE 8: Norml Mode Compositions of Amide II Vibrtions of D 2 N, ND-Isotopomers of Al 3 deuterted PU ν,cm -1 PED, % R-helix N-terminus 1487 C-term PU: N H inp b (47), -C N s (20), -C Rb H Rb inp b (9), N C Rb s (6), CH 3b sym def (3), -C O inp b (3), C C R. s (2), -CH 3 sym def (2), -CH 3b sym def (1), CH 3b rocking (1), C O s (1) C-terminus 1489 N-term PU: NH inp b (47), -CN s (25), -CO inp b (4), -C RC s (3), -CH 3 sym def (2), CO s (1) C-term PU: NC R s (7), C R H R inp b (4), CH 3 sym def (2), C R H R outp b (1), NC β C R b (1) PPII N-terminus 1495 C-term PU: N H inp b (49), -C N s (28), N C R.b s (7), -C O inp b (5), C C R s (4), -C Rb H Rb inp b (1), N C βb C Rb b (1), -CH 3 sym def (1), CH 3b sym def (1), C Rb H Rb outp b (1), C R H R inp b (1), -N C pc Rb b (1) C-terminus 1491 N-term PU: NH inp b (43), -CN s (25), -CO inp b (4), C RC s (4), -CH3 sym def (1), CO s (1), C RH R inp b (1) C-term PU: NC R s (6), -C R H R inp b (6), CH 3 sym def (3), NC β C R b (1), -CH 3 sym def (1) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch, b, bending; inp b, in-plne; outp b, out-of-plne bending; scs, scissoring. TABLE 9: Norml Mode Compositions of Loclized Amide III 3 Vibrtions of D 2 N, ND-Isotopomers of Al 3 deuterted PU ν,cm -1 PED, % R-helix N-terminus 1221 C-term PU: C N s (19), N H inp b (18), -C C R s (16), C O inp b (8), -C Rb H Rb outp b (7), -N C Rb s (6), C Rb H Rb inp b (4), CH 3b rock (2), -NC β C R b (2), C NC R b (2), NC R s (2), -CH 3 rock (2), CH 3 rock (2), -CH 3 sym def (1), CH 3 sym def (1), CH 3b rock (1), CH 3b sym def (1), N C pc Rb b (1), C R C β s (1), N C βb C Rb b (1), -C po p inp b (1), C C Rb N b (1) C-terminus 1227 N-term PU: NH inp b (24), CN s (19), -C RC s (16), -CO inp b (8), CN pc R b (3), -ND 2 sciss (2), -CO s (1), CH 3 rock (1), -ND 2 rock (1), C RC β s (1), -C βn pc R b (1), -CH 3 rock (1), CC βc R b (1), -CH 3 sym def (1) C-term PU: C R H R outp b (10), NC R s (2), C R H R inp b (4), CH 3 rock (1), CH 3 rock (1), CH 3 sym def (1) PPII N-terminus 1206 C-term PU: C N s (23), N H inp b (17), -N C Rb s (13), C R H R outp b (10), C O inp b (7), OH p* inp b (6), -C Rb H Rb outp b (4), CH 3b rock (4), C R H R inp b (3), -CH 3 rock (2), -C C R s (2), -C NC R b (1), N C βb C Rb b (1), N C pc Rb b (1), -C po p inp b (1) N-term PU: NC RC b (1) C-terminus 1207 N-term PU: CN s (24), NH inp b (14), CO inp b (8), C RH R inp b (7), C RH R outp b (4), -CN pc R b (2), -C RC s (1), -CH 3 rock (1), -ND 2 rock (1) C-term PU: -NC R s (16), CH 3 rock (5), -C R H R outp b (4), NC β C R b (2), -N C R s (1), C R N C b (1), C R CN b (1), C NC R b (1), CH 3 sym def (1), C R H R inp b (1), C C R s (1), CH 3 rock (1) Frequencies re scled by fctor Abbrevitions: PU, peptide unit; s, stretch; b, bending; inp b, in-plne; outp b, out-of-plne bending; scs, scissoring. will be the dipole-dipole interctions. In ddition, the closer the distnce between CdO bonds, the stronger the dipoledipole interctions. An R-helix conformtion hs smller pitch thn the more extended PPII structure; the CdO nd N-H bonds of neighboring peptide bonds re closer to ech other compred to PPII or β-strnd conformtions. Deutertion of the peptide bond NH nd penultimte mino group does not ffect the coupled mide I frequencies nd

7 Peptide Bond Vibrtionl Coupling J. Phys. Chem. B, Vol. 111, No. 16, TABLE 10: Vibrtionl Coupling Frequency Shifts of Amide Bnds conformtion R-helix PPII Δν mide I, cm -1 Δν mide II, Δν mide III3, cm -1 cm -1 in-phse out-of-phse in-phse no coupling no coupling -5 out-of-phse occurs occurs 6 TABLE 11: Mesured PPII AP Frequencies, Clculted Frequencies of PPII Al 3 in Vcuum nd in Al 3 -Wter Complex, nd Clculted Hydrogen-Bonding Frequency Shifts ν mide I,cm -1 ν mide II,cm -1 ν mide III,cm -1 l 3 vcuum l 3 4H 2O Δν HB PPII AP Δν HB ) ν Al3 4W - ν Al3 gs. norml mode compositions in the R-helicl conformtion compred to the mide I frequencies of norml bundnce Al 3. In the PPII conformtion, the mide I frequencies slightly shift upon deutertion (Tbles 6 nd 7). In the norml bundnce PPII Al 3 conformtion, these modes re minly CdO stretching vibrtions of ech individul peptide unit contining minor contributions (2%) from N-H bending. In ddition to the N-H bending, the locl mide I vibrtion of the N-terminl peptide unit hs contribution from NH 2 scissoring (4%) (Tble 1). Deutertion of the NH 2 group or N-H bond elimintes contributions of N-H bending nd NH 2 scissoring vibrtions from the norml mode compositions, which results in slight frequency shifts (4-10 cm -1 ) of the mide I frequencies (Tble 7). Amide II. No vibrtionl coupling occurs between mide II bnds in the PPII conformtion of Al 3. These mide II frequencies re lmost equl to the locl frequencies (1496 nd 1491 cm -1 ) of isotopiclly substituted Al 3 (Tbles 7 nd 8). The difference between two frequencies of regulr Al 3 (4 cm -1 ) nd two locl frequencies of the Al 3 -isotopomers (5 cm -1 ) origintes from slight difference between the C-N bond lengths of the two peptide bonds nd is unrelted to ny coupling. We clculte tht coupling between the mide II bnds of R-helicl Al 3 results in formtion of two deloclized vibrtions which re up- nd down-shifted by 8 cm -1 compred to the uncoupled loclized mide II vibrtions of the ND-substituted Al 3 (Tbles 7 nd 10). However, for ND-deuterted R-helicl Al 3, we lso clculte tht the uncoupled mide II vibrtion should occur round cm -1 (excluding frequency Figure 2. Wter bridges in PPII structure. shift due to hydrogen bonding). This differs from the coupled mide II bnd frequencies clculted t 1480 nd 1496 cm -1. These results indicte tht we should observe more often the nrrow mide II bnd in prtilly deuterted peptides thn those fully protonted bnds in pure wter. It is possible tht this shift ws obscured by the overlp of the mide II bnd with n rginine bnd nd the moleculr oxygen stretching bnd. Amide III 3. For R-helicl NH 2, NH-deuterted Al 3 isotopomers, our clcultions show 6cm -1 frequency difference between locl mide III 3 bnds (1221 nd 1227 cm -1 )ofthe N- nd C-terminl peptide bonds. In ND 2 -substituted R-helicl Al 3, the mide III 3 vibrtions re minly loclized. The higher frequency mide III 3 bnd (1232 cm -1 ) is dominted by the motion of the N-terminl peptide unit with only minor contribution from the C-terminl peptide unit (Tble 4); the low frequency mide III 3 vibrtion (1218 cm -1 ) contins mjor contribution from the C-terminus peptide unit. The locl mide III 3 vibrtions of ND, ND 2 - deuterted Al 3 isotopomers occur t 1227 cm -1 (N-terminus vibrtion) nd t 1221 cm -1 (C-terminus vibrtion) (Tble 9). Vibrtionl coupling with the other peptide unit up-shifts this bnd by 5 cm -1. Consequently, mide III 3 bnds re 5 up- nd 3cm -1 down-shifted (Tble 10). We conclude tht R-helicl mide III 3 bnd coupling is smll becuse the frequencies shift little from the frequencies of locl vibrtions. However, the norml mode compositions of these two clculted mide III 3 vibrtions indicte some contributions from the djcent peptide unit. The PPII conformtion N- nd C-terminus mide III 3 vibrtions of the ND 2, ND-substituted Al 3 isotopomers hve lmost identicl frequencies (1206, 1207 cm -1 ). Therefore, in nturl bundnce Al 3, the symmetricl component (1201 cm -1 )of mide III 3 is down-shifted by 5 cm -1 nd the symmetricl TABLE 12: Amide Frequencies of AP (Mesured) nd Al 3 (Clculted) in PPII Conformtion in Gs-Phse nd in Peptide-Wter Complex mide I, cm -1 mide II, cm -1 mide III 3,cm -1 N-term. C-term. N-term. C-term. in-phse out-of-phse PPII-l 3, clc 1690 (1648) 1699 (1657) 1491 (1554) 1496 (1558) 1201 (1245) 1212 (1256) PPII-AP in H 2O, experimentl PPII-AP in H 2O/D 2O experimentl PPII-AP in H 2O/D 2O modeled spectr without coupling Vlues in prentheses include Δυ HB (see Tble 11).

8 4278 J. Phys. Chem. B, Vol. 111, No. 16, 2007 Myshkin et l. TABLE 13: Mesured Frequencies of Gs-Phse nd Liquid NMA, Clculted Hydrogen-Bonding Frequency Shifts (Δν HB ), Clculted Frequencies of r-helicl Al 3 in Vcuum, Frequencies of the r-helicl Al 3 Including Δν HB, nd Mesured Frequencies of r-helicl AP ν mide I,cm -1 ν mide II,cm -1 ν mide III3,cm -1 NMA, gs phse mesured NMA, net liquid mesured b Δν HB R-Al 3, gs phse clcd R-Al 3 + Δν R-AP, experimentl Kubelk, J.; Keiderling, T. J. Phys. Chem. A 2001, b Δν HB ) ν NMA liquid - ν NMA gs. component (1212 cm -1 ) is up-shifted by 6 cm -1 due to vibrtionl coupling (Tbles 4 nd 10). Our clcultions show wek coupling of the PPII mide III 3 bnds. This PPII mide III 3 coupling cn be explined by its norml mode compositions. Besides the C-N stretch nd N-H bending, which re coupled in-phse with C R -H bending, the PPII mide III 3 modes contin contributions from the N-C R stretching vibrtion (Tble 4). The N-C R bond bridges djcent peptide units. This stretching motion fcilittes coupling with the C R -H bending motions. The C R -H bending cn efficiently couple with N-H bending of the djcent peptide unit. The contribution from the N-C R stretch fcilittes delocliztion of the PPII mide III 3 bnd. The mide III 3 vibrtion of R-helicl Al 3 does not include the N-C R stretching. Insted, this norml mode contins C-C R stretching. Frequency Shifts of the Amide Bnds Due to Hydrogen Bonding. Our clculted mide frequencies differ from the experimentlly mesured frequencies becuse we hve not tken into ccount the effects of hydrogen bonding. The hydrogenbonding ptterns differ in the R-helix nd PPII conformtions. Hydrogen bonding in the PPII conformtion involves hydrogen bonding to wter. Hydrogen bonding in the R-helix conformtion involves peptide bond-peptide bond hydrogen bonding. Hydrogen-Bonding Shifts in PPII Conformtion. To estimte the effects of the hydrogen-bonding differences on the frequencies of the mide vibrtions we compred mide I, mide II, nd mide III 3 frequencies clculted for the PPII Al 3 in vcuum to the Al 3 -wter complex. Sreerm et l. 55 studied the network of wter molecules involved in hydrogen bonding to the bckbone of polylnine in β-strnd nd PPII conformtions by moleculr dynmics simultions. They nlyzed popultions of different types of hydrogen-bonding bridges. For the PPII conformtion, they found tht bridge of two wter molecules connecting the i-th CdO nd (i + 2)-th N-H bonds ws the most populted. We clculted the frequencies of n Al 3 -wter complex in the PPII conformtion for this rrngement of wter molecules (see Figure 2). We included four wter molecules, which mde two wter bridges: one connects the first residue CdO bond with the third residue N-H bond nd the other connects the remining N-H nd CdO groups in the second residue (Figure 2). This hydrogen-bonding network down-shifts the mide I frequency of Al 3 by 42 cm -1 nd up-shifts the mide II nd mide III 3 bnds by 63 nd 44 cm -1, respectively (Tble 11). Overll, the mide frequencies clculted for the Al 3 -wter complex gree well with the experimentlly mesured frequencies of PPII AP (Tble 12). Hydrogen-Bonding Shifts in R-Helicl Conformtion. Theoreticl simultion of the intermoleculr hydrogen bonding in the R-helix conformtion is more complicted. We estimted the R-helix hydrogen-bonding frequency shifts from difference between UVRR mide bnd frequencies of the gs phse 56 nd liquid stte 35 of N-methylcetmide (NMA) (Tble 13). The frequency of the mide I bnd decreses by 63 cm -1 in liquid NMA, compred to the gs stte, nd the mide II nd mide III 3 frequencies increse by 60 nd 43 cm -1, respectively. We pplied these frequency shifts to correct the clculted frequencies of vcuum R-l 3. This correction brings clculted Al 3 frequencies into good greement with the mesured frequencies of R-helicl AP (Tble 14). Conclusion Our clcultions hve demonstrted vibrtionl coupling between djcent peptide units of the mide I nd mide II modes in the R-helicl conformtion where these crbonyl bonds re closest to ech other nd their projection ngles re smllest. This coupling decreses in the PPII conformtion, becuse the structure is more extended nd the projection ngle increses. The fvorble orienttion of the CdO bonds in the R-helix conformtion fcilittes trnsitionl dipole coupling. Therefore, coupling of the mide I bnds is much lrger thn coupling between the mide II bnds. Coupling interctions between mide III 3 bnds is less thn tht of the mide I nd mide II vibrtions. The mide III 3 bnds cn be treted s locl vibrtions of independently Rmn scttering peptide bonds. The clculted mide III 3 frequencies re not significntly perturbed compred to the frequencies of locl mide III 3 modes even though our clcultions indicte tht their norml mode compositions contin minor contributions from the djcent peptide units. Acknowledgment. We grtefully cknowledge Alexnder Mikhonin for useful discussions. This work ws supported by NIH grnt GM8RO1EB TABLE 14: Mesured nd Clculted Frequencies of AP nd Al 3 in r-helicl Conformtions mide I, cm -1 mide II, cm -1 mide III 3,cm -1 in-phse out-of-phse in-phse out-of-phse in-phse out-of-phse R-Al 3, clcd 1716 (1653) 1702 (1639) 1480 (1539) 1496 (1555) 1218 (1261) 1232 (1275) R-AP in H 2O, experimentl R-AP in H 2O/D 2O, experimentl R-AP in H 2O/D 2O modeled spectr without coupling Vlues in prenthesis include Δν HB (see Tble 11).

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