Distribution of Conformations Sampled by the Central Amino Acid

Feb 11, 2009 - The conformational preference of individual amino acid residues in the unfolded state of peptides and proteins is the subject of a cont...
1 downloads 14 Views 2MB Size
Download PDF
2922

J. Phys. Chem. B 2009, 113, 2922–2932

Distribution of Conformations Sampled by the Central Amino Acid Residue in Tripeptides Inferred From Amide I Band Profiles and NMR Scalar Coupling Constants Reinhard Schweitzer-Stenner* Department of Chemistry, Drexel UniVersity, 32nd and Chestnut Streets, Philadelphia, PennsylVania 19104 ReceiVed: October 03, 2008; ReVised Manuscript ReceiVed: December 17, 2008

The conformational preference of individual amino acid residues in the unfolded state of peptides and proteins is the subject of a continuous debate. Research has mostly been focused on alanine, owing to its abundance in proteins and its relevance for the understanding of helix T coil transitions. In the current study, we have analyzed the amide I band profiles of the IR, isotropic and anisotropic Raman, and VCD profiles of trialanine in terms of a conformational model which, for the first time, explicitly considers the entire ensemble of possible conformations rather than representative structures. The distribution function utilized for a satisfactory simulation of the amide I band profiles was found to also reproduce a set of five J coupling constants reported by Graf et al. (Graf, J.; et al. J. Am. Chem. Soc. 2007, 129, 1179). The results of our analysis reveal a PPII fraction of ∼0.84 for the central alanine residue, which strongly corroborates the notion that alanine has a very high PPII propensity, exceeding the values obtained from restricted coil libraries. We performed a similar analysis for trivaline and found that the dominant fraction of its central residue is a β-strand. The fraction of the respective distribution is 0.68. The remaining fraction contains contributions from helical and PPII conformations. The results of our analysis enable us to decide on the suitability of force fields used for MD simulations of short alanine-containing peptides. The paper establishes vibrational spectroscopy as a suitable method to explore the energy landscape of amino acid residues. Introduction Over the last 15 years, the unfolded states of proteins and peptides have become the subject of increasing interest owing to (a) the discovery of so-called intrinsically disordered proteins (IDPs) and peptides and (b) the increasing experimental and theoretical evidence in support of the notion that the unfolded state is conformationally less random than predicted in the classical statistical (random) coil model of Flory.1,2 Flory’s model is based on the isolated pair hypothesis, which assumes that the conformational manifold sampled by an individual amino acid residue is independent of the conformation of its respective neighbors in a polypeptide chain. The conformational entropy of a residue (with the exception of proline) is believed to be large because of its ability to sample the entire sterically allowed region of the Ramachandran plot, which encompasses a major part of its upper left quadrant as well as regions associate with right- and, to some minor extent, left-handed helical conformations.3 Hence, the unfolded state is thought to be basically without structure. This view has recently been challenged on two different levels. First, results from NMR and hydrogen exchange experiments on a variety of unfolded proteins suggest that regular compact structures like short helices and turns can be formed, which serve as initiation steps for the folding process. These local structures are generally thought to be imbedded in an otherwise random coil conformation.4-7 Second, the results of multiple experimental investigations of short peptides suggest that the conformational space of at least some amino acid residues is much more restricted than generally assumed and that the structural propensities of the individual amino acid residues in the unfolded state might be substantially different from each other.8 The corresponding conformational * Telephone: (215) 895-2268. Fax: (215) 895-1265. E-mail: [email protected].

ensembles deviate from the canonical picture, which predicts a more or less equal population of all structurally accessible conformations in the Ramachandran space with no substantial energy barrier between PPII and more extended β-strand conformations.1,3 Some amino acid residues like alanine, lysine, and glutamic acid also seem to exhibit a high propensity for polyproline-II-type conformations,9-14 whereas residues with branched aliphatic or aromatic side chains have a larger preference for β-strand-like conformations.11,13,15-18 These results are in qualitative agreement with the distributions of the respective amino acids in various coil libraries, for which regular structures like the helix and β-sheet have been omitted,19-22 but are, for example, concerning alanine, still at variance with the results of many molecular dynamics (MD) simulations.23-26 Apparently, the new view of the unfolded state implies (a) that the number of accessible conformations is smaller than and (b) that the respective conformational ensemble depends on the primary structure of the protein or peptide. Recent results from a structural analysis of the naturally unfolded peptides Aβ1-28 and salmon calcitonin indicate that this is indeed the case.27-29 Over the last 10 years, alanine has emerged as a model residue for studying the propensity of amino acid residues in the unfolded state. This is, to a significant extent, due to its high helical propensity and the use of polyalanine peptides as model molecules for protein folding studies.30,31 Shi et al., for instance, used NMR and ECD measurements to study the structure of Ac-X2(A)7O2-NH2 (XAO, X, and O denote diaminobutyric acid and ornithine, respectively) and interpreted their results as indicating that the individual residues predominantly adopt a PPII conformation at room temperature.9 The results of Shi et al. have been corroborated by numerous experimental and theoretical studies on short peptides, which all revealed a substantial PPII propensity for alanine.11,13,18,32-34 This notion

10.1021/jp8087644 CCC: $40.75  2009 American Chemical Society Published on Web 02/11/2009

Central Amino Acid Residue in Tripeptides is also in perfect agreement with distributions which Serrano22 and Jha et al.20 inferred from coil libraries but at variance with a less restricted library investigated by Dobson and associates.35,36 The results of MD simulations are force-field-dependent and generally do not reproduce a PPII propensity of alanine without force field modification.23,25 Zagrovic et al. investigated XAO by small-angle X-ray scattering (SAXS) experiments and obtained a radius of gyration of 7.4 Å,26 which corresponds to an average end-to-end distance of 18.1 Å. This is significantly shorter than what one would expect for a pure PPII structure (radius of gyration ) 13.1 Å, end-to-end distance ) 32.04 Å). Makowska et al. combined ECD and NMR measurements of XAO (involving the measurement of 3JCRHNH coupling constants, NOEs, and chemical shifts) with MD simulations performed with the AMBER 99 force field.37,38 Their results led the authors to conclude that PPII is one of many conformations sampled by alanine. On the basis of a simultaneous analysis of amide I′ band profiles and 3JNHCRH constants, Schweitzer-Stenner and Measey modified this view by assigning the sampling of nonextended conformations to the N-terminal segment, XXA, of the peptide, whereas the remaining alanines were found to predominantly adopt PPII-like conformations.39 While most of the available experimental data agree in suggesting a PPII propensity of alanine, the reported propensities (i.e., PPII fraction in a given ensemble of residue conformations) are still substantially different. By combining several vibrational spectroscopies, Eker et al. obtained a 50:50 mixture of PPII and an extended β-strand at room temperature.15,40 For tetraalanine, however, the same method yielded a much higher PPII fraction (∼0.8).41 Kallenbach and associates reported fractions between 0.8 and 0.9 for alanine in XAO and Ac-GGADD-NH2, respectively.9,42 Recently, Graf et al. conducted a very thorough and important NMR study of several polyalanines (A3, A4, A7, and alanine segments in peptides of different lengths),43 which utilized a total of seven scalar coupling constants as a measure of φ and ψ.44 They fitted the obtained coupling values with a model which can be described as a linear combination of distributions of conformations assignable to PPII, βs, and a right-handed helical. The structure and energies of the subensembles were obtained from MD simulations based on an Amber force field. Thus, the authors obtained PPII fractions of 0.92 for trialanine and values between 0.83 and 0.86 for the longer polyalanines. A length dependence of the alanine propensity was not obtained. However, the significance of this study was recently questioned based on discrepancies between the empirically and computationally obtained values for the constants in the Karplus equations used in the study of Graf et al.45 A recent study from our own laboratory, in which we analyzed the Raman, IR, and VCD amide I band profiles and 3 JNHCRH constants of A3, A4, and A2KA in terms of an ensemble of structures representing PPII, βs, and helical distributions, yielded PPII fractions between 0.52 (for A3) and 0.73 (for one of the central A4 residues).33 A suitable model of the unfolded state of proteins and peptides requires rather accurate information about the individual propensity of amino acid residues and the corresponding manifold of sampled conformations. Thus far, conformational distributions of amino acids have been experimentally studied mostly in their respective unfolded protein or peptide context by comparing the dipolar coupling and J coupling constants, as well as nuclear Overhauser enhancement (NOE) values obtained from multidimensional NMR measurements with corresponding values obtained by averaging over distributions obtained from coil libraries.35,46-48 Only recently,

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2923 Graf et al. performed the aforementioned study on short polyalanines and on trivaline in water.43,49 They used distributions obtained from MD simulations rather than from coil libraries for their analysis. In the current paper, we demonstrate for the first time how vibrational spectroscopy can be used to explore the conformational distribution of short tripeptides in water. Our protocol exploits the excitonic coupling between amide I modes.50 It involves the simulation of the amide I band profile of the respective IR, isotropic Raman, anisotropic Raman, and VCD spectra in terms of a superposition of Gaussian distributions centered in the PPII, β-strand, turn, and helix regions of the Ramachandran plot. In earlier studies, we utilized a somewhat more coarse-grained approach based on representative conformations to simulate the amide I band profiles of IR, Raman, and VCD spectra of peptides.39,51 In contrast to NMR, vibrational spectroscopy is a fast method, so that the corresponding spectra represent a superposition rather than an average of spectra from different conformations. We selected trialanine and trivaline, two of the peptides studied by Graf. et al.43 Thus, we could use their J coupling constants to check the validity of our analysis. The relevance of alanine has been described above. In contrast to alanine, valine is considered to be a helix breaker, and studies on valine-containing peptides seem to indicate a higher βs propensity than that on alanine.11,13,15-18 However, the available propensity values from experimental, theoretical, and coil library studies are again vastly different (between 1.0 and 0.26).15-17,42 The current study unambiguously demonstrates that the analysis of amide I profiles in terms of realistic distribution models is capable of obtaining reliable propensities and distribution functions of amino acid residues. While the paper focuses on the employed method of structure analysis, the obtained results are nevertheless of biological relevance in that they provide reliable values for the propensities of alanine in their respective homopeptide contexts. Since the influence of an alanine residue on its nearest neighbors is small, the propensity value of alanine can be considered as intrinsic. Theoretical Backgroud Excitonic Coupling. The interaction between amide I modes in a polypeptide chain can be described in terms of the excitonic coupling model, which accounts for the mixing of the respective lowest excited vibrational states by means of the bilinear contribution50

∆ ) fex(q1, q2)q1q2

(1)

where q1 and q2 are the normal coordinates of the unperturbed amide I modes and fex reflects the strength of excitonic coupling, which leads to a mixing of vibrational states and a shift of the eigenenergies. The theoretical description of excitonic states is based on elementary quantum mechanics. It has been frequently described in the literature.32,50,52-57 Excitonic coupling causes redistributions of the intensities of individual amide I bands, which are different for the respective isotropic Raman, anisotropic Raman, and IR bands.56-58 The different band profiles reflect the fact that the ratio of IR and anisotropic Raman intensities of the two amide I bands directly depends on the relative orientation of the corresponding peptide groups and thus on the dihedral angles of the central amino acid residue.56 It is well established that the coupling constant ∆ is determined by through-space (electrostatic) and through-bond coupling.59-61 In earlier studies, we used coupling parameters obtained from ab inito calculations on a glycine dipeptide by

2924 J. Phys. Chem. B, Vol. 113, No. 9, 2009

Schweitzer-Stenner

Torii and Tasumi59 as starting values for the analysis of amide I band profiles.27,28,33,39,62 In most cases, the final values used for the best fit of the experimental data were identical to, or only slightly different from, the starting values. Since the current study is aimed at calculating the amide I profiles of distributions of backbone conformations, a more handy strategy for the consideration of ∆ had to be developed. To this end, we constructed an empirical formalism based on simple geometrical and physical considerations, which is described in the following. The coupling strength ∆ is written as a sum of four contributions ∆′j (j ) 1, 2, 3, 4) 4

∆)

∑ ∆′j

(2)

j)1

The first term accounts for the distance and orientational dependence of ∆

[ ]

∆′1 ) ∆′10

( ) ( )

R n rOO R 1+ rOO

n

· cos(m1θzz)

(3)

where R, n, m, and ∆′10 are empirical constants. The rOO is the distance between the carbonyl oxygens of the two peptide groups. It is the vector sum, written as

b r OO ) b r CO(1) + b r CN(1) + b r NCR + b r CRC + b r CO(2) (4) in a coordinate system introduced earlier, with the NCR bond as the x-axis and the y-axis pointing toward the CO bond of the peptide. The z-axis is perpendicular to the peptide plane; its orientation follows the three finger rule. The vectors b rCO(1), rNCR, b rCRC, b rCO(2), and so forth exhibit the orientation b rCN(1), b and length of the indicated bonds CO, CN, NCR, CRN, and CO in this coordinate system. It is obvious that b rOO, as well as the angle θzz between the z-axes of the N- and C-terminal peptides, depends on φ and ψ. The latter can be calculated by first transforming the unit vector zˆ1(1) ) (0 0 1) from the N-terminal into the C-terminal coordinate system56,57 and by subsequently calculating a cos(zˆ1(2)zˆ2(2)), where zˆi(j), i, j ) 1, 2 is the unit vector of the ith peptide unit in the jth coordinate system. Equation 3 describes a contribution to the coupling energy which for n . 1 varies sharply between ∆′10 · cos(m1θzz) and 0 only at around R ) rOO. In order to meet cyclic boundary conditions, m1 has to be a positive integer; cos(m1 · θzz) insures that |∆′1| is maximal for extended conformations. The second term is directly related to the dihedral angles φ and ψ

( φ +2 π ) · cos( ψ -2 π )

∆′2 ) ∆′20 cos

(5)

where ∆′20 is an empirical constant. This interaction energy is again maximal for extended conformations and disappears if one of the dihedral angles is 0. The third term is rather technical as it was solely introduced to polish coupling constants in the four corners of the Ramachandran plot, so as to move them closer to results from ab initio calculations. It is written as

∆′3 ) ∆′30

[

xl yl + 1 + xl 1 + yl

]

(6)

where xl ) φ/φ0 and yl ) ψ/ψ0 and ∆′30, l, φ0, and ψ0 are empirical parameters. The fourth term ∆4 is a constant by means of which the absolute values of the coupling parameter were adjusted to make them comparable with contour plots from DFT calculations.61,63 It should be emphasized that this is a rather heuristic approach aimed at reproducing contour maps of the nearest-neighbor coupling reported in the literature.59,61,63 It is based on the assumption that the nearest-neighbor coupling should periodically depend on the dihedral angles, on the relative orientations of the two peptide groups, and on the two transition dipole moments. The distance dependence is modeled as a rather shortrange type of interaction. We did not explicitly consider the contribution of transition dipole coupling because this formalism becomes inadequate at short distances.55 Different simulations were carried out with different empirical parameters until we obtained the contour plot in Figure 1, which very closely resembles the coupling strength plots reported by Torii and Tasumi59 and Gorbunov et al.61 The utilized empirical parameters are listed in the figure legend. It should be emphasized that they do not bear any specific significance; we do not exclude the possibility that a different set of values or even some other mathematical formalism might produce similar results. What counts in the context of this paper is that we were able to quantitatively model the negative trough in the center of the Ramachandran plot and the two maxima centered at (φ,ψ) ) (0, (180°). The maximum at (φ,ψ) ) (0, 180°) is particularly relevant in that its rather large gradient overlaps with the conformational region assigned to PPII, in agreement with the above-cited ab initio calculations. As shown in the Results and Discussion sections, this gradient has a major impact on how the PPII-like fraction of a peptide ensemble affects the band shape of amide I. Since Gorbunov et al. did not obtain any significant difference between the contour maps of diglycine and dialanine peptides,61 we consider our model as applicable to peptides with different amino acid residues. It should be noted in this context that, in principle, our model considers excitonic coupling as the sole mechanism by which conformational changes can affect the wavenumber position of the two amide I′ bands of the investigated tripeptides. This seems to be an oversimplification in view of the conformational dependence of the intrinsic wavenumbers of both amide I′ modes predicted by DFT calculations.60,61,64 However, Gorbunov et al. showed that PPII T β-strand transitions do not cause a significant change of the amide I wavenumber position, owing to the superposition of variations caused by the conformational change itself and by the change of the peptide’s solvation shell.64 This agrees with experimental data from our group.39,40 For transitions into the (right-handed) helical conformations, Gorbunov et al. predict a downshift of the N-terminal amide I modes, whereas the C-terminal mode remains nearly unaffected.61 This was taken into account for our simulations as described below. Distributions of Conformations. For the simulation of the amide I profiles and J coupling constants of tripeptides, we assumed a statistical ensemble for the corresponding central amino acid residue consisting of five normalized two-dimensional Gaussian distributions. The (φ,ψ) positions of their maxima are associated with the following conformations: (1) PPII (-60° > φmax,1 > -80°; 150° > ψmax,1 > 130°), (2) β-strand (-110° > φmax,2 > -150°; 150° > ψmax,2 > 115°), (3) right-handed

Central Amino Acid Residue in Tripeptides

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2925

Figure 1. Contour and 3-dimensional plot of the nearest-neighbor coupling constant as function of φ and ψ calculated with a heuristic model described in the text. The parameters used for this simulation are ∆′10 ) 7 cm-1 ∆′20 ) 2 cm-1, ∆′30 ) 4 cm-1, n ) 60, R ) 1.2 Å, m1 ) m2 ) 1, l ) 10, φ0 ) ψ0 ) 100°.

R-helix (-60° > φmax,3 > -80°; -20° > ψmax,3 > -40°), (4) left-handed R-helix (80° > φmax,4 >60°; 40° > ψmax,4 > 20°), and (5) type IV β-turn (γ-turn) (-60° > φmax,5 >-80°; 80° > ψmax,5 > 60°). The latter has been considered because recent experimental and theoretical investigations indicated the possibility that amino acid residues can sample this region to a significant extent.65,66 The partition sum for the central residue ensemble can be written as 5

Z)

∑ ∫-π ∫-π fj(φ, ψ)dφdψ π

π

(7)

with

(√ ) χj

2π |Vˆj |

exp[-0.5(→ F -→ F j0)TVˆj-1(→ F -→ F j0)] (8a)

where

()

φ → F) ψ

(8b)

and

Vˆj )

(

σφ,j σφψ,j σφψ,j σψ,j

)

〈x〉 )

∫-ππ ∫-ππ xf(φ, ψ)dφdψ Z

(9)

Results

j)1

fj )

The expectation value of any observable x depending on φ and ψ (IR and Raman intensities, rotational strengths, J coupling constants) can be written as

(8c)

The vector b F0j points to the position of the maximum of the jth distribution in the Ramachandran coordinate system. The χj is the corresponding fraction. The diagonal elements of the matrix Vˆj are the half half-widths of the jth distribution along the coordinates φ and ψ, and the corresponding off-diagonal element σφψ,j ) σψφ,j reflects correlations between variations along the two coordinates. If Vˆj is diagonal, the φ,ψ projection of the distribution is an ellipse with its main axis parallel to the φ and ψ axes. Correlation effects rotate the ellipse in the (φ,ψ) plane.

This section of the paper is organized as follows. First, some simulations of amide I profiles of a tripeptide calculated for different mixtures of PPII, β-strand, and right-handed helical conformations for the central residue are presented. The second part describes the fits to the amide I′ profiles of trialanine and trivaline in D2O. In what follows, we will use the term amide I′ for the experimental band profiles of the two peptides investigated, whereas amide I will be used for the more general descriptions of this mode. Simulating Spectra for Different Distributions. In order to demonstrate how the amide I band reflects different types of conformational distributions, we simulated the IR, Raman, and VCD profiles for different scenarios. To this end, we employed the spectral parameters (i.e., intrinsic wavenumbers and Gaussian bandwidth), which were utilized for the fitting of the band profiles described below. This ensured the comparability with our experimental data. The assumed widths of the Gaussian distribution (σφ ) σψ ) 20 cm-1) reflect the distribution pattern obtained from coil libraries of alanine and MD simulations of alanine-based peptides. We adjusted the peak positions of the subensembles to (φ,Ψ) ) (-70°,150°) for PPII, (φ,Ψ) ) (-136°, 32°) for the β-strand, and (φ,Ψ) ) (-60°,-30°) for the (right-handed) helical-type conformations (Rr), so that the respective distributions nearly reproduced the J coupling constants, which Graf et al.43 reported in Table 1 of their paper for the distributions of individual PPII, β-strand, and righthanded helical conformations. For this adjustment, we calculated the J coupling constants by using the Karplus equations reported by Graf et al.43 Most of the respective dihedral coordinates are close to the maxima of the coil library distributions of alanine as reported by Avbelj and Baldwin,19,67 Serrano,22 Jha et al.,20

2926 J. Phys. Chem. B, Vol. 113, No. 9, 2009

Figure 2. Isotropic Raman, anisotropic Raman, IR, and VCD amide I profiles of tripeptides simulated for different conformational ensembles, that is, 100% PPII (solid line), 100% β-strand (dashed line), 50:50 mixture of PPII and β-strand (dashed gray), and 100% righthanded helical (dashed-dot-dot).

and Fiebig et al.36 Only the maximum of the corresponding β-strand distribution of Avbelj and Baldwin (φ ) -155°) deviates from our model. Since the VCD couplet is slightly negatively biased, we assumed an intrinsic magnetic transition moment of m ) 5 × 10-24 esu · cm for the C-terminal amide I′ mode.41 In order to quantitatively reproduce the IR and VCD profiles, we invoked the electronic dipole transition moment of 2.7 × 10-19 esu · cm, which Measey et al. observed for cationic and anionic dialanine.29 Figure 2 depicts the band profiles calculated for (a) 100% right-handed helical, (b) 100% β-strand, (c) 100% PPII, and (d) a mixture of 50% PPII and 50% β-strand. As expected, the IR and Raman amide I profiles of PPII and β-strand distributions are qualitatively similar but differ quantitatively in that the anisotropic Raman scattering and IR absorption profiles are more asymmetric for β-strand conformations, in principle agreement with earlier simulations for representative conformations.62 However, the differences between the IR and Raman band profiles of PPII and the β-strand are substantially less pronounced than those between respective bands of representative conformations reported earlier.62 This shows that the explicit consideration of distributions somewhat blurs the spectral differences between these conformations.

Schweitzer-Stenner

Figure 3. IR and VCD spectra of zwitterionic trialanine in D2O between 1600 and 1650 cm-1 as reported by Eker et al.15 The simulations described in the text are displayed as follows: (a) optimized simulation based on a 4-conformation model described in the paper (solid red line), (b) optimized simulation based on a 2-conformation model described in the paper (solid black line), (c) simulation with the mole fractions reported by Graf et al.43 (solid blue), (c) simulation with the mole fractions reported by Schweitzer-Stenner et al.33 (dashed black).

However, the situation is quite different for the VCD spectrum. The β-strand conformation exhibits a much less pronounced VCD signal, as expected from DFT-based calculations on model peptides.68 All profiles for the purely helical ensemble are qualitatively different from those of PPII and β in that IR and both Raman profiles are now dominated by the high-frequency amide I mode, as expected.59 The VCD profile is the most sensitive tool. This becomes apparent if one compares the corresponding amide I profiles of PPII, the β-strand, and the 50:50 mixture of both types of conformations in Figure 2, which are all clearly distinguishable. Conformational Analysis of Trialanine in Water. Figure 3 exhibits the amide I′ band profile of the corresponding isotropic Raman, anisotropic Raman, IR, and VCD spectra of zwitterionic trialanine in D2O, which were reported earlier by Eker et al.15 It is somewhat easier to analyze than the respective spectra of the cationic and anionic state. Our earlier data provide unambiguous evidence for the notion that the conformation of the central residue, which we probe with our spectroscopic data,

Central Amino Acid Residue in Tripeptides

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2927

TABLE 1: Calculated and Experimental J Coupling Constants of the Central Residue of Trialaninea

3

J(HN,HR) J(HN,C′) 3 J(HR,C′) 3 J(C′,C′) 3 J(HN,Cβ) 1 J(N,CR) 3

experimental43

fit43

simulation amide I′ (two conformers per residue)

simulation amide I′ (four conformers per residue)

5.68 1.13 1.84 0.25 2.39 11.34

5.6 1.1 1.5 0.6 2.1 10.9

6.3 (6.2) 0.88 (0.83) 1.71 0.72 (0.57) 1.91 11.18

5.64 (5.27) 1.03 (1.05) 1.53 0.6 (0.46) 2.13 11.08

a The unit of the coupling constants is Hz. J coupling constants calculated with the Karplus constants of Case et al.69 are listed in parentheses.

is not significantly affected by the protonation state of the termini.15 The amide I′ profiles are rather typical for an ensemble which predominantly populates extended conformations like PPII and βs, that is, there is a clear lack of coincidence between the positions of the intensity maxima of isotropic Raman scattering and IR absorption, with the latter at lower and the former at higher wavenumbers.59 The rather pronounced negative VCD couplet indicates a substantial population of PPII.43 We performed several simulations of these profiles with different statistical weights, χj, for the conformational distributions introduced in the Theoretical Background section. Along with the simulation of the amide I′ band profiles, we concomitantly calculated the respective set of scalar coupling constants by utilizing the corresponding Karplus equations43 and compared them with the values which Graf. et al.43 obtained in their recent study on trialanine. Moreover, we calculated a set of 3J constants by using the Karplus parameters which Case et al. observed from DFT calculations on A2-NH2.69 These experimental coupling constants are listed in Table 1, together with the results of a fit which Graf et al. performed by first calculating the average coupling constants for subensembles of molecular dynamics structures assignable to specific conformations, and subsequently calculating the effective J coupling constant of the ensemble as a weighted sum of the average coupling constants of the subensembles. These subensembles play the same role for their analysis as the above introduced Gaussian distributions do for our simulations of amide I′ profiles and J coupling constants. In a first step, we performed simulations based on three above-introduced subensembles associated with PPII, β-strand, and right-handed helix-like conformations. We utilized the mole fractions, which Schweitzer-Stenner et al. reported for an ensemble consisting of the three conformations representing these subensembles, that is, χ1(PPII) ) 0.52, χ3(β) ) 0.23, and χ3(Rr) ) 0.25.33 The result is shown in Figure 3 (dashed lines). Generally, the agreement between experimental and simulated profiles was modest and much less satisfactory than the modeling with representative conformations by SchweitzerStenner et al.33 This particularly concerns the VCD couplet, which is substantially underestimated. The calculated set of J coupling constants could not compete with the accuracy of the values which Graf et al. obtained with their fitting (results not shown). The use of computationally obtained Karplus parameters69 did not improve the accuracy of this calculation. In the second step, the amide I′ profiles were simulated by considering different mixtures of PPII and β-strand conformations with the molar fraction of PPII varying between 0.6 and 1.0 (in increments of 0.02). The J coupling constants were calculated concomitantly. The simulations performed for χ1(PPII) values between 0.8 and 0.9 yielded a satisfactory agreement with the experimental band profiles. Since the VCD

signal is most sensitive to changes of the structural composition, we searched for the minimum of the difference between experimental and theoretical peak values (∆εexp and ∆εsim) for optimizing the simulation, that is

δ)



jmax+1

∑

jmax-1

(∆εjsim - ∆εjexp)2

(10)

This yielded χ1(PPII) ) 0.84, χ2(β) ) 0.16, and the solid black line band profiles in Figure 3. We decided not to use the χ2 or the reduced χ2 function because we found that this puts too much of an emphasis on (smaller) systematic discrepancies between simulated and experimental data which emerge from a somewhat incomplete modeling of the band profiles. For the sake of simplicity, we have used Gaussian profiles for the individual excitonic transitions, in accordance with common practice. However, the real band profiles are Voigtian with a Lorentzian half-width of ∼11 cm-1.70 The J coupling values obtained from the above simulation are listed in Table 1. The agreement with the experimental data reported by Graf et al. is not particularly good and clearly inferior to what these authors obtained from their modeling.43 This judgment remains valid if one uses the Karplus parameters of Case et al.69 for calculating some of the J values (cf. Table 1). It has been argued that the use of these Karplus parameters yields a lower PPII fraction (between 60 and 80%) and, correspondingly, a larger β-strand formation (40-20%).45 We cannot reproduce these results. With our distributions, a 70:30 mixture of PPII and β yields a 3JNHCH value of 6.65 Hz, which substantially deviates from the respective experimental value (5.68 Hz). We wondered whether a good reproduction of both amide I profiles and J coupling constants could also be obtained by a mixture of more conformational manifolds. We found that the addition of a helical fraction (χ3(Rr) ) 0.05-0.1) generally deteriorates the fit to all band profiles. Again, the most pronounced deviation from experiment is obtained for the VCD signal. However, the negative impact of considering a righthanded helical conformation can be nearly compensated by allowing the additional admixture of a small fraction of γ-turnlike conformations. The consideration of γ-turns is motivated by a recent theoretical study of Gong and Rose.66 The canonical coordinates of a γ-turn are (φ,Ψ) ) (-85°,78°). We obtained a rather satisfactory fit with χ1(PPII) ) 0.84, χ2(β) ) 0.08, χ3(Rr) ) 0.04, and χ5(γ) ) 0.05. We optimized the simulation further by varying the φ and ψ values of the PPII distribution. The values listed in Table 2 correspond to a simulation for which the difference function δ was minimized. The final simulation is shown by red solid lines in Figure 3. Compared with the

2928 J. Phys. Chem. B, Vol. 113, No. 9, 2009

Schweitzer-Stenner

Figure 4. Three-dimensional plot of the distribution function used for the optimized simulation of the amide I′ profiles and J coupling constants of trialanine. The parameters are listed in Table 2.

TABLE 2: Parameters of Conformational Distributions and Their Mole Fractions Used for Fit 1 of Amide I′ Band Profiles and the J Coupling Constants of Trialanine in Table 1 PPII βs Rr γ

χ

φmax[°]

σφ[°]

ψmax[°]

σψ[°]

0.84 0.08 0.04 0.04

-69 -136 -60 -85

10 10 10 10

140 132 -30 78

10 10 10 10

optimized simulation based on the 2-conformation model (PPII and β-strand), the agreement with the Raman and IR band profiles is only marginally improved. The J coupling constants of the 4-conformation simulation listed in Table 1 are much closer to the experimental values than those which emerged from the 2-conformation simulation. Their accuracies are similar to those of the values reported by Graf et al.43 Figure 4 displays the Ramachandran space distribution obtained with the 4-conformation model. We investigated the significance of the optimized parameter set obtained with the 5-conformation simulation by calculating the difference between the experimental and simulated peak values of the VCD signal as a function of (a) the PPII molar fraction and (b) the dihedral angles associated with the maximum of the PPII distribution. For case (a), the variations of the molar fractions of the other conformers were synchronized, that is, we assumed that χ2(β) ) 2χ(RR) ) 2χ(γ) ) 2χ(γ′) and ∑j*1 χj ) 1 - χ1. The confidence interval for the investigated parameter x ) χ1,φ,ψ was conservatively calculated as

∆x ) x(2δmin) - x(δmin)

(11)

where δmin is the δ value for the optimal simulation. Thus, we obtained ∆χ1 ) (0.08, ∆φ ) (10°, and ∆ψ ) (5°. Conformational Analysis of Trivaline in Water. Figure 5 exhibits the amide I′ band profiles of zwitterionic trivaline in D2O. On a first view, the profiles look similar to those obtained for trialanine. However, the comparison of the corresponding profiles in Figure 6 reveals substantial differences. For trivaline, the isotropic Raman band is less asymmetric. With respect to the IR profile, the differences between trialanine and trivaline parallel corresponding spectral differences between the amide I′ profiles of the alanine and valine dipeptides, recently reported by Grdadolnik et al.71 The splitting between the two amide I′

Figure 5. IR and VCD spectra of zwitterionic trivaline in D2O between 1600 and 1650 cm-1 as reported by Eker et al.15 The simulations described in the text are displayed as follows: (a) optimized simulation described in the paper (solid red line), (b) simulation with the mole fractions reported by Graf et al.43 (solid blue), (c) simulation for χ1 ) 0.4 and χ2 ) 0.6 (dashed black), and (d) simulation for χ1 ) 0.6 and χ2 ) 0.4 (dashed pink).

bands is slightly reduced, and the first moments of all profiles are slightly red-shifted, in accordance with the lower intrinsic amide I′ wavenumber of a valine residue.29 The greater integrated intensity of the IR amide I′ band of trivaline reflects the larger electronic dipole strength which Measey at al. observed for the amide I′ modes of valine residues.29 Altogether, even this comparison of the experimental amide I′ profiles of trialanine and trivaline clearly suggests that the conformational manifolds sampled by the central residues of these peptides must be substantially different. The simulation of the trivaline amide I′ band profiles was carried out as described for trialanine, but the distribution parameters were changed to account for the different average J coupling constants for the PPII, β-strand, and right-handed helical fractions of valine reported by Graf et al.43 For PPII and the β-strand, the thus obtained (φ,Ψ) coordinates of the distribution maxima are again in good agreement with the respective peaks in the coil library distributions.19,22,36 For the distribution of helical conformers, Graf et al. reported an effective 3JNHCRH constant of 7.1, which indicates that most of the φ values are below -80°. This is in agreement with Avbelj

Central Amino Acid Residue in Tripeptides

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2929 described strategy and obtained a rather large asymmetric uncertainty of +0.2,-0.12 for χ2(β). The uncertainties of the dihedral angles are relatively small, that is, ∆φ ) ∆ψ ) (5°. In agreement with Graf et al., our results suggest that the central amino acid residue of trivaline has a substantial β-strand propensity. The results explain the absence of any detectable PPII signal in the electronic circular dichroism (ECD) spectrum of trivaline.16 The three-dimensional Ramachandran plot of the distribution function obtained from our analysis is shown in Figure 7. We also simulated the amide I′ profiles of trivaline with a two-state model which again comprised only PPII and the β-strand. This did not yield satisfactory fitting for various types of mixtures. This is demonstrated by the two simulations with χ1(PPII) ) 0.4, χ2(β) ) 0.6 and χ1(PPII) ) 0.6, χ2(β) ) 0.4, the results of which are depicted by dashed lines (black and pink) in Figure 5. Taken together, the simultaneous reproductions of amide I′ band profiles and J coupling constants by our distribution model demonstrate its suitability for determining the structural manifold of amino acid residues.

Figure 6. Comparison of amide I′ profiles of zwitterionic trialanine (black) and trivaline (red). Note that the IR and VCD spectra are plotted in absolute units. Since the Raman spectra were normalized on an internal standard, they can also be compared in quantitative terms.

and Baldwin, whereas the distribution reported by Fiebig et al. exhibits the corresponding maximum between -75 and -70°. In a first step, we utilized the molar fractions reported by Graf et al., namely, χ1(PPII) ) 0.29, χ2(β) ) 0.52, and χ3(rh) ) 0.19 to obtain the simulations represented by solid blue lines in Figure 5. The agreement with the experimental profiles is satisfactory for IR and the two Raman profiles but less so for the VCD signal. As indicated by the list of calculated J coupling constants in Table 3, the agreement with the experimental values is satisfactory. In a second step, the molar fractions of the three distributions were varied while the ratio χ1/χ3 was kept constant. Once the δ value for the VCD spectrum was minimized, we varied the χ1/χ3 ratio for further optimization. Finally, we optimized the simulation further by small changes of the respective distribution parameters. The result is displayed by solid red lines in Figure 5. The corresponding molar fractions are χ1(PPII) ) 0.16, χ2(β) ) 0.68, and χ3(rh) ) 0.16. The distribution parameters are listed in Table 4 and the respective J coupling constants in Table 3. Our reproduction of the NMR data is slightly less accurate than the results from the MD-based fit of Graf et al.43 With respect to the mole fractions of the subensembles, our results are not very different from their values. These differences are quantitative rather than qualitative. We determined the uncertainty of the obtained parameters (i.e., for χ2(β) and the dihedral angles) by means of the above-

Figure 7. Three-dimensional plot of the distribution function used for the optimized simulation of the amide I′ profiles and J coupling constants of triavaline. The parameters are listed in Table 4.

Discussion Comparison with Earlier Analyses. In earlier studies, we performed two different analyses of the amide I′ profiles of trialanine. The first one by Eker et al.15 used the intensity ratios of the two discernible amide I′ bands of the Raman and IR profiles to obtain the dihedral angles of a conformation, which was positioned between the PPII and β-strand troughs of the Ramachandran plot. The authors interpreted their result as reflecting the nearly 50:50 mixing of two dominant conformations, namely, PPII and the β-strand. The respective ECD spectra could be interpreted in a similar way.16 The second analysis reported by Schweitzer-Stenner et al.33,39 explicitly used representative conformations for distinguishable distributions of PPII, β-strand, and right-handed helical-type conformations to model the conformational manifold of the central residue. The respective simulation of amide I′ was restricted by the 3JNHCRH coupling of the central residue. The result yielded again a PPII fraction of nearly 0.5, but the remaining fraction was nearly equally right-handed helical and β-strand. A higher PPII fraction (between 0.6 and 0.75) was obtained for alanine in tetrapep-

2930 J. Phys. Chem. B, Vol. 113, No. 9, 2009

Schweitzer-Stenner

TABLE 3: Calculated and Experimental J Coupling Constants of the Central Residue of Trivalinea experimental (from ref 43)

fit43

simulation amide I′ (mole fractions from ref 43)

simulation amide I′ (after optimization

7.94 0.58 2.42 0.34 1.38 10.8

7.6 0.8 2.2 1.0 1.3 10.3

7.68 1.08 2.13 1.2 1.2 10.9

8.08 1.1 2.24 1.38 1.0 10.8

3

J(HN,HR) J(HN,C′) 3 J(HR,C′) 3 J(C′,C′) 3 J(HN,Cβ) 1 J(N,CR) 3

a

The unit of the coupling constants is Hz.

TABLE 4: Parameters of Conformational Distributions and Their Mole Fractions Used for the Simulation of Amide I′ Band Profiles and the J Coupling Constants of Trivaline in Table 3 (rh: right-handed, lh: left-handed) PPII βs rh helical

χ

φmax[°]

σφ[°]

0.16 0.68 0.16

-80 -130 -70

20 20 20

tides.41 All of these values are substantially lower than what we have obtained in the present study. The reason for this quantitative (though not qualitative) discrepancy is the gradient of the excitonic coupling constant in the region of PPII conformations (cf. Figure 1), to which even slightly different PPII conformations give rise to significantly different nearestneighbor coupling. PPII conformations with φ values below -65° and ψ values below 140° exhibit much weaker coupling than those conformations which sample the upper-right fraction of the PPII trough (φ > -65°, ψ > 150°). The representative conformations used for the earlier analyses consisted predominantly of the latter fraction, owing to the necessity to reproduce the asymmetry of the isotropic Raman band profile. The heterogeneity of nearest-neighbor coupling in the PPII region renders normal-mode analyses, which are carried out for a single conformation, rather useless. Recently, Myshakina and Asher reported the results of their DFT-based normal-mode calculation for trialanine as indicating that the two amide I modes of this peptide are not vibrationally coupled in the PPII conformation.72 They had used the conformation (φ,ψ) ) (-67°,132°) for their analysis, which is, in fact, more type II β-turn than PPII and for which the coupling is known to be weak.59 Interestingly, the discrepancy between the results obtained from the distribution model employed in the present study and the modeling with representative structures performed in our earlier work is nearly negligible for trivaline. We performed a simulation based on the representative structure model and found χ1(PPII) ) 0.27, χ2(βs) ) 0.63, and some minor populations of helical conformations. The reason for the more realistic modeling with the representative conformation model is that the heterogeneity of the coupling constant is substantially less pronounced in the β-strand region. Comparison with Literature. The structural propensity of alanine has been the subject of a very intensive and controversial debate, which has been briefly outlined in the Introduction. Roughly, the field can be divided into three views of the alanine world. (a) Alanine exhibits a statistical coil distribution with PPII as one of many possible conformations,23,36-38,73 (b) alanine has an above-average, but still moderate, PPII propensity (0.5 < χ1(PPII) < 0.7),15,41 and (c) alanine has a very high PPII propensity (0.8 < χ1(PPII) < 1.0) and thus deviates significantly from statistical or random coil predictions. 9,42,53,74 Work from our laboratory was, thus far, supportive of option (b).33,39,75 The much more thorough analysis of the current study, however, which, for the first time, is based on realistic distributions of conformations rather than on an ensemble of representative

ψmax[°] 150 135

-35

σψ[°]

σφψ[°]

20 20 20

4 4 0

structures, clearly reveals the superiority of option (c). The quantitative agreement with the results from the NMR study of Graf et al. corroborates this notion further and demonstrates that at least for tripeptides, our spectroscopic method may be considered as a somewhat less time-consuming and materialintensive alternative. A combination of both methods is, of course, ideal. As mentioned above, Best et al.45 recently questioned the validity of the Karplus constants used by Graf et al. for alanine.43 They invoked different Karplus parameter sets derived from DFT calculations on Ac-A-NMe and AA-NH2 by Case et al.69 With these parameters, they obtained substantially larger β and helical fractions for alanine than Graf et al. However, it is not clear at all from the study of Case et al.69 whether the discrepancies between the empirical and theoretical Karplus parameters are due to a side-chain dependence of the latter in small peptides or whether they are caused by motional averaging, which is not taken into account by the DFT calculations. Our own simulations with the Karplus parameters of Case et al. suggest that the differences between distributions obtained with empirical and DFT-based parameter values are not so significant for the considered distributions. The high PPII propensity of alanine confirmed in this study is at variance with the results of many MD simulations of either the alanine dipeptide or trialanine itself, which were carried out with a variety of force fields.23,25,26,76 Most of these simulations overestimate the sampling of the helical trough of the Ramachandran plot and/or underestimate the PPII fraction. A recent conformational analysis performed by Tran et al.,17 which is based on an excluded volume concept (i.e., a purely repulsive potential energy term), underestimates the PPII propensity of alanine. One exception from the general trend is the MD simulation of trialanine that Gnanakaran and Garcia performed with a modified AMBER force field.34 They obtained a distribution clearly dominated by PPII at room temperature (χ1(PPII) ∼ 0.8), the remaining fraction being equally divided between β-strand and right-handed helical conformations. On the basis of MD simulations of alanine-based peptides of differing lengths, Garcia recently concluded that some propagation free energy exists for PPII. This notion seems to be in agreement with our own vibrational spectroscopy data on triand tetraalanine41 and corresponding ROA data from Barron’s group.77 However, the very high PPII propensity of alanine obtained in the current study suggests that there is not much to gain by increasing the number of residues. This is in line with the findings of Graf et al.,43 who even obtained a slight decrease

Central Amino Acid Residue in Tripeptides of χ1(PPII) with an increasing number of alanine residues. The reported far-UV ECD spectra of tri- and tetraalanine are indicative of a higher PPII propensity for the latter peptide.16,18 However, the spectra from very recent ECD experiments on di-, tri-, and tetraalanine, which we recently carried out with new cuvettes lacking any internal dichroism above 185 nm, yielded rather similar spectra, with only modest differences which could also result from a different electronic coupling mechanism.51 Taken together, the above experiments and analyses do not suggest that the PPII propensity of an individual alanine residue in polyalanine peptides depends on the length of the peptide. However, this finding does not completely rule out that cooperativity is operative, as suggested by Garcia.78 Cooperativity means, in this context, that the persistence length of a PPII segment is larger than that suggested by the isolated pair hypothesis, which treats every residue as a statistically independent entity.2 Recently, Chen et al. concluded from the analysis of a series of temperature-dependent measurements of the 3JNHCRH coupling constant of a single alanine in a glycine host system (Ac-G2AnGGNH2, n ) 1-3) that the nucleation factors, σ, for the A1, A2, and A3 segments are all close to 1, which argues against cooperativity.12 However, two objections can be raised against their conclusion. First, their data, in fact, suggest that the temperature dependence of 3JNHCRH of A* in AcGGAA*AGGNH2 can best be fitted by a Zimm-Bragg model with a nucleation parameter between 1.2 and 1.3 (Figure 2F in their paper). Second, their analysis was based on a two-state model with representative coupling constants for PPII and βs. To obtain a definite result, one would have to explicitly consider distributions, as we did in the present study. While the PPII propensity of alanine in short peptides can now be considered as well-established, the unfolded state of longer polyalanine chains is still not fully understood. The data reported by Graf et al. do not indicate any major differences between the individual PPII propensities of alanine in, for example, A3 and A7.43 This is in line with what Shi et al. reported about the XAO peptide, which contains a segment of seven alanines.9 Short-angle X-ray scattering data and a MD-based fit of the 3JNHCRH coupling constants of the individual amino acid residues, however, indicate a more compact structure due to the sampling of many nonextended, turn-like conformations.26 The data led Makowska et al. to conclude that PPII is only one of many conformations which alanine can adopt.37,38 More recently, Schweitzer-Stenner and Measey analyzed the amide I′ band profile and the 3JNHCRH coupling constants of XAO with a statistical model which utilized representative conformations to describe the statistical manifold of the peptide’s individual residues.39 The results of their analysis suggests a considerable sampling of nonextended structures of the N-terminal XXA segment of the peptide, whereas the remaining alanines depict a rather high (χ1 > 0.6) polyproline II propensity. This model reproduces not only all spectroscopic data but also the radius of gyration obtained from SAXS measurements.26 These results and a study on another alanine-based peptide79 suggest that (a) the propensity of alanine might be changed in a context containing residues with charged side chains and (b) this can lead to an increased sampling of nonextended conformations. The structural propensity of lysine itself changes in an alanine context from merely PPII to a random coil-like distribution with a substantial sampling of right-handed helical conformations.33 Recently, Chen et al. proposed that for XAO, a radius of gyration of 8.1 Å can be reproduced by an ensemble which has 81% extended structures, the remaining part being assignable to helix-like conformations.80 It is unclear whether such a

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2931 distribution can still reproduce the observed 3JNHCRH values. Moreover, the radius of gyration (7.2 Å) is still overestimated. All of these contradictions make clear that a systematic analysis of polyalanine peptides doped with charged residues is necessary. This is currently being conducted in our laboratory. Data on the propensity of valine are not as abundantly available as those for alanine. Results from vibrational,15 ECD,16,81 and NMR43 spectroscopies, as well as coil library distributions,19,20,36 agree in suggesting that valine has a much higher β-strand propensity than, for example, alanine. However, the propensity is again unclear. On the basis of their amide I′ and ECD data, Eker et al. concluded that trivaline is practically locked into an extended β-strand-like structure.16 These authors obtained a similar result for AVA, even though the ECD data are less clear.13 Shi et al. used a two-state model to derive a βs mole fraction of 0.26 for valine in GGxGG host peptides, which has to be compared with 0.18 for x ) A.42 Compared with other residues investigated by Shi et al., valine does not have a significant β-propensity. On the contrary, the two-state analysis of the 3JNHCRH constant of the C-terminal residue of AV suggests a χ2(βs) value of 0.65.18 Tran et al. calculated conformational distributions of valine in different contexts, which agree in suggesting mostly right-handed helical and so-called PPIIhyp conformations, which is like a type II β-turn.17 In agreement with the results of Graf et al., our data clearly suggest that valine has a β-strand propensity (χ2 > 0.5), though it is much less pronounced than the PPII propensity of alanine. The ECD investigations of valine in proline hosts conducted by Creamer and co-workers indicate that valine samples βs more than alanine, but their data do not allow a quantitative assessment for the individual residue.81 While we think that the analysis presented in this paper should be considered as rather reliable with respect to the determination of χ2(βs), we would like to emphasize that it is more than likely that the propensity of valine in trivaline is substantially more influenced by its neighbors than alanine in trialanine. Jha et al.20 and Tran et al.20 have provided evidence for an increasing βs propensity in a context of βs preferring residues. This notion is in line with the observation that the 3JNHCRH value of the central residue in trivaline (7.94 Hz) is higher than the value which Shi et al. observed for Ac-GGVGG-NH2 (7.05 Hz).42 The concrete distribution of valine in denaturated and unfolded proteins and peptides might well depend on the respective neighbors and could therefore vary between different proteins. Summary We have subjected the amide I′ profiles of the IR, isotropic Raman, anisotropic Raman, and VCD spectra as well as a set of scalar NMR J coupling constants of trialanine and trivaline to a thorough analysis in terms of a structural model, which, for the first time, explicitly accounts for the distribution of conformations in distinguishable troughs of the Ramachandran plot. Our simulations yielded an excellent reproduction of all experimental data with the same distribution. Thus, we found that alanine predominantly samples the polyproline II trough (84%). This result finally confirms that alanine has, indeed, a very high PPII propensity. For valine, we found a significant propensity for β-strand-like conformations (∼68%); the remaining fractions are associated with helical and PPII-like structures. Our results are in excellent agreement with a recent study by Graf et al.43 These results demonstrate the usefulness of our amide I analysis for exploring the conformational propensity of amino acids in solution.

2932 J. Phys. Chem. B, Vol. 113, No. 9, 2009 Acknowledgment. This work was, in part, supported by a research grant from the National Science Foundation (Chem 0804492). We thank Dr. Franc Avbelj for providing us with his coil library distributions. References and Notes (1) Brant, D. A.; Flory, P. J. J. J. Am. Chem. Soc. 1965, 87, 2791. (2) Flory, P. J. Statistical Mechanics of Chain Molecules; Wiley Sons: New York, 1969. (3) Ramachandran, G. N.; Ramakrishnan, C.; Sasisekharan, V J. Mol. Biol. 1963, 7, 95. (4) Wright, P. E.; Dyson, H. J.; Lerner, R. A. Biochemistry 1988, 27, 7167. (5) Bai, Y.; Chung, J.; Dyson, H. J.; Wright, P. E. Protein Sci. 2001, 10, 1056. (6) Shortle, D. AdV. Protein Chem. 2002, 62, 1. (7) Dyson, H. J.; Wright, P. E. AdV. Protein Chem. 2002, 62, 311. (8) Shi, Z.; Shen, K.; Liu, Z.; Kallenbach, N. R. Chem. ReV. 2006, 106, 1877. (9) Shi, Z.; Olson, C. A.; Rose, G. A.; Baldwin, R. L.; Kallenbach, N. R. Proc. Natl. Acad. Sci., U.S.A. 2002, 99, 9190. (10) Rucker, A. L.; Creamer, T. P. Protein Sci. 2002, 11, 980. (11) Rucker, A. L.; Pager, C. T.; Campbell, M. N.; Qualls, J. E.; Creamer, T. P. Proteins: Struct., Funct. Genet. 2003, 53, 68. (12) Chen, K.; Liu, Z.; Kallenbach, N. R. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 15352. (13) Eker, F.; Griebenow, K.; Cao, X.; Nafie, L.; Schweitzer-Stenner, R. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 10054. (14) Eker, F.; Griebenow, K.; Cao, X.; Nafie, L.; Schweitzer-Stenner, R. Biochemistry 2004, 43, 613. (15) Eker, F.; Cao, X.; Nafie, L.; Schweitzer-Stenner, R. J. Am. Chem. Soc. 2002, 124, 14330. (16) Eker, F.; Griebenow, K.; Schweitzer-Stenner, R. J. Am. Chem. Soc. 2003, 125, 8178. (17) Tran, H. T.; Wang, X.; Pappu, R. V. Biochemistry 2005, 44, 11369. (18) Hagarman, A.; Eker, F.; Measey, T.; Griebenow, K.; SchweitzerStenner, R. J. Phys. Chem. B 2006, 110, 6979. (19) Avbelj, F.; Baldwin, R. L. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 5742. (20) Jha, A. K.; Colubri, A.; Zaman, M. H.; Koide, S.; Sosnick, T. R.; Freed, K. F. Biochemistry 2005, 44, 9691. (21) Swindells, M. B.; MacArthur, M. W.; Thornton, J. M. Nat. Struct. Biol. 1995, 2, 596. (22) Serrano, L. J. Mol. Biol. 1995, 254, 322. (23) Duan, Y.; Wu, C.; Chowdury, S.; Lee, M. C.; Xiong, G.; Zhang, W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T.; Caldwell, J.; Wang, J.; Kollman, P. J. Comput. Chem. 2003, 24, 1999. (24) Hovmo¨ller, S.; Zhou, T.; Ohlson, T. Acta Crystallogr. 2002, D58, 768. (25) Hu, H. E., M.; Herman, J. Proteins: Struct., Funct. Genet. 2003, 50, 451. (26) Zagrovic, B.; Lipfert, J.; Sorin, E. J.; Millett, I. S.; van Gunsteren, W. F.; Doniach, S.; Pande, V. S. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 11698. (27) Eker, F.; Griebenow, K.; Schweitzer-Stenner, R. Biochemistry 2004, 43, 6893. (28) Schweitzer-Stenner, R.; Measey, T.; Hagarman, A.; Eker, F.; Griebenow, K. Biochemistry 2006, 45, 2810. (29) Measey, T.; Hagarman, A.; Eker, F.; Griebenow, K.; SchweitzerStenner, R. J. Phys. Chem. B 2005, 109, 8195. (30) Scholtz, J. M.; Marqusee, S.; Baldwin, R. L.; York, E. J.; Stewart, J. M.; Santoro, M.; Bolen, D. W. Proc. Natl. Acad. Sci. U.S.A. 1991, 88, 2854. (31) Scholtz, J. M.; Baldwin, R. L. Annu. ReV. Biophys. Biomol. Struct. 1992, 21, 95. (32) Woutersen, S.; Hamm, P. J. Phys. Chem. B 2000, 104, 11316. (33) Schweitzer-Stenner, R.; Measey, T.; Kakalis, L.; Jordan, F.; Pizzanelli, S.; Forte, C.; Griebenow, K. Biochemistry 2007, 46, 1587. (34) Gnanakaran, S.; Garcia, A. E. J. Phys. Chem. B 2003, 107, 12555. (35) Smith, L. J.; Bolin, K. A.; Schwalbe, H.; MacArthur, M. W.; Thornton, J. M.; Dobson, C. M. J. Mol. Biol. 1996, 255, 494. (36) Fiebig, K. M.; Schwalbe, H.; Buck, M.; Smith, L. J.; Dobson, C. M. J. Phys. Chem. 1996, 100, 2661. (37) Makowska, J.; Rodziewicz-Motowidlo, S.; Baginska, K.; Vila, J. A.; Liwo, A.; Chmurzynski, L.; Scheraga, H. A. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 1744.

Schweitzer-Stenner (38) Makowska, J.; Rodziewicz, S.; Baginska, Makowski, M.; Vila, J. A.; Liwo, A.; Chmurzyn`ski, Scheraga, H. A. Biophys. J. 2007, 92, 2904. (39) Schweitzer-Stenner, R.; Measey, T. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 6649. (40) Eker, F.; Cao, X.; Nafie, L.; Griebenow, K.; Schweitzer-Stenner, R. J. Phys. Chem. B 2003, 107, 358. (41) Schweitzer-Stenner, R.; Eker, F.; Griebenow, K.; Cao, X.; Nafie, L. J. Am. Chem. Soc. 2004, 126, 2768. (42) Shi, Z.; Chen, K.; Liu, Z.; Ng, A.; Bracken, W. C.; Kallenbach, N. R. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 17964. (43) Graf, J.; Nguyen, P. H.; Stock, G.; Schwalbe, H. J. Am. Chem. Soc. 2007, 129, 1179. (44) Petri, W.; Hennig, M.; Smith, L. J.; Schwalbe, H. J. Am. Chem. Soc. 2000, 122, 12017. (45) Best, R. B.; Buchete, N.-V.; Hummer, G Biophys. J. 2008, 94, L07. (46) Bernado, P.; Blanchard, L.; Timminis, P.; Marion, D.; Rugrok, R. W. H.; Blackledge, M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 17002. (47) Peti, W.; Hennig, M.; Smith, L. J.; Schwalbe, H. J. Am. Chem. Soc. 2000, 122, 12017. (48) Meier, S.; Grzesiek, S.; Blackledge, M. J. Am. Chem. Soc. 2007, 129, 9799. (49) Bernado, P.; Mylonas, E.; Petoukhov, M. V.; Blackledge, M.; Svergun, D. I. J. Am. Chem. Soc. 2007, 129, 5656. (50) Schweitzer-Stenner, R. Vibr. Spectrosc. 2006, 42, 98. (51) Schweitzer-Stenner, R., Measey, T., Hagarman, A., Dragomir, I. the Structure of Unfolded Peptides and Proteins Explored by Raman and Ir Spectroscopies In Vibrational Spectroscopy on Peptides and Proteins; Longhi, S., Uversky, V. N., Eds.; Wiley & Sons: Chichester, U.K., 2008; In press. (52) Choi, J.-H.; Ham, S.; Cho, M. J. Chem. Phys. 2002, 117, 6821. (53) Woutersen, S.; Hamm, P. J. Chem. Phys. 2001, 114, 2727. (54) Hamm, P.; Manho, L.; Hochstrasser, R. M. J. Phys. Chem. B 1998, 102, 6123. (55) Moran, A.; Mukamel, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 506. (56) Schweitzer-Stenner, R. Biophys. J. 2002, 83, 523. (57) Schweitzer-Stenner, R. J. Phys. Chem. B 2004, 108, 16965. (58) Huang, Q.; Schweitzer-Stenner, R. J. Raman Spectrosc. 2004, 53, 586. (59) Torii, H.; Tasumi, M. J. Raman Spectrosc. 1998, 29, 81. (60) Ham, S.; Cha, S.; Choi, J.-H.; Cho, M. J. Chem. Phys. 2003, 119, 1452. (61) Gorbunov, R. D.; Kosov, D. S.; Stock, G. J. Chem. Phys. 2005, 122, 224904. (62) Schweitzer-Stenner, R. J. Phys. Chem. B. 2004, 108, 16965. (63) Ham, S.; Cho, M. J. Chem. Phys. 2003, 118, 6915. (64) Gorbunov, R. D.; Nguyen, P. H.; Kobus, M.; Stock, G. J. Chem. Phys. 2007, 126. (65) Motta, A.; Reches, M.; Pappalardo, L.; Andreotti, G; Gazit, E. Biochemistry 2005, 144, 14170. (66) Gong, H.; Rose, G. D. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 3321. (67) Avbelj, F. B. Private communication. (68) Kubelka, J.; Keiderling, T. A. J. Am. Chem. Soc. 2001, 123, 12048. (69) Case, D. A.; Scheurer, C.; Bru¨schweiler, R. J. Am. Chem. Soc. 2000, 122, 10390. (70) Schweitzer-Stenner, R. J. Raman Spectrosc. 2001, 32, 711. (71) Grdadolnik, J.; Grdadolnik, S. G.; Avbelji, F. J. Phys. Chem. B 2008, 112, 2712. (72) Myshakina, N. S.; Asher, S. A. J. Phys. Chem. B 2007, 111, 4271. (73) Vila, J. A.; Baldoni, H. A.; Ripoli, D. R.; Gosh, A.; Scheraga, H. Biophys. J. 2004, 86, 731. (74) Graf, J. N.; Nguyen, P. H.; Stock, G.; Schwalbe, H. J. Am. Chem. Soc. 2007, 129, 1179. (75) Measey, T.; Schweitzer-Stenner, R. J. Raman Spectrosc. 2006, 37, 248. (76) Mu, Y.; Stock, G. J. Phys. Chem. 2002, 106, 5294. (77) McColl, I. H.; Blanch, E. W.; Hecht, L.; Kallenbach, N. R.; Barron, L. D. J. Am. Chem. Soc. 2004, 126, 5076. (78) Garcia, A. E. Polymer 2004, 120, 885. (79) Jun, S.; Becker, J. S.; Yonkunas, M.; Coalson, R.; Saxena, S. Biochemistry 2006, 45, 11666. (80) Chen, K.; Liu, Z.; Zhou, C.; Bracken, W. C.; Kallenbach, N. R. Angew. Chemie, Int. Ed. 2007, 46, 9036. (81) Kelly, M. A.; Chellgren, B. W.; Rucker, A. L.; Troutman, J. M.; Fried, M. G.; Miller, A.; Creamer, T. P. Biochemistry 2001, 2001, 14376.

JP8087644