Improved Theoretical π-π* Absorption and Circular Dichroic Spectra of HelicalPolypeptides Using New Polarizabilities of Atoms and NC′O Chromophores

Kimberly A. Bode and Jon Applequist*Department of Biochemistry and Biophysics, Iowa State UniVersity, Ames, Iowa 50011

ReceiVed: July 16, 1996X

Polarizability andπ-π* transition parameters for the amide NC′O chromophore are reoptimized from opticalproperties of amides and peptides using the dipole interaction model and updated atom polarizabilities. Theparameters differ somewhat from those of a similar optimization in 1979 due to the inclusion of the newatom values and additional experimental target data. The effects of shifting the NC′O center within a small“optimal” neighborhood of the NC′ bond center are examined. The new parameters are used to calculateπ-π* absorption and circular dichroic spectra of several helical polypeptide structures, including theR-helix,the parallel and antiparallelâ-sheets, the 310-helix, and the poly(proline) I and II helices. The results are ina form that permits estimation of properties for any choice of NC′O center within the optimal neighborhood.New findings include the following: (i) the predicted CD intensities of the undistorted parallel and antiparallelâ-sheets are sensitive to the choice of NC′O center and are comparable to experiment for suitable choices ofthat center; (ii) the CD spectrum of the poly(proline) II helix agrees best with experiment when the prolinering conformation is near the predicted energy minimum, a result which is more reasonable than the higherenergy conformations predicted previously with the 1979 parameters; and (iii) the predicted CD spectrum forthe right-handed 310-helix is consistent with the observed spectrum for a decapeptide believed to be in thisform. The predicted spectra of theR-helix and the poly(proline) I helix show small improvements overprevious calculations in the agreement with experiment.

Introduction

Among physical methods for studying molecular structures,electronic circular dichroism (CD) stands out as a property thatis easy to measure yet remarkably difficult to predict theoreti-cally. In particular, the CD spectra of polypeptides and proteinsare highly sensitive to conformation, and a large body ofempirical correlation has been established to identify conforma-tions from observed spectra. The empirical approach is limited,however, because the correlations require measurements of CDon samples whose structures are known by independent methods.In principle, the theory of interaction of light with matter shouldprovide a general basis for relating CD spectra to molecularstructures without independent knowledge of conformations orabsolute configurations. Research on the theory as it appliesto polypeptides has been one of the most active areas in opticalactivity theory for over 40 years. The present status of thetheory can be described as partially successful in providing aconnection between spectra and structure, though the extremesensitivity of the predictions to molecular details that hasplagued optical activity theorists for the past century is still alimiting factor. Recent reviews by Woody1,2 summarize thecurrent status of studies from many laboratories.The purpose of this paper is to report new theoretical results

on theπ-π* absorption and CD spectra of several major helicalpolypeptide structures. The new results are based on reopti-mized polarizabilities of the nonchromophoric atoms3 and theNC′O chromophore. We explore in particular the sensitivityof predictions to the polarizability center of the NC′O group, aparameter that is not easily established by any empirical ortheoretical method. We wish to learn whether a self-consistentset of polarizability parameters is capable of accounting for allof the observed spectra for the helical structures and thus presenta broad overview of the current status of our model. For

particular polypeptide structures we address the followingquestions that have not been answered in previous work: (i)Can the relatively large CD intensities observed inâ-sheetstructures be accounted for by a model with an undistortedplanar lattice? (ii) Is the highly nonconservative CD spectrumof poly(proline) II consistent with the proline ring structuresthat have been proposed on energetic grounds? (iii) Is thepredicted spectrum for the unusual 310-helix consistent withrecent experimental data for this structure? We make com-parisons between experiment and theory wherever possible forboth absorption and CD spectra in the region of theπ-π* band,as both spectra show conformational effects and both shouldbe consistent with the same model.The theoretical model adopted in this study is the dipole

interaction model, which predicts molecular properties from theknown electric dipole polarizabilities of the atoms or functionalgroups making up the molecule, using classical formalism tocalculate the response of a molecule to a light wave from theresponses of the atoms and functional groups to the local fieldswithin the molecule. In a series of earlier studies4-12 the modelwas used to calculate the ultravioletπ-π* absorption and CDspectra of several major peptide structures, using a consistentset of parameters that had been optimized in the 1970s to fitexperimental data on small organic molecules. For the peptidesthe agreement between theory and experiment was good forthe most part. A particular virtue of the model, noted in thesestudies, is that it reproduces the highly nonconservative CDspectra observed for several major peptide structures. Thepresent work updates these studies by using the reoptimizedatom polarizabilities of the accompanying paper.3 This requiresa reoptimization of the polarizability parameters of the NC′Ochromophore to be consistent with the new atom polarizabilities.The question raised above regarding the CD intensity

observed forâ-sheets prompted us in this study to undertake asystematic exploration of the sensitivity of predicted spectra toX Abstract published inAdVance ACS Abstracts,November 1, 1996.

17825J. Phys. Chem.1996,100,17825-17834

S0022-3654(96)02120-X CCC: $12.00 © 1996 American Chemical Society

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the location of the NC′O polarizability center. It has beenpointed out by Snir et al.13 and by Woody14 that the CD intensityfor the amide chromophore inâ-sheets is sensitive to thepolarizability location because the helix axis passes through theNC′O group near the NC′ bond center. It was pointed out tous by Dr. Robert Woody that the unrealistically small CDintensities previously predicted8 by our model forâ-sheets couldbe due to the fact that we placed the NC′O center at the NC′bond midpoint. We will show that very small displacementsof the NC′O center from the NC′ bond midpoint produce largechanges in the CD intensity ofâ-sheets, while having little effecton the CD spectra of other major peptide structures when usinga set of parameters that are optimized in a self-consistent way.

Theory

The dipole interaction model considers units made up ofindividual atoms or groups of atoms to interact by mutallyinduced dipole moments when in the presence of an electricfield.15-17 The induced dipole moments depend on the polar-izability of each unit, and a molecular polarizability may bedetermined and various optical properties calculated. Atomsare assumed to have isotropic polarizabilities while chro-mophoric groups such as the NC′O group in amides and peptidesare considered to have anisotropic polarizabilities consisting ofdispersive contributions from electronic transitions in the spectralrange of interest and nondispersive contributions from higherenergy transitions. The inputs required for the calculation arethe coordinates of the atomic nuclei and chromophore centersand the polarizability parameters of all atoms and chromophores.Theπ-π* transition is modeled as a harmonic oscillator with

a Lorentzian dependence on wavenumberνj while all higherenergy transitions make up the nondispersive core polarizabilityrA of the NC′O group. The total polarizabilityrA of the NC′Ogroup is the sum of these contributions:

whereD0 is the dipole strength,u0 is the transition momentunit vector rotated from the NC′ bond by the angleθ0 shownin Figure 1,νj0 is the natural frequency in wavenumbers, andΓis the half-peak bandwidth of theπ-π* transition. The dipoleinteraction model makes use of a normal mode analysis18 inwhich the direction and relative magnitude of electronicoscillation in each unit are given by eigenvectorst(k), and thewavenumbers of oscillationνjk are determined fork ) 1 ... q,whereq is the number of dispersive oscillators.Theoretical amide optical properties for visible light (mean

polarizabilityRj , optical anisotropy|δ|, and molar Kerr constant[K]) are calculated from the polarizability tensor as previouslydescribed.3,19 Peptide spectral properties considered in this study

are maximum absorption wavelengthλmax, band splitting∆,mean oscillator strengthfh, and ratio of oscillator strengthsf|/f⊥,where subscripts|| and⊥ indicate values for light polarizedparallel and perpendicular, respectively, to the helix axis. Werelate these peptide properties to the calculated normal modeproperties as follows:

The values forλmax and∆ are averages overq normal modesweighted by normal mode dipole strengthDk or its parallel andperpendicular componentsDk| andDk⊥. The latter are uncon-ventional quantities, used in our normal mode formalism,defined in terms of the normal mode electric dipole momentµ(k) ) ∑istis

(k)uis by Dk ) [µ(k)]2, Dk| ) [µ|(k)]2, and Dk⊥ )

[µ⊥(k)]2. Conventional oscillator strength is converted from

dipole strength by the factor4 (4meπ2c2/3e2) whereme, c, andeare the electron mass, speed of light, and electron charge,respectively. A normal mode magnetic moment ism(k) )∑istis

(k)r i × uis, wherer i is the Cartesian position vector of uniti. Normal mode rotational strength isRk ) m(k)‚µ(k). The molarabsorption coefficientε and circular dichroism∆ε, both on aresidue molar basis, are calculated by the following equations4

assuming a medium with refractive index of unity:

whereNA is Avogadro’s number andp is the number of peptideresidues, which is equal toq in the present treatment since thereis one dispersive oscillator per residue. The oscillator strengthsof eqs 4-6 are “per residue”. Likewise, rotational strengthsreported here are given in debye‚bohr magnetons (D‚µB) perresidue.4

The small amides contain a single NC′O chromophore, sothe above treatment yields a single normal mode at wavelengthλ1 with oscillator strengthf1 and transition moment angleθ1with respect to thex axis in Figure 1. The polarizabilities ofthe small amides are obtained as a sum of a dispersive termand a nondispersive term of the form of eq 1. The amide

Figure 1. NC′O group and parameters. The NC′ bond center is locatedat the origin of the coordinate system. The ellipse represents the NC′Opolarizability, which is centered at (∆x,∆y). φ and θ0 are the polarangles of theRA,1 axis and theπ-π* transition moment, respectively.

rA ) rA + D0u0u0(νj02 - νj2 + iΓνj)-1 (1)

λmax) [∑k)1

q

νjk2Dk/∑

k)1

q

Dk]-1/2 (2)

∆ ) ⟨νj⊥2⟩1/2 - ⟨νj|

2⟩1/2

) [∑k)1

q

νjk2Dk⊥/∑

k)1

q

Dk⊥]1/2 - [∑

k)1

q

νjk2Dk|/∑

k)1

q

Dk|]1/2 (3)

fh ) (4meπ2c2/3e2q)∑

k)1

q

Dk (4)

f⊥ ) (4meπ2c2/3e2q)∑

k)1

q

Dk⊥ (5)

f| ) (4meπ2c2/3e2q)∑

k)1

q

Dk| (6)

ε ) (8π2νj2NAΓ/6909p)∑k)1

q

Dk/[(νjk2 - νj2)2 + Γ2νj2] (7)

∆ε ) (32π3νj3NAΓ/6909p)∑k)1

q

Rk/[(νjk2 - νj2)2 + Γ2νj2] (8)

17826 J. Phys. Chem., Vol. 100, No. 45, 1996 Bode and Applequist

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properties in visible light are obtained from the real part of thepolarizability at the sodium D line (νj ) 16 969 cm-1).

Methods

The NC′O parameters were optimized by minimization of aê2 error function between theoretical and experimental propertiesusing the Levenberg-Marquardt method of nonlinear optimiza-tion.20 The ê2 error function is

whereσi is the weighting factor for quantityYi anda is the setof parameters to be optimized. The values ofσi are not wellestablished experimentally, and we have chosen reasonablerelative values to obtain a reasonable overall fit. For smallamides theσi were assigned as follows: 1% inRj andλ1; 3% in|δ|, [K], θ1, andf1. For peptides the values assigned were 1%in λmax, 5% in∆, and 7% infh and f|/f⊥.The optimization was carried out in the following steps, which

are essentially similar to those of our 1979 study4,17with someadditions to the experimental target data.Step 1 (Parameter SetG). In this step the polarizability

tensor of the NC′O group in small amides is optimized, treatingthe group as a single point and the remaining atoms of eachamide as isotropic points. For the polarizability in visible lightthe experimental target data (Rj , |δ|, [K]) are the same as thoseof the accompanying paper,3 where the NC′O group was treatedas three isotropic points. Simultaneously, that part of the NC′Opolarizability associated with the NC′O π-π* transition near190 nm is found by fitting ultraviolet spectral data on smallamides (λ1, f1, θ1).Step 2 (Parameter SetH). In this step theπ-π* transition

parameters (f0, λ0, θ0) were optimized to fit the absorptionspectral data of theR-helix (λmax, ∆, fh, f|/f⊥), while keepingrA

from setG. Here we assume that the core polarizability of theNC′O group is transferable between small amides in nonpolarsolvents and peptides in the polar environment of theR-helix,while the π-π* transition parameters do not appear to betransferable.Step 3 (Parameter SetJ). In this step theπ-π* transition

parameters (f0, λ0) were optimized to fit the absorption spectraldata of poly(proline) form II (λmax, fh), while keepingrA fromsetG and a fixed value ofθ0 ) 20°, which was within therange of the values in setG.Amide structures from our previous account3 were used in

this study, and peptide structures were generated as describedby Applequist.5,6 Proline side chain atom coordinates werecreated using the structural data given by Thomasson andApplequist.21 Standard deviations of the parametersa wereestimated from the Hessian matrix ofê2 as described else-where.22

The optimizations incorporated updated polarizabilities of thenonchromophoric atoms described in the accompanying paper.3

Several attempts were made to treat the coordinates of theNC′O tensor center as optimization variables. It is significantthat the optimum was always found in a region within 0.25 Åfrom the NC′ bond center, but the standard deviations of thesequantities were always relatively large (ca. 0.1-0.2 Å), whichprecludes a precise determination of the optimum. Instead, weadopted the following procedure for a systematic examinationof the effect of small displacements of the NC′O center oncalculated properties. Optimizations of parameters were carriedout at three assumed positions (∆x, ∆y) of the NC′O center inthe coordinate frame of Figure 1. Those positions, in angstroms,

are (0.0, 0.0), (0.1, 0.0), and (0.0, 0.1). In the symbols forparameter sets (G, H, J) these positions are designated bysubscripts 0,x, y, respectively, indicating the axis of displace-ment from the NC′ bond center. The following considerationillustrates the way the various optimizations may be used. LetF(∆x,∆y) be a quantity which depends on the choice of theNC′O center.Fmay be any of the molecular optical properties,or it may be any of the polarizability parameters that would beoptimized with the particular choice of center. Then, forarbitrary small displacements (∆x,∆y), we have

where

We have confirmed the accuracy of this approximation for CDspectra within the range of displacements of the order of 0.1Å.Computations were performed on a DEC 3000/300L worksta-

tion using double-precision Fortran programs.Experimental spectra shown in the figures were obtained by

scanning the published graphs using Arc software in the GISSupport and Research Facility, Iowa State University.

Results

Our approach is to optimize NC′O parameters as fully aspossible by fitting optical measurements on simple amides.Minor adjustments are then made to fit polypeptide absorptionspectra, as described in the Methods section.Optimized NC′O parameters are listed in Tables 1-3 along

with the 1979 values for comparison. For setG the principalcomponents of both the total polarizability and core polariz-

TABLE 1: NC ′O Parameter Set G Optimized To Fit Dataon Simple Amides

parameter Gy Gx G0 1979

(∆x, ∆y) (Å) (0.0, 0.1) (0.1, 0.0) (0.0, 0.0) (0.0, 0.0)RA,1 (Å3) 3.293( 0.165 3.272( 0.181 2.947( 0.158 2.50( 0.24RA,2 (Å3) 1.288( 0.100 1.303( 0.110 1.304( 0.107 0.89( 0.34RA,3 (Å3) 3.592( 0.765 3.535( 0.829 3.335( 0.835 2.58( 1.52φ (deg) 45.0( 2.6 45.2( 2.8 45.8( 3.2 41.3( 5.4RA,1 (Å3) 2.744 2.716 2.452 1.94RA,2 (Å3) 1.137 1.144 1.127 0.76RA,3 (Å3) 3.592 3.535 3.335 2.58φ (deg) 54.2 55.0 57.4 52.3f0 0.099( 0.022 0.100( 0.024 0.096( 0.023 0.098( 0.026λ0 (nm) 173.8( 7.7 174.3( 8.2 173.1( 8.1 172.2( 16θ0 (deg) 21.7( 4.4 21.7( 4.5 20.4( 4.8 21.5( 14

TABLE 2: NC ′O Parameter Set H Optimized to FitrR-Helix Absorption Spectrum Using rA, O from Set G

parameter Hy Hx H0 1979

(∆x, ∆y) (Å) (0.0, 0.1) (0.1, 0.0) (0.0, 0.0) (0.0, 0.0)f0 0.149( 0.040 0.167( 0.045 0.157( 0.042 0.196λ0 (nm) 173.6( 10.1 172.9( 9.9 172.0( 10.0 170.3θ0 (deg) 9.3( 3.0 11.6( 2.6 10.9( 2.8 21.5

TABLE 3: NC ′O Parameter SetJ Optimized To Fitpoly(Pro) II Absorption Spectrum Using rA, O from Set Gand a Fixed Value for θ0

parameter Jy Jx J0 1979

(∆x, ∆y) (Å) (0.0, 0.1) (0.1, 0.0) (0.0, 0.0) (0.0, 0.0)f0 0.165 0.158 0.152 0.196λ0 (nm) 177.7 178.4 176.7 170.3θ0 (deg) 20.0 20.0 20.0 21.5

F(∆x, ∆y) ) F(0, 0)+ (∂F/∂x)y∆x+ (∂F/∂y)x∆y (10)

(∂F/∂x)y ) [F(0.1, 0)- F(0, 0)]/0.1 (11)

(∂F/∂y)x ) [F(0, 0.1)- F(0, 0)]/0.1 (12)

ê2 ) ∑i

[Yi,expt- Yi,theo(a)]2/σi

2 (9)

Spectra of Helical Polypeptides J. Phys. Chem., Vol. 100, No. 45, 199617827

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ability are larger in the present work, a consequence of therevised nonchromophoric atom polarizabilities, the displacementof the NC′O center, and the inclusion of more amide data inthe optimization. However, the discrepancies are comparableto the ranges of the standard deviations. The standard deviationsare mostly smaller in the present optimization, indicating thatthe parameters are more precisely determined and probably morereliable. For setH the most notable differences are thesomewhat smallerf0 and substantially smallerθ0 values in thepresent work. SetJ differs from setH primarily in the largerλ0 andθ0 values, arising from the fact that setH does not givea suitable absorption spectrum for poly(proline) II.Table 4 gives the rms deviations between theory and

experiment for all compounds in this study using all of thepresent parameter sets as well as the 1979 parameters appliedto the same experimental data as used in this work.The calculations for various molecules are described in the

following.Small Amides. Tables 5-7 show the calculated properties

of amides using parameter setGy, including comparisons withthe experimental values used as target data in the optimization.Results for setGy differ only slightly from those for the otherchoices of NC′O center, so it is unnecessary to show resultsfor all sets. However, results for they displacement are ofparticular interest in connection with the results given belowfor peptide CD spectra. In comparison with the 1979 param-eters, the most notable distinctions in Table 4 are someimprovement in the fit toRj and a somewhat poorer fit to [K].Interestingly, the fit toRj and [K] is comparable to that obtainedby treating the NC′O group as three isotropic atoms.3 Thecalculated|δ| values forN-methylacetamide andN,N-dimethyl-acetamide (the two amides for which experimental data areavailable) are farther from the experimental values here than inthe isotropic atom study, though the overall predictions ofanisotropy inherent in the Kerr constant data do not indicate asuperiority of one treatment over the other.Molecular polarizability components for amides and halo-

amides calculated with the present parameters are given inTables 5 and 6. Principal polarizability components in Table5 are defined such thatR1 > R2, andR3 is perpendicular (ornearly so) to the NC′O plane. The angleψ is the counterclock-wise rotation from the NC′ bond to the projection of theR1

axis onto the NC′O plane. The conformation of the CX3 groupin acetamides was chosen so that one dihedral angleθ(O,C′,C,X)is equal to 90°. The xy plane is not a plane of molecularsymmetry in this conformation; hence, theR1 andR2 axes donot necessarily lie in that plane. For completeness the full

molecular polarizability tensors for haloacetamides in the amidecoordinate system are given in Table 6. Treatment of the NC′Ogroup as a single unit yields molecular tensors which, in somecases, shift polarizability out of the amide plane into theR3

component, compared to polarizability components obtained forthe three-atom model.3 The direction of theR1 componentpredicted by both treatments is the same within 20° for all

TABLE 4: Root-Mean-Square Deviations (%) betweenExperimental Properties and Theoretical PropertiesCalculated with Parameter Sets at Displacementsy, x, 0

molecule property y x 0 1979a

amidesb Rj 12.2 13.0 13.5 22.8|δ| 65.3 70.7 71.0 59.5[K] 31.3 32.7 33.2 18.5f1 29.7 31.0 28.1 28.2λ1 4.2 4.3 4.1 4.2θ1 1.1 2.9 2.0 2.4

R-helixc λmax 0.7 0.7 0.7 3.0∆ 23.4 23.0 23.4 28.3fh 28.1 27.8 28.1 42.2f|/f⊥ 2.3 2.2 1.7 218.3

(Pro)n II d λmax 0.0 0.0 0.0 1.3fh 0.0 0.0 0.0 39.7

a For 1979 parameters of Tables 1-3 with same experimental dataas used in this work.b For setsGy, Gx, andG0 in this work. c For setsHy, Hx, andH0 in this work. d For setsJy, Jx, andJ0 in this work.

TABLE 5: Anisotropies (Å 3), Molar Kerr Constants (1012esu), Polarizabilities (Å3), and Polar Angle (deg) of AmidesCalculated with SetGy

compda |δ| [K] Rj R1 R2 R3 ψ

FAb expt36-38 290 4.08calc 2.15 314 3.67 4.94 2.46 3.61 38.3

ACb expt36,38,39 242 5.91calc 1.37 225 5.49 6.40 4.98 5.09 28.4

NMFb expt36 210 5.91calc 1.35 144 5.28 6.17 4.89 4.76 10.1

NMA b expt36,37,39,40 1.98 175 7.97calc 2.79 104 7.24 9.09 6.14 6.48 166.6

DMFb expt36-38 415 7.81calc 3.55 587 7.56 9.92 6.50 6.25 29.2

DMA b expt37,38,40 2.14 354 9.24calc 3.91 488 9.47 12.01 8.72 7.69 7.6

TFAc expt39 291 6.03calc 1.32 95 5.70 6.57 5.23 5.28 38.3

TCAc expt39 275 12.20calc 2.19 205 10.42 11.61 9.09 10.56 32.1

TBAc expt39 279 17.40calc 3.32 259 14.05 15.63 11.91 14.59 33.7

mTFAc expt39 417 8.49calc 2.36 469 7.36 8.93 6.56 6.58 164.1

mTCAc expt39 366 14.20calc 2.76 435 12.20 13.92 10.77 11.90 173.7

mTBAc expt39 358 19.90calc 3.32 401 15.85 17.71 13.88 15.95 178.8

a FA, formamide; AC, acetamide; NMF,N-methylformamide; NMA,N-methylacetamide; DMF,N,N-dimethylformamide; DMA,N,N-di-methylacetamide; TFA, trifluoroacetamide; TCA, trichloroacetamide;TBA, tribromoacetamide; mTFA,N-methyltrifluoroacetamide; mTCA,N-methyltrichloroacetamide; mTBA,N-methyltribromoacetamide;b R1

andR2 lie within the NC′O plane,R3 ⊥ NC′O plane.c R1 andR2 lienear the NC′O plane,ψ is the polar angle of the projection of theR1

axis onto the NC′O plane.

TABLE 6: Haloamide Polarizability Components (Å3)Calculated with SetGy

compd R11 R21 R31 R22 R32 R33

TFA 5.01 0.32 0.00 5.65 0.02 5.28TCA 10.09 0.78 0.05 9.63 0.17 10.58TBA 13.92 1.23 0.09 12.65 0.29 14.66mTFA 7.87 -0.70 -0.01 6.73 0.01 6.58mTCA 13.15 -0.41 -0.01 10.82 0.13 11.88mTBA 17.03 -0.08 -0.01 13.90 0.23 15.92

TABLE 7: Oscillator Strengths, Transition Wavelengths,and Transition Moment Angles of Amides Calculated withSetGy

compda f1 λ1 (nm) θ1 (deg)

FA expt41 0.240 170calc 0.169 181 19.5

AC expt42,43 0.140 178 16.7a

calc 0.134 184 16.9NMF expt42 0.090 190

calc 0.132 184 13.1NMA expt42 0.170 184

calc 0.101 185 4.0DMF expt42 0.230 199

calc 0.228 187 21.8DMA expt42 0.230 196

calc 0.177 191 20.5

a Value observed for myristamide, assumed valid for acetamidebecause similar spectra are observed for many primary amides.

17828 J. Phys. Chem., Vol. 100, No. 45, 1996 Bode and Applequist

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amides except acetamide, dimethylacetamide, and trifluoro-acetamide; in the latter cases discrepancies of 25-36° occur.A recent study by Clark23 on polarized UV spectra of amides

provides additional data for comparison with theθ1 values ofTable 7. For propanamide, a primary amide, Clark obtainsθ1) 20 ( 3° (transformed to our coordinate system), whichcompares well with the acetamide values in Table 7. ForN-acetylglycine, a secondary amide, Clark obtainsθ1 ) 0 (5°, which compares well with the calculated value of 4° forN-methylacetamide in Table 7.

rR-Helix. The notationRR-(X)n indicates a right-handedR-helix of the polypeptide (X)n. Table 8 gives the calculatedabsorption and CD spectral properties using parameter setsHand the 1979 parameters forRR-(Ala)12. Figure 2 shows thecalculatedπ-π* absorption and CD spectra for this molecule.Comparison is made with experimental data for helical (Glu)n,a reasonable choice because calculated spectra for theR-helixare insensitive to the nature of the side chain.4,7 The compari-sons show that any of the setH parameters provide a better fitto theRR-helix absorption and CD spectra than is obtained withthe 1979 parameters. (This fact is evident in the rms deviationsfor the absorption data in Table 4 as well.) The close agreement

among the setsH shows that the calculations are insensitive tothe NC′O center location in the neighborhood of the NC′ bondcenter, though it was previously found that large deviations fromthis position give unrealistic CD spectra.4 It is worth notingthat attempts to find a parameter set for theR-helix with a valueof θ0 closer to that in setsG andJ were unsuccessful becausethe larger values of that angle result in smaller splittings of theparallel and perpendicular bands.Theπ-π* CD spectrum shows two major bands of opposite

sign above and below 200 nm. The sum of rotational strengthsin each of these regions, designatedR1 andR2, respectively,are given in Table 8 for comparison with observed rotationalstrengths of the bands. The wavelength extrema of the CDbands are designatedλCD1 and λCD2. A similar resolution ofthe bands is adopted in the other cases below where two majorCD bands are found in both experiment and theory.The experimental CD band near 225 nm in this and other

polypeptide structures is attributed to then-π* transition, whichcurrently is not included in the dipole interaction model forreasons discussed previously.4 It should be noted that Itoetal.24 have done similar calculations by a closely related methodwhich includes then-π* transition but omits the nonchro-mophroric polarizabilities.

âP-Sheet. The notationâP-(X)n×m indicates a parallelâ-sheetof m strands of the polypeptide (X)n. Table 9 gives thecalculated absorption and CD spectral properties using parametersetsH and the 1979 parameters forâP-(Ala)6×3. Figure 3 showsthe corresponding absorption and CD spectra. The most strikingdifference among the parameter sets is the relatively large totalrotational strength for setHy, Rtot ) 0.17 D‚µB. (In cases suchas this, where the calculated CD spectrum is dominated by aband of one sign, only the sumRtot of rotational strengths of allmodes is given.)A comparison with experiment is possible for poly(Val),

which is believed to be predominantly in theâP form intrifluoroethanol.25-27 Calculations forâP-(Val)6×3 are comparedwith the experimental CD spectrum of (Val)7 in Figure 4, usingparameter setsH and the staggered conformationø1 ) 60° ofthe Val CR-Câ bond giving the greatest intensity of the majorCD band.8 For setHy ∆ε is nearly twice the peak valuecalculated forâP-(Ala)6×3 and is about half the experimentalvalue. Figure 4 shows also the absorption and CD curves at(∆x, ∆y) ) (0.20, 0.25) Å calculated from the curves for setsH using the approximation of eq 10. With this NC′O centerthe CD intensity nearly matches the observed intensity. Thisfinding sheds new light on a long-standing puzzle regardingthe large intensity of the observed CD spectrum ofâ-sheets.Theoretical predictions for such sheets in undistorted planarlattices have given peak∆ε values in the range 2-8 L/(molcm) near 200 nm,8,14 which is up to an order of magnitudesmaller than the observed magnitude for poly(Val). It is evident

TABLE 8: Spectral Properties of the π-π* Transition inthe rR-Helix

(Ala)12property

(Glu)nexpt Hy Hx H0 1979

λmax (nm)a 18844 190 190 190 194∆ (cm-1)a 4370, 452045,46 3403 3424 3405 3187fh a 0.1344 0.17 0.17 0.17 0.18f | 0.0244 0.02 0.02 0.03 0.07f⊥ 0.1144 0.14 0.14 0.14 0.12f |/f⊥ 0.1844 0.18 0.18 0.18 0.57R1 (D‚µB)b -0.3544 -0.87 -0.81 -0.82 -1.01R2 (D‚µB)c 0.6344 0.90 0.93 0.91 1.32λCD1 (nm) 20544 204 204 204 206λCD2 (nm) 18844 190 190 190 192

aData included in peptide optimizations.bSum of rotational strengthsfor modes at or above 200 nm.c Sum of rotational strengths for modesbelow 200 nm.

Figure 2. Absorption and CD spectra forRR-(Ala)12. Theoreticalspectra calculated with a half-peak bandwidth of 4000 cm-1 andH0

(s), Hy (- - -), Hx (---), or 1979 parameters (- - -). Experimentaldata (O) of poly(L-glutamic acid) in water are from Tinocoet al.56

(absorption, pH 4.9) and from Johnson and Tinoco57 (CD, pH 4.5).

TABLE 9: Spectral Properties of the π-π* Transition inthe Parallel â-Sheet

(Ala)6×3property

heptapeptideexpt Hy Hx H0 1979

λmax (nm) 195a 25 194 195 195 194∆ (cm-1) 4601 4465 4517 2989fh 0.28 0.29 0.29 0.26f| 0.14 0.15 0.15 0.08f⊥ 0.14 0.14 0.15 0.18f|/f⊥ 1.03 1.04 1.00 0.48Rtot (D‚µB) 0.17 0.11 0.05 0.09λCD1 (nm) 203b 26,27 204 204 204 202λCD2 (nm) 180b 26,27 182 184 184 184

a Boc-(L-Ile)7-OMe. b Boc-(L-Val)7-OMe.

Spectra of Helical Polypeptides J. Phys. Chem., Vol. 100, No. 45, 199617829

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that a displacement of the NC′O center by a few tenths of anangstrom from the NC′ bond center would account for theobserved intensity without invoking distortions of the planarlattice. The agreement seen in Figure 4 must be interpretedwith caution; i.e., the intensity can also be affected by differenttorsion angles of the side chain and by distortions of the lattice.The parameters used here simply give an example of areasonable structure that would be consistent with the experi-mental CD spectrum.

A further prediction of interest for theâP structures is thelarge splitting of the absorption peak. This is not confirmedby the observed partial spectrum of poly(Ile) in Figure 4, apolymer which is also believed to be predominantly in theâPform.25 It may be that our model exaggerates the splitting,though it would be desirable to test the predictions with aspectrum showing the full absorption band on a molecule knownto be fully in theâP form. If confirmed by experiment, thepredicted large splitting could be a diagnostic test for theâP-sheet. We have investigated the origin of the splitting bymaking calculations for chains of 1-10 residues in sheets of1-5 strands. The splitting increases with chain length, reachinga plateau of around 5000 cm-1 for the longer chains, but isalmost independent of the number of strands. This shows thatthe splitting is primarily the result of nearest-neighbor interac-tions within each strand. The splittings near 5000 cm-1

calculated here are considerably larger than those near 3000cm-1 calculated earlier with the 1979 parameters8 in our modeland by other workers using exciton models.28-32

âA-Sheet. The notationâA-(X)n×m indicates an antiparallelâ-sheet ofm strands of the polypeptide (X)n. Table 10 showsthe calculated absorption and CD spectral properties usingparameter setsH and the 1979 parameters forâA-(Ala)6×3.Comparison is made with experimental data for (Lys)n in theâA form. The most striking changes with the new parametersare the larger∆ values and the largerRtot with setHy. Thelatter corresponds to a severalfold increase in the intensity ofthe main CD band near 200 nm, again showing the sensitivityof the intensity to displacement of the NC′O center in theydirection. Figure 5 shows the calculated absorption and CDspectra forâA-(Ala)6×3 corresponding to the parameter sets inTable 10. Figure 6 shows spectra calculated forâA-(Abu)6×3(Abu ) L-R-aminobutyric acid) using parameter setHy alongwith experimental spectra for (Lys)n. The Abu residue, havingan ethyl side chain, is more appropriate than Ala for comparisonwith data for (Lys)n. It is seen that the CD intensity for Abu inconformations nearø1 ) 150° are indeed comparable toexperiment. (The figure omits calculations at the expectedenergy minimumø1 ) 60° as this conformation is stericallyhindered in theâA-sheet.) We have not attempted to find acombination of side chain conformations of Abu and NC′Ocenter displacements that would more accurately reproduce theexperimental CD spectrum, but it is clear that only minoradjustments of these structural parameters would give a realisticspectrum; hence, the observed CD spectrum is consistent withan undistorted planarâA-sheet structure.The splitting predicted for the absorption spectrum is not as

great as that found above for theâP-sheet and is opposite insign to that found with the 1979 parameters. (The value∆ )-20 cm-1 in Table 9 differs from the value-1017 cm-1

reported previously8 for the 1979 parameters because thesplittings in that paper were calculated from the wavenumbers

Figure 3. Absorption and CD spectra forâP-(Ala)6×3. Theoreticalspectra calculated with a half-peak bandwidth of 4000 cm-1 andH0

(s), Hy (- - -), Hx (---), or 1979 parameters,(- - -).

Figure 4. Absorption and CD spectra forâP-(Val)6×3. Theoreticalspectra calculated with a half-peak bandwidth of 4000 cm-1 andø1 )60° with these parameters:H0 (s), Hx (---), Hy (- - -). Curve(- - -) is calculated for (∆x,∆y) ) (0.20,0.25) Å. Experimentalabsorption data (]) of Boc-(L-Ile)7-OMe in TFE (25°) are fromToniolo.25 Experimental CD spectra of Boc-(L-Val)7-OMe in TFE (25°)are from Tonioloet al.26 (O) and as solid film from Balcerskiet al.27

(4). The ordinate of the film spectrum is scaled to match the positivepeak of the solution spectrum.

TABLE 10: Spectral Properties of the π-π* Transition inthe Antiparallel â-Sheet

(Ala)6×3property

(Lys)nexpt Hy Hx H0 1979

λmax (nm) 19546 195 196 195 194∆ (cm-1) 2474 2264 2325 -20fh 0.188 0.32 0.34 0.33 0.29f| 0.22 0.22 0.22 0.14f⊥ 0.11 0.11 0.11 0.15f|/f⊥ 1.99 2.00 1.94 0.89Rtot (D‚µB) 0.13-0.2647,48 0.07 -0.04 -0.04 -0.02λCD1 (nm) 19849 200 202 202 198λCD2 (nm) 17549 182 182 182 186

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of two dominant normal modes instead of the weighted averageof eq 3.) An insight into the difference between splittinginteractions inâP andâA is gained by calculating the effect ofsheet size on splitting, as described above. For a singleâA chainthe splitting is nearly the same as that in a singleâP chain, asone might expect. As chains are added to the sheet inantiparallel fashion, the splitting is diminished and becomesnegative for very short oligomers. This shows that interchaininteractions are significant in theâA-sheet and that they tend toreverse the splitting produced by intrachain interactions. Thedifference between the parallel and antiparallel cases is seen inthe absorption spectra of Figures 3-6, where the calculated

splitting is smaller than the bandwidth forâA-sheets but largerthan the bandwidth forâP-sheets.The only direct experimental observation of the splitting, so

far as we know, is the linear dichroic spectrum ofâ-(Lys)n ofRosenheck and Sommer.28 This showed the longer wavelengthband to be polarized parallel to the long axis of moleculesoriented in a film, and this would correspond to positive splittingin our convention if the long axis coincides with the chain axes.310-Helix. The notation 310-(X)n indicates the 310-helical form

of the polypeptide (X)n, taken to be right-handed in our usage.Table 11 lists theoretical properties calculated with setsH and1979 parameters for 310-(Ala)12. Figure 7 shows the absorptionand CD spectra predicted with both setH and the 1979parameters. The theoretical results are compared to theexperimental CD spectrum of the decapeptide Boc-Aib-Pro-Val-Aib-Val-Ala-Aib-Ala-Aib-Aib-OMe in methanol from Sudhaet al.33 The achiral residue aminoisobutyric acid (Aib) iscapable of promoting either a right-handed or left-handed helix;however, crystallographic studies on the experimental peptide34

indicate existence of a right-handed helix. The spectral featuresare insensitive to the NC′O displacements in the parameter setsH, though there are notable differences from the spectra using

Figure 5. Absorption and CD spectra forâA-(Ala)6×3. Theoreticalspectra calculated with a half-peak bandwidth of 4000 cm-1 andH0

(s), Hy (- - -), Hx (---), or 1979 parameters (- - -).

Figure 6. Absorption and CD spectra forâA-(Abu)6×3. Theoreticalspectra calculated with a half-peak bandwidth of 4000 cm-1 andHy

parameters with theseø1 values: -60° (s), -150° (---), 180°(- - -), and 150° (s s). Experimental data (O) of poly(L-lysine) inwater are from Rosenheck and Doty46 (absorption, pH 10.8) and fromBrahmset al.49 (CD, pH 11.2).

TABLE 11: Spectral Properties of the π-π* Transition inthe 310-Helix

(Ala)12property

decapeptidea

expt Hy Hx H0 1979

λmax (nm) 189 189 189 194∆ (cm-1) 5010 5026 5177 6889fh 0.17 0.18 0.17 0.21f| 0.02 0.03 0.02 0.07f⊥ 0.14 0.15 0.15 0.14f|/f⊥ 0.17 0.17 0.17 0.54R1 (D‚µB)b -0.70 -0.65 -0.64 -0.79R2 (D‚µB)c 0.69 0.67 0.71 0.95λCD1 (nm) 20933 210 208 210 216λCD2 (nm) 184 184 184 184

a Boc-Aib-Pro-Val-Aib-Val-Ala-Aib-Ala-Aib-Aib-OMe in metha-nol.33 b Sum of rotational strengths for modes at or above 196 nm.c Sum of rotational strengths for modes below 196 nm.

Figure 7. Absorption and CD spectra for 310-(Ala)12. Theoreticalspectra calculated with a half-peak bandwidth of 4000 cm-1 andH0

(s), Hy (- - -), Hx (---), or 1979 parameters (- - -). Experimentaldata (O) of Boc-Aib-Pro-Val-Aib-Val-Ala-Aib-Ala-Aib-Aib-OMe inmethanol are from Sudhaet al.33

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the 1979 parameters. The sign and intensity of the CD bandnear 210 nm predicted with setsH agree well with experiment.The large calculated splitting near 5000 cm-1 is seen to showa marked shoulder at 210 nm in the absorption spectrum. Thisfeature, as well as the positive CD band at 185 nm, could beuseful for diagnostic purposes. Further experimental workwould be desirable to test these predictions.Pro I Helix. (Pro)n I denotes the right-handed poly(L-proline)

helix characterized by thecisconformation of the peptide bonds.Table 12 gives the spectral quantities calculated with parametersetsJ and the 1979 parameters for (Pro)10 I with ø2 ) 20°, aconformation that is within the low-energy region calculatedfor the proline ring.21 (Torsion angleø2 is defined by atomsCRCâCγCδ; the ring conformation is fixed by this torsion anglein the side chain and the backbone torsion angleφ.12) The tableincludes experimental data from various sources for comparison.Figure 8 displays the corresponding absorption and CD spectra.The spectra are insensitive to the displacement of the NC′Ocenter among setsJ, and the predictions are very similar to thoseusing the 1979 parameters, showing reasonable agreement withexperiment. The calculated rotational strengths in Table 12 arequite large compared with the experimental values; this was

noted in an earlier study as well,6 where it was pointed out thatthe experimental values are strongly dependent on assumptionsmade about the band shape. Figure 9 shows absorption andCD spectra calculated with theJy parameters and variousø2values from-40° to +40°. The spectra are only slightlysensitive to the choice of ring conformation, as found also inan earlier study.12

Pro II Helix. (Pro)n II denotes the left-handed poly(L-proline)helix characterized by thetrans conformation of the peptidebonds. Table 13 gives the spectral quantities calculated withparameter setsJ and the 1979 parameters for (Pro)10 II with ø2) 20°, along with experimental data from various sources.Figure 10 shows the corresponding absorption and CD spectra.Again, the spectra are insensitive to the displacement of theNC′O center. The most notable differences between thecalculations with theJ sets and the 1979 parameters are thesmaller splitting, oscillator strength, rotational strength, and bandwavelengths in the newer results. The present results are morenearly consistent with experiment, with the possible exceptionof the splitting; this quantity, however, is subject to a largeexperimental uncertainty. It should be noted that the 1979parameters gave results comparable with experiment when side

TABLE 12: Spectral Properties of the π-π* Transition inthe Pro I Helixa

(Pro)10 I

property(Pro)n Iexpt Jy Jx J0 1979

λmax (nm) 209, 21150,51 206 206 206 206∆ (cm-1) 1960, 286050,51 2709 2986 3142 3304fh 0.21, 0.3350,52 0.34 0.32 0.32 0.43f| 0.1250 0.22 0.21 0.21 0.25f⊥ 0.0950 0.12 0.12 0.11 0.18f|/f⊥ 1.3450 1.92 1.78 1.85 1.41R1 (D‚µB)b 0.78, 0.3148,50 2.59 2.47 2.35 2.48R2 (D‚µB)c -0.55,-0.2048,50 -2.32 -2.21 -2.07 -2.00λCD1 (nm) 21552 214 214 214 216λCD2 (nm) 20052 200 200 200 202

a Theoretical predictions made withø2 ) 20°. b Sum of rotationalstrengths for modes at or above 207 nm.c Sum of rotational strengthsfor modes below 207 nm.

Figure 8. Absorption and CD spectra for (Pro)10 I. Theoretical spectracalculated with a half-peak bandwidth of 4000 cm-1 and J0 (s), Jy(- - -), Jx (---), or 1979 parameters (- - -) andø2 ) 20°. Experi-mental data (O) of poly(L-proline) I in trifluoroethanol are from Boveyand Hood52 (extrapolated6).

Figure 9. Absorption and CD spectra for (Pro)10 I with various ringconformations. Theoretical spectra calculated withJy parameters andhalf-peak bandwidth of 4000 cm-1. The ring torsion anglesø2 are-40.0° (s s), -20.0° (- - -), 0.0° (---), 20.0° (s), and 40.0°(- - -). Experimental data are as in Figure 8.

TABLE 13: Spectral Properties of the π-π* Transition inthe Pro II Helix a

(Pro)10 II

property(Pro)n IIexpt Jy Jx J0 1979

λmax (nm) 20253 202 202 202 205∆ (cm-1) 1740, 451050,51 904 1207 1033 1810fh 0.21, 0.2950,53 0.29 0.29 0.29 0.41f| 0.1050 0.11 0.12 0.11 0.17f⊥ 0.1150 0.18 0.17 0.18 0.23f|/f⊥ 0.9250 0.64 0.74 0.66 0.76Rtot (D‚µB) -0.4853 b -0.44 -0.47 -0.52 -1.47λCD (nm) 20553 206 206 206 212

a Theoretical predictions made withø2 ) 20°. b Estimated byMoscowitz’s formula54 converted to D‚µB units:55 Rk ≈ 0.439∆ε°k ∆°k/λ°k, where∆ε°k is the maximum CD value,∆°k2 is the Gaussian varianceof the CD band on the wavelength scale, andλ°k is the wavelength ofthe CD maximum.

17832 J. Phys. Chem., Vol. 100, No. 45, 1996 Bode and Applequist

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chain conformations nearø2 ) (50° were used.12 This rangefalls in a higher elevation of the energy map,21 and it isinteresting that the present results give reasonable agreementwith experiment for a lower-energy side chain conformation.Figure 11 shows absorption and CD spectra calculated with theJy parameters and variousø2 values from-40° to +40°. Asnoted previously,12 the CD spectrum is rather sensitive to theproline ring conformation; in the present results the amplitudeof the major CD band agrees most nearly with experiment forø2 in the range-20° to +20°. This entire range falls withinthe low energy region calculated for the proline ring.21 It is to

be noted that calculations for (Pro)n II with setHy (not shown)give unrealistic CD spectra with three bands in a-/+/- pattern,apparently the result of the small value ofθ0 in setHy.

Discussion

This study has produced new sets of NC′O chromophoreparameters that are consistent with the new isotropic atompolarizabilities given in the accompanying paper.3 The abilityof the new atom and chromophore parameters to reproduceexperimental absorption and CD spectra of polypeptide helicesprovides a more extensive demonstration of the validity of theparameters and the model than has previously been ac-complished.The effects of displacing the NC′O center within the

“optimal” neighborhood of the NC′ bond center are found tobe small in most respects, but they have a major effect on thepredicted CD intensities forâ-sheets. The predicted absorptionand CD spectra of helical polypeptides in theπ-π* band near200 nm are in better agreement with experiment than those basedon our 1979 parameters; this is particularly true for the CDspectra ofâ-sheets, the (Pro)n II helix in its putative low-energyside chain conformations, and the 310-helix.It is worthwhile to consider the origin of the sensitivity of

the CD spectrum ofâ-sheets to the NC′O center, a point whichhas been brought out by Sniret al.13 and Woody.14 Accordingto Moffitt’s theory,35 the rotational strength of exciton bandsin a helix is proportional to the distance of the chromophorefrom the helix axis. This is a consequence of the fact that themagnetic dipole moment associated with electron motions inthe chromophore is proportional to this distance. In theâ-sheetsthe NC′ bond center lies close to the axis of each helical chain.Hence, small displacements of the NC′O center from that pointare expected to produce large changes in the rotational strengths.In fact, the displacements in the positive∆x and∆y directionsboth result in increases of the radial distance of the NC′O centerin theâ chains, consistent with Moffitt’s theory. For all of theother helical structures the NC′ bond center is further removedfrom the axis, and the sensitivity of CD spectra to the NC′Ocenter is correspondingly small. A further effect of the NC′Ocenter location on the optical properties in our model comesfrom its effect on the interaction of the chromophore with thenonchromophoric atoms; i.e., the relative positions of atoms andchromophores are changed when the center is moved, causingthe local dipole fields to change. The size of this effect wouldbe difficult to anticipate by any means short of the full numericalcalculations which are given here.A question raised by this work is, which, if any, of the

parameter sets tested here would serve as the best choice forpredictingπ-π* absorption and CD spectra of general polypep-tide structures? If one were limited to a single parameter set,set Hy is probably the best general choice, since it givesreasonable agreement with experiment for the most commonstructures. The major exception is (Pro)n II, which requires atransition moment angleθ0 that is about 10° larger than that inset Hy. This study emphasizes the need to consider thesensitivity of predictions to the choice of parameters in anysystem, and it would be useful to try various choices suggestedby the range of parameters in Tables 1-3.Of course, an underlying hope in this and our previous related

studies has been to find a parameter set that would be fullytransferable among polypeptides of various structures. Thedistinction between parameter setsH andJ, particularly in thevalue ofθ0, means that full transferability has not been achieved.There are various possible reasons for this: (i) the electronicstructures of the atoms and NC′O chromophores may themselves

Figure 10. Absorption and CD spectra for (Pro)10 II. Theoretical spectracalculated with a half-peak bandwidth of 4000 cm-1 and J0 (s), Jy(- - -), Jx (---), or 1979 parameters (- - -) andø2 ) 20°. Experi-mental data (O) of poly(L-proline) II in trifluoroethanol from are Jennesset al.53

Figure 11. Absorption and CD spectra for (Pro)10 II with various ringconformations. Theoretical spectra calculated withJy parameters andhalf-peak bandwidth of 4000 cm-1. The ring torsion anglesø2 are-40.0° (s s), -20.0° (- - -), 0.0° (---), 20.0° (s), and 40.0°(- - -). Experimental data are as in Figure 10.

Spectra of Helical Polypeptides J. Phys. Chem., Vol. 100, No. 45, 199617833

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not be accurately transferable; (ii) the dipole interaction modelmay not represent the interactions accurately enough; and (iii)errors in experimental data used for the optimizations may distortsome of the parameters. Future research may help to clarifythe prospects for better transferability. In the meantime, thepresent work gives a basis for improved use of the dipoleinteraction model for prediction of peptide absorption and CDspectra.

Note Added in Proof. In the above we overlooked the workof Manning and Woody58 on CD spectra of the 310 helixcalculated by quantum mechanical exciton theory. Their results,covering a range ofφ, ψ angles for this structure, are roughlycomparable to ours in band signs, wavelengths, and magnitudes.The spectra in our Figure 7 were calculated withφ ) -49°, ψ) -26°.59

Acknowledgment. This investigation was supported by aresearch grant from the National Institute of General MedicalSciences (GM-13684). We are grateful to Dr. BalasubramaniamShanker for helpful discussions.

References and Notes

(1) Woody, R. W. InCircular Dichroism Principles and Applications;Nakanishi, K., Berova, N., Woody, R. W., Eds.; VCH Publishers: NewYork, 1994; Chapter 17, pp 473-521.

(2) Woody, R. W. InCircular Dichroism and the ConformationalAnalysis of Biomolecules; Fasman, G. D., Ed.; Plenum Publishing: NewYork, 1996; Chapter 2, pp 25-67.

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Phys.1980, 73, 3521.(5) Applequist, J.Biopolymers1981, 20, 387.(6) Applequist, J.Biopolymers1981, 20, 2311.(7) Applequist, J.Biopolymers1982, 21, 703.(8) Applequist, J.Biopolymers1982, 21, 779.(9) Caldwell, J. W.; Applequist, J.Biopolymers1984, 23, 1891.(10) Sathyanarayana, B. K.; Applequist, J.Int. J. Peptide Protein Res.

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1986, 27, 86.(12) Thomasson, K. A.; Applequist, J.Biopolymers1991, 31, 529.(13) Snir, J.; Frankel, R. A.; Schellman, J. A.Biopolymers1975, 14,

173.(14) Woody, R. W.Tetrahedron: Asymmetry1993, 4, 529.(15) Applequist, J.; Carl, J. R.; Fung, K.-K.J. Am. Chem. Soc.1972,

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Chem. Soc.1976, 98, 3470.(28) Rosenheck, K.; Sommer, B.J. Chem. Phys.1967, 46, 532.(29) Woody, R. W.Biopolymers1969, 8, 669.(30) Denisov, D. A.Biophysics1969, 14, 11.(31) Pysh, E. S.J. Chem. Phys.1970, 52, 4723.(32) Zubkov, V. A.; Vol’kenshtein, M. V.Mol. Biol. 1970, 4, 483.(33) Sudha, T. S.; Vijayakumar, E.; Balaram, P.Int. J. Peptide Protein

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(49) Brahms, S.; Brahms, J.; Spach, G.; Brack, A.Proc. Natl. Acad.Sci. U.S.A.1977, 74, 3208.

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23, 283. Data from Table 5.

JP962120S

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