Secondary Structure Analysis of Polypeptides Based on an Excitonic

J. Phys. Chem. B 2004, 108, 16965-16975

16965

Secondary Structure Analysis of Polypeptides Based on an Excitonic Coupling Model to Describe the Band Profile of Amide I′ of IR, Raman, and Vibrational Circular Dichroism Spectra Reinhard Schweitzer-Stenner* Department of Chemistry, Drexel UniVersity, 32nd and Chestnut Streets, Philadelphia, PennsylVania 19104 ReceiVed: May 24, 2004; In Final Form: July 16, 2004

FTIR and, to a lesser extent, visible Raman spectroscopy are frequently used to determine the secondary structure composition of peptides and proteins in solution. This generally allows distinguishing between R-helices, β-strand, and what is often called a random coil conformation. Thus, these vibrational spectroscopies generally appear as useful but low resolution techniques. We developed a novel approach, which allows a more precise structure analysis of short and intermediate sized peptides. It is based on exploiting the delocalization of amide I′ over several peptide groups owing to excitonic coupling. The vibrational eigenfunctions obtained by diagonalizing the complete Hamiltonian of the interacting amide I′ modes were used to calculate the amide I′ band profile in the IR, isotropic, and anisotropic Raman and vibrational circular dichroism spectrum. A combined use of these profiles is a tool to distinguish between helical segments of different length and between different conformations adopted in what is inappropriately termed the random coil state. Our algorithm is particularly useful to identify the polyproline II conformation, which is adopted by many unfolded proteins at room temperature.

Introduction The amide I band of the IR and, to a lesser extent, of the Raman spectra of polypeptides and proteins is frequently used to determine their secondary structure composition.1,2 The structural sensitivity of the corresponding amide I mode, which is predominantly a CO stretching vibration, is generally attributed to the influence of hydrogen bonding on the force constant of the carbonyl bond3 and to the structure sensitivity of vibrational mixing between amide I modes.4-6 The latter mechanism provides the degree of structure sensitivity distinguishing amide I from other backbone modes such as amide II and III.4 Despite numerous theoretical studies aimed at identifying the physical parameters determining the delocalized amide I states, only a few attempts have been undertaken thus far to obtain a more quantitative understanding of the relationship between amide I band profiles and peptide/protein structure. The classical article by Krimm and Bandekar4 reports a normal-mode analysis for nearly all biologically relevant secondary structures and provides valuable spectroscopic fingerprints for the use of IR and Raman spectra for structure analysis of unknown peptides and proteins. Torii and Tasumi simulated the IR-bands of several proteins based on a normal-mode analysis, which describes vibrational mixing in terms of transition dipole coupling.7,8 They demonstrated for the first time that particularly the amide I profile of RR-helices depends on the length of the helix, thus pointing to the necessity of band profile measurements as a tool for structure analysis. During the past years, Keiderling and associates have used molecular force fields, atomic polar tensors, and axial tensors obtained from ab initio calculations on smaller model peptides to model the IR and vibrational circular dichroism (VCD) spectra for various secondary structures, including parallel and antiparallel β-sheets.9-11 Cho and co* Corresponding author. Telephone: (215) 895-2268. Fax: (215) 8951265. E-mail: [email protected].

workers performed very detailed DFT calculations at a high level of theory to characterize the excitonic state of amide I.12-15 Among a variety of insights, their studies provide conclusive evidence for the applicability of the excitonic coupling model for describing the vibrational mixing between adjacent amide I modes in a polypeptide chain.15 Our research group has developed a more empirical approach, which utilizes the excitonic coupling concept to analyze the amide I band profiles of IR, VCD, isotropic, and anisotropic Raman spectra of triand tetrapeptides to determine their main chain torsional angles.16-19 In the present study we developed and applied an extension of this algorithm to simulate the IR, isotropic, and anisotropic Raman and VCD band profiles for intermediate sized peptides, which can be considered as representative for secondary structure motifs in proteins. Our results reveal that vibrational spectroscopy can be utilized for a much more detailed structure analysis of polypeptides than is generally assumed. The advantage of our approach is the combined use of different vibrational spectroscopies and a theoretical approach, which is based on spectroscopically determined coupling parameters. Theory Calculation of Raman and IR Intensities. Our model is based on two well-established facts, namely that the amide I mode of polypeptides is delocalized owing to through-bond and through-space coupling5,14 and that its vibrational states can be described by a model invoking interactions between local oscillators (coupled oscillator model).15,20 Hence, the Schro¨dinger equation for amide I of a polypeptide with n residues can be written as

(H ˆ0 + H ˆ ext)|χ′〉 ) E|χ′〉

(1)

where |χ′〉 is the state vector comprising the n-1 excitonic amide I states, H ˆ 0 is the Hamiltonian of the uncoupled local modes,

10.1021/jp0477654 CCC: $27.50 © 2004 American Chemical Society Published on Web 10/01/2004

16966 J. Phys. Chem. B, Vol. 108, No. 43, 2004

Schweitzer-Stenner

H ˆ ext accounts for the excitonic coupling between the modes, and E represents a set of n-1 excitonic eigenenergies. In what follows we used the term residue to describe an entity comprising a peptide group and the subsequent CR-atom with its side chain and H atom. We start to count the residues at the N-terminal end and disregard the first side chain. For the purpose of the present study we considered all interactions between an oscillator in the jth residue and its neighbors in the residues j(1, j(2,......, j(4. This is sufficient to describe the excitonic states of the extended and helical conformations analyzed in this study, while the calculations for β-sheets would require a more extended Hamiltonian. Thus, the excitonic Hamiltonian can be written as

[

H ˆ ext ) ν˜ 1 ∆12 ∆21 ν˜ 2 δ31 ∆32 δ41 δ42 δ51 δ52 δ61 δ62 ‚ ‚ ‚ ‚ 0 ‚ 0 0

δ13 ∆23 ν˜ 3 ∆43 δ53 δ63 ‚ ‚ ‚ 0

δ14 δ24 ∆34 ν˜ 4 ∆54 δ64 ‚ ‚ ‚ 0

δ15 δ25 δ35 ∆45

δ16 δ26 δ36 δ46

‚ ‚ δ37 δ47

‚ ‚ ‚ δ48

‚ ‚ ‚ ‚ ‚

‚ ‚ ‚ ‚ ‚ ‚

‚ ‚ ‚ ‚ ‚ ‚

‚ ‚ ‚ ‚ ‚ ‚

‚ ‚ ‚ ‚ ‚ ν˜ n-2 ‚ δn-1,n-3 ∆n-1,n-2

]

0 0 0 0 ‚ ‚ ‚ δn-3,n-1 ∆n-2,n-1 ν˜ n-1 (2)

In our notation we distinguish between nearest neighbor coupling ∆j, j(1 and interactions δj, j′ ( j ′ ) j(2, j(3, j(4) between more distant residues. The former involves throughbond as well as through-space coupling.5,14 Coupling parameter values were obtained from recent studies on tripeptides17 and from results of ab initio and DFT calculations,14 whereas δjj′ were assumed to predominantly result from transition dipole coupling (TDC),5 so that they can be calculated by utilizing4

δjj′ ) ξ

(

)

b µj ‚ b µ j′

T jj′)(µ bj′ B T jj′) (µ bj ‚ B -3 5 |T Bjj′| |T Bjj′| 3

(3)

where b µj, b µj′ are the vibrational transition dipole moments of the jth and j′th residues and B Tjj′ is the distance vector from the jth to the j′th residue. ξ is a constant that depends on the units µj, and B Tjj′. chosen to express δjj′, b The vibrational eigenfunctions resulting from the diagonalization of the Hamiltonian H ˆ ext can be written as linear combinations of the basis functions χj of the uncoupled, local oscillators: n-1

χ′i )

aij χj ∑ i)1

n-1

aij Rˆ j ∑ j)1

(5a)

n-1

b µ ′i )

aij b µj ∑ j)1

For the present study we assumed identical Raman tensors and transition dipole moments for the local modes written as18

( ) ( )

a* c* 0 Rˆ j ) Rˆ ) c* 1 0 0 0 d* µ0 ‚ cosϑ µ ) µ0 ‚ sinϑ b µj ) b 0

(5b)

(6a)

(6b)

where Ryy ≡ 1 and the elements a*, c*, and d* are thus expressed in units of ayy. Equation 6a describes the Raman tensor in the earlier described molecular frame shown in Figure 1. Its x-axis coincides with the rotational axis associated with the dihedral angle φ. The xy-plane is nearly coplanar to the peptide plane. The elements c* and d* are linearly dependent.16 µ0 is the amount of the transition dipole moment of the amide I mode, ϑ is its angle with respect to the x-axis of the coordinate system. The use of eqs 6 requires all Raman tensors and dipole moments to be transformed into a common reference system. For the individual tensors and vectors we defined coordinate systems the x-axes of which coincide with the rotational axes of φ. Figure 1 depicts the position and relative orientation of these coordinate systems for a tripeptide.16 We select the coordinate system associated with the C-terminal peptide group as the final reference system.16 Thus, a tensor and a vector in the jth coordinate system have to be rotated (n-1)-j times in order to have their elements expressed in the basis of the reference system. The respective transformations from the jth to the (j+1)th residue read as follows:18

(4)

where the mixing coefficients aij reflect the amplitude of the ith excitonic wave function at the position of residue j. Correspondingly, the Raman tensor and the transition dipole moment of the ith excitonic state are written as

Rˆ ′i )

Figure 1. Location of the coordinate systems chosen for expressing the Raman tensor, transition dipole, and distance vectors in a model system comprising three glycine residues. The depicted peptide conformation is obtained for (φ,ψ) ) (180°, 180°). The z-axes have been omitted for the sake of clarity; they all point out of the drawing plane. The oxygen atoms are drawn in red, nitrogen atoms in blue, carbon atoms in dark gray, and hydrogen atoms in light gray.

Rˆ j (Sj+1) ) U T(ω,ψj ,ξ,φ′j)Rˆ j (Sj)U(ω,ψj ,ξ,φ′j)

(7a)

µ j (Sj) b µ j (Sj+1) ) U(ω,ψj ,ξ,φj) b

(7b)

U(ω,ψj ,ξ,φ′j) ) R(ω)R(ψj)R(ξ)R(φ′j)

(7c)

where

First, the coordinate system Sj of the jth residue has to be rotated by an angle φ′j ) φj-π. Subsequently, a rotation by ξ in the xy-plane is necessary so that the y-coordinate coincides with the CRC bond, which is the rotational axis for ψj. ξ is the angle formed by the yj-axis and the CRC bond. Next, the system is

Secondary Structure Analysis of Polypeptides

J. Phys. Chem. B, Vol. 108, No. 43, 2004 16967

rotated by the dihedral angle ψj. The fourth step involves the rotation by an angle ω, which is formed by the CRC bond and the yj-axis. This rotation causes the x-axis to coincide with the NCR bond. ω and ξ can be obtained from textbooks on peptide structure with 96° and 20°, respectively. The distance vector used in eq 3 can be written as a sum of nearest neighbor vectors j-1

B T ij )

B T l,l+1 ∑ l)i

(8a)

where

r Cl,l + b r Ca + (b r Cl+1 - b r Ca ) B T l,l+1 ) b l

(8b)

where

Bl,l+1(Sj) B T l,l+1(Sj+1) ) U(ω,ψj ,ξ,φj)T

(9)

The Raman tensor Rˆ i of the ith excitonic state obtained by combining eqs. 5a-7a can be used to calculate the isotropic and anisotropic Raman intensity:

1 β′2s,i ) (Tr Rˆ ′i)2 9

Ri ) Im

The respective depolarization ratio is written as

Fi )

2 3γaniso,i 2 45β 2s,i + 4γaniso,i

(11)

The IR intensity of the ith excitonic mode can be calculated by employing

IiIR ) ζ

b µ‚b µ ν˜ 0

(12)

where ζ is a constant that depends on the units of b µi and ν˜ 0. The IR and Raman amide I profiles can be calculated as a superposition of Gaussian bands representing the respective bands of the excitonic modes: n-1

Iiso(Ω) )

[β2s,i fi] ∑ i)1 [γ2i fi] ∑ i)1

[I IR ∑ i fi] i)1

(

3

iπ

)]

(14) where m b j is the magnetic transition moment associated with the local amide I mode of the jth residue. The term ν˜ 12B T12 × (ai1b µ1 - ai2 b µ2) describes the chirality brought about by the magnetic moment at residue 1 induced by the transition dipole moment of residue 2. The terms ν˜ 13B T13 × (ai1b µ1 - ai3 b µ3) and ν˜ 23 B T23 × µ2 - ai3 b µ3) account for the corresponding interaction be(ai2 b tween the first and the third residue and the second and third residue, respectively.22 We can now easily generalize eq 14 to yield the following expression for a polypeptide with n-1 residues. This yields

[

n-1

(

n-1

aij b µ j ∑ aik m bk ∑ j)1 k)1 iπ 2

(∑ ∑

n-2 n-1

ν˜ lmB T lm × (ailb u l - aimb u m)

l)1 m)1

))]

(15)

A simple check reveals that eq 15 becomes identical to eq 14 for n ) 4. Special versions of eq 15 (for m b k ) 0) have been derived earlier by Diem and co-workers.23,24 The contribution of the respective terms in eq 15 depends on the amplitude aij, which the jth residue contributes to the ith excitonic state and, thus, on the strength of excitonic coupling. Since the latter is short-ranged, VCD is generally thought to reflect the relative orientation of adjacent residues.25 A closer look on the above terms, however, suggests that this notion is problematic, since the quantum mechanical mixing between degenerated or nearly degenerated states can in principle yield a high degree of delocalization and, thus, excitonic states with amplitudes on residues that are not in close proximity can contribute to Ri. The VCD profile of amide I was calculated as a superposition of Gaussians by using the expression

∆(Ω) )

ν˜ 0 23 × 10-39

n-1

[Ri fi(Ωi)] ∑ i)1

(16)

where ν˜ 0 is the first moment of the entire amide I′ band profile. Results and Discussion

(13b)

n-1

IIR(Ω) )

[

3

aij b µ j ∑ aij m b j - (ν˜ 12B T 12 × (ai1b µ 1 - ai2 b µ 2) + ∑ 2 j)1 j)1

(13a)

n-1

Ianiso(Ω) )

(13d)

ν˜ 13B T 13 × (ai1b µ 1 - ai3 b µ 3) + ν˜ 23B T 23 × (ai2 b µ 2 - ai3 b µ 3))

Ri ) Im

1 2 γ′aniso,i ) [(Rˆ ′xx,i - Rˆ ′yy,i)2 + (Rˆ ′yy,i - Rˆ ′zz,i)2 + 2 3 (Rˆ ′zz,i - Rˆ ′xx,i)2] + [(Rˆ ′xy,i + Rˆ ′yx,i)2 + 4 (Rˆ ′yz,i - Rˆ ′zy,i)2 + (Rˆ ′zx,i - Rˆ ′xz,i)2] (10)

)

2

Here, Ωi denote the eigenenergy of the ith mode in units of cm-1 and σi is a measure of the bandwidth. Calculation of the VCD Signal. In a recent contribution we reported the following equation for the rotational strengths of the excitonic states of a tetrapeptide:21

l

where b rCl and b rCal are the vectors from the origin of the coordinate system Sj of the jth residue to the peptide carbon of the same residue and to the CR-atom of the (j+1)th residue, respectively. b rCl+1 is the vector from the origin of Sj to the carbonyl carbon of the (j+1)th residue. The distance vectors B Tl,l+1 used in eq 8 have to be transformed into the common reference system by means of the subsequent performance of the operation

(

(Ω - Ωi) 1 exp fi ) 2σi2 σix2π

(13c)

Concepts. We used the formalism outlined in the preceding section to simulate amide I band profiles for various secondary structures of polypeptides of various length by using MATLAB software. Our calculations do not explicitly consider any solvent effects, but local wavenumbers and some coupling parameters were obtained for peptides in D2O. Thus, we implicitly assume

16968 J. Phys. Chem. B, Vol. 108, No. 43, 2004 that D2O is used as solvent so that the analyzed mode is in fact amide I′. This allows us to neglect vibrational coupling between amide and the water bending mode, which seriously complicates the interpretation of spectra of peptides in H2O.26 Furthermore, we do not consider any inhomogeneity owing to side chain dependent peptide-solvent interactions, which has been suggested to be relevant for the folding of alanine-based peptides.27 In what follows, the term “amide I′ ” is used if specific conformations are dealt with. The term “amide I” is used for general considerations. In a first step we focused on conformations assignable to the upper left-hand quadrant of the Ramachandran plot. For the sake of simplicity we assume that the local wavenumbers in a polypeptide chain are identical, knowing that this might be an oversimplification, since amide I wavenumbers have been shown to depend on the conformation14 as well as on the choice of the amino acid residue.28 The second step describes in detail the band profiles of right-handed helical conformations. In this context we evaluate in detail the length dependence of the band profiles for RR-helical conformations. To make touch on recent experimental results on isotopically labeled peptides, we discuss the simulated amide I profiles of peptides with 13C substitutions at their backbone carbonyl carbons. More complex calculations for β-sheets and hairpins will be described in future publications. Amide I′ Simulation for Conformations in the Upper Left Square of the Ramachandran Plot. Figure 2 depicts the IR, isotropic, and anisotropic Raman depolarization ratio dispersion and VCD profiles of amide I′ for the following conformations of a polypeptide with 20 residues: canonical PPII ((φ,ψ) ) -75°, 145°), antiparallel β-strand (APβ)((φ,ψ) ) -139°, 134°), extended (E) conformation ((φ,ψ) ) -140°, 160°), and parallel β-strand (Pβ) ((φ,ψ) ) -119°, 113°). The corresponding nearest neighbor coupling parameters provided in the figure legend were taken from earlier data on tri- and tetrapeptides (for PPII and E)18,21 and from the theoretical calculations of Choi et al. (for APβ and Pβ).14 TDC between second, third, etc. neighbors were calculated by using eq 3. All these simulations were carried out with σ ) 9 cm-1 for the half-halfwidth of the individual Gaussian bands and a wavenumber value of 1658 cm-1 for the local amide I′ modes. This is close to the experimentally observed value for the band of the central residue in tetraalanine.21 For the sake of simplicity, we did not consider intrinsic magnetic dipole moments for the VCD calculations (m b j ) 0). For the orientational angle of the transition dipole moment (2.0 esu cm) we used ϑ ) -96°,29 which corresponds to 20° with the carbonyl bond. For all conformations investigated we obtained a noncoincidence between the isotropic Raman and IR peak wavenumber. The IR band appears at lower wavenum˜ IR bers. The wavenumber difference ∆iso-IR ) ν˜ iso peak - ν peak is -1 most pronounced for APβ (20 cm ). For the other conformations we obtained a splitting of 13 cm-1. As reported earlier, the anisotropic profile is useful to discriminate between PPII on one side and Aβ and E on the other side, since it exhibits a larger upshift from the IR band position for the former (∆aniso-IR -1 ) ν˜ aniso ˜ IR peak - ν peak ) 7 cm ) than for the latter (∆aniso-IR ) -2 cm-1 for Aβ and 2 cm-1 for E). The IR and isotropic Raman profiles of Pβ are positioned close to those of PPII, but its anisotropic profile is peculiar in that it depicts the largest ∆aniso-IR (11 cm-1) and smallest ∆iso-IR (4 cm-1) value. Our results confirm the earlier stated notion that the anisotropic Raman band is most useful for discriminating different conformations in the left-handed quadrant of the Ramachandran plot.30 For the isotropic band profiles, only Aβ discriminates itself from the other conformations owing to the higher wavenumber position

Schweitzer-Stenner

Figure 2. Isotropic Raman band, anisotropic Raman band, IR band, depolarization ratio dispersion, and VCD couplet of amide I′ simulated for conformations assignable to the upper-left quadrant of the Ramachandran plot: polyproline II (∆j,j(1 ) 5 cm-1, red, solid line), antiparallel β-strand (∆j,j(1 ) 6 cm-1, solid, black line), parallel β-strand (∆j,j(1 ) 4 cm-1, dash, green line), and extended β-strand (∆j,j(1 ) 4 cm-1, dash, black line). IR-absorption and VCD spectra were calculated in units of M-1 cm-1. The vertical lines mark the position of the IR band (solid red) and the isotropic Raman band (dashed red) for the PPII conformation.

(defined as the position of its maximum). Interestingly, all IR bands are very similar in terms of their band position and profile. They all peak around 1653 cm-1 and exhibit an asymmetry toward higher wavenumbers. From this finding it follows that IR spectroscopy alone is not a suitable tool for a detailed analysis of the unfolded state of peptides and proteins. The depolarization ratio dispersion curves of the conformations are very similar. They all reflect the noncoincidence between isotropic and anisotropic Raman scattering. Apparently, Aβ shows a somewhat more pronounced change at the low wavenumber side of the Raman bands. To elucidate the general relevance of the noncoincidence between the peak position of three amide I′ profiles for the discrimination between different conformers in the upper left square of the Ramachandran plot we calculated the respective wavenumber positions as a function of φ for a fixed ψ-value of 150°. As shown in Figure 3, ∆iso-IR significantly decreases with increasing φ values. Decreasing the φ value from its PPII (or PPII-like) values to that of more extended conformations causes the anisotropic band position to downshift away from the position of the isotropic to that of the IR band. Apparently the φ-sensitivity of the relative band positions is most pronounced in the region between -50° and -100°. This demonstrates that the noncoincidence parameters are particularly suitable for


Figure 3. Wavenumbers of the peak position of the amide I′ band of IR, isotropic and anisotropic Raman spectra calculated as a function of φ for ψ ) 150°.

identifying PPII and PPII-like conformations, as recently shown for the monomeric state of the amyloid peptide Aβ1-28.30

J. Phys. Chem. B, Vol. 108, No. 43, 2004 16969 The VCD spectra for the above conformations are different. PPII exhibits a strong negative couplet, in agreement with experimental spectra of polypeptides, which predominantly adopt this conformation.25 The positive couplet of E is much less pronounced. The VCD signals of the two β-strand conformations are very small compared with those of PPII and E. Our result is also in qualitative agreement with simulations, which Keiderling and his associates carried out for several short and medium-sized peptides.9,10 Their simulations were based on the ab initio calculated parameters. For β-strand conformations they obtained a less symmetric, more negatively biased signal,9 in agreement with what we experimentally observed for trivaline.17 This reflects intrinsic magnetic transition dipole moments, which we did not take into consideration. Altogether, the above calculations demonstrated that a combined use of the considered spectroscopies enables one to discriminate between PPII, Aβ, and Pβ conformations of long and intermediate sized peptides. In this context the use of the anisotropic band profile and VCD for the identification of PPII is particularly noteworthy in view of it’s relevance for the understanding of the unfolded state of proteins and peptides.31,32

Figure 4. Isotropic Raman band, anisotropic Raman band, IR band, depolarization ratio dispersion, and VCD couplet of amide I′ simulated for right-handed helical conformations: RR(∆j,j(1 ) 7 cm-1, solid) and 310(∆i,i(1 ) 0.5 cm-1, dash). The vertical lines mark the position of the IR-(solid) and the isotropic Raman band (dash) of the RR conformation. IR-absorption and VCD spectra were calculated in units of M-1 cm-1.


Schweitzer-Stenner

Figure 5. Isotropic Raman band, anisotropic Raman band, IR band, depolarization ratio dispersion, and VCD couplet of amide I′ simulated for RR helices with 20 (solid), 15 (dash), 12 (dotted), 6 (dash-dot) and 4 (dash-dot-dot) residues. In the lowest panel only the VCD couplets for n ) 20 and 12 are depicted. The vertical lines mark the position of the respective bands for n ) 20 (solid) and n ) 4 (dash) to visualize the peak shift. IR-absorption and VCD spectra were calculated in units of M-1 cm-1.

Amide I′ Simulation for Right-Handed Helices. Figure 4 depicts the IR, Raman, and VCD profiles for the RR- and 310 conformations of the 20-residue peptide. The nearest neighbor coupling parameters were again obtained from Choi et al.14 We chose a somewhat lower value (compared with that for PPII and β-strands) for the wavenumber of the local modes (1640 cm-1) to mimic the combined influence of intramolecular hydrogen bonding, conformational effects,6 and hydrogen bonding between D2O and the carbonyl bonds of the peptides.33,34 This shift moves the peak position of the IR-band to1633 cm-1, which coincides with the experimentally observed amide I′ position of the model peptide suc-FS 21 (A5(A3RA)3A-NH2 (suc ) succinyl).35 It is substantially downshifted from the classical wavenumber found for R-helices in proteins, i.e, 1655 cm-1,1 most likely due to the partial hydration of the backbone carbonyl groups.33,34 The wavenumber positions of the bands are nearly coincident, but a small ∆iso-IR value of 4 cm-1 is noteworthy. The anisotropic peak is slightly asymmetric toward lower wavenumbers. This is also reflected by the depolarization ratio

dispersion, which is particularly pronounced at the low wavenumber wing of the amide I′ Raman band. For the 310-helix, our simulation reveals a downshift from the respective RR-position for all three band profiles. For the IR band this is in agreement with simulations on nanopeptides by Bour et al.10 Even more important is our finding that the anisotropic Raman band appears now slightly upshifted with respect to the isotropic band position (∆aniso-iso ) 2.5 cm-1). As a consequence, the depolarization ratio dispersion is qualitatively different from that of RR. Hence, our results suggest that polarized Raman spectroscopy can be used to discriminate between RR and 310 helices. The difference between the spectroscopic properties reflects a qualitatively different set of coupling parameters. While nearest neighbor coupling is strong for RR (7 cm-1), it is nearly negligible for 310 (0.5 cm-1). The excitonic coupling scheme of the latter is rather dominated by second neighbor coupling.6 The calculated VCD signal of RR exhibits a positive couplet. In principle this is in full agreement with experiments on a


J. Phys. Chem. B, Vol. 108, No. 43, 2004 16971

Figure 6. Normalized IR and anisotropic Raman band of amide I′ simulated with 20 (solid), 15 (dash), 12 (dotted), 6 (dash-dot) and 4 (dashdot-dot) residues.

variety of peptides and proteins,25,36 but the situation becomes more complicated for deuterated peptide groups (NHfND), for which a W-shaped signal has been frequently observed.36 For 310, we obtained a smaller positive couplet. Bour et al. calculated W-shaped signals for the 310 conformation of an A9-peptide with significantly different intensities for the protonated and deuterated peptide.10 Yoder et al. obtained a positive, though somewhat more negatively biased, couplet for the 310-helix of blocked L-(RMe)Val homopeptides in trifuoroethanol.37 To evaluate the length dependence of the band profiles we first performed calculations for R-helical peptides of different length. Figure 5 displays the amide I′ profiles, depolarization ratio dispersion, and (some) VCD signals for R-helices with n ) 20, 15, 12, 6, and 4 residues. The IR band shows an upshift with decreasing residue number. For the shortest peptide (n ) 4), the upshift is 5 cm-1 with respect to the n ) 20 wavenumber position. The corresponding shifts of isotropic and anisotropic Raman are slightly less pronounced. Depolarization dispersion differences are significant at the low wavenumber side of the amide I′ band region. The lower panel shows only two (positive) VCD couplets for n ) 20 and n ) 12. Couplets for shorter helices are significantly less intense. All these changes occur predominantly for residue numbers below n ) 12, because larger n positions and band shapes remain nearly unaffected by changes of the residue number. This is even better illustrated in Figure 6, which displays

normalized IR profiles for the investigated residue numbers. Changes between n ) 20 and 12 are marginal, but for smaller numbers of residues the band shifts down and becomes significantly more asymmetric. The corresponding changes of the anisotropic band shift are less pronounced, though clearly detectable. This asymmetry of the IR band of amide I′ has already been discussed in earlier papers.7,8,10 Particularly relevant are the detailed studies of Torii and Tasumi,7,8 in that these authors demonstrated the relevance of this finding for a more detailed analysis of protein IR spectra. It should be noted that the asymmetry of the real band shape of short helices might even be more pronounced than simulated, because very recent semiempirical quantum chemistry calculations by Ham et al. suggested a significant heterogeneity of the local amide I′ wavenumbers for short helical peptide, whereas longer helices (n > 10) exhibited significant variations of the local wavenumber only close to the terminal groups.38 The above result indicates that care has to be taken in using the IR amide I′ as a tool for secondary structure composition. One of the generally applied methods involves decomposition into Gaussian bands, which are assigned to different secondary structures.39 With respect to R-helices, this is apparently an appropriate strategy only for helices containing at least nine residues. Many proteins, however, contain relatively short helical sections, the amide I′ band of which are definitely not describable by a symmetric band. As we will discuss in more detail


Schweitzer-Stenner

Figure 7. Isotropic Raman band, anisotropic Raman band, IR band, and depolarization ratio dispersion of amide I′ simulated for a 20-residue peptide containing an RR-helical segment of 20 (dash), 15 (dotted), 12 (dash-dot), 6 (solid-dot) and 4 (dash-dot-dot) and zero (solid) residues. The positions of the respective bands are marked for the fully RR helical (solid) and the fully PPII (dash) conformation. IR absorption was calculated in units of M-1 cm-1.

below, the extent of amide I′ band asymmetry depends on the strength of excitonic coupling, which complicates the case even further. The IR amide I′ band is frequently used in a variety of experiments to probe the thermal folding and unfolding of helices.35,36,40,41 Recently, elegant temperature jump experiments were carried out to monitor these processes on a nanosecond time scale.35,42 We make reference to the paper of Williams et al.,35 who used steady-state and time-resolved IR spectroscopy to probe the thermodynamics and kinetics of the helix unfolding of suc-FS 21 in D2O, respectively. The IR spectra were measured between 8.3° and 50°. At 8° the amide I′′ appears at 1633 cm-1. With increasing temperature the band shifts to higher wavenumbers (we estimated ca. 7 cm-1 from Figure 1a of their paper) and the band shape becomes asymmetric toward higher wavenumbers. A series of difference spectra obtained by subtracting the spectrum obtained at the lowest temperature from all the other spectra depict a maximum at 1655 cm-1 (unfolded state) and a minimum at 1626 cm-1 (folded state). There are two possible models to interpret these results. For short helices the Zimm-Bragg theory43 reduces to a two-state, all-or-nothing model for which the entire peptide is either in the helical or in random coil state. However, isotopic substitution experiments by Silva et al. have clearly shown for another alanine-based polypeptide that the helix unwinds noncooperatively from the ends.44 This clearly suggests that one has to consider mixtures of peptides with helical segments of different length. The simulations plotted in Figure 7 reflect such a situation in that

they were carried out for a 21-residue peptide with nR ) 21, 15, 12, 9, 6, 4, and 0 consecutive residues in the RR conformation. The helical segment was always assumed to be in the center of the peptide in order to account for the unwinding from the ends. For the nonhelical part we assumed a PPII conformation, since ECD measurements on a peptide similar to suc-FS 2145 must be interpreted as indicating that the thermal denaturation produces an unfolded state with significant PPII content. Our results indicate that the choice of a conformation for the unfolded state is nearly irrelevant for the IR-band profile. However, some differences might be experimentally detectable owing to the modest conformational dependence of the local wavenumber on the dihedral angles in the upper-left quadrant of the Ramachandran plot.15 Our simulations show how the respective PPII band (1656 cm-1 for IR) increases at the expense of the RR-helix band. In the IR spectrum, the PPII peak intensity is already larger than the RR intensity for nR ) 9. For nR ) 12, the RR peak appears upshifted by 3 cm-1 from the corresponding position of the fully helical peptide. In the experiment, the RR peak measured at the highest temperature (50 °C) is upshifted by ca. 7 cm-1 from its 8.3 °C position. As shown by Lednev et al.,45 this involves a thermal shift of 4 cm-1, so that only 3 cm-1 can be assigned to the shift caused by conformation changes. Hence, the comparison between our simulations and the data of Williams et al.35 suggests an average helical length of 12 at 50 °C. The thermodynamic data reported by these authors yield a helical fraction of 0.64 at 50 °C. This is in good accordance with our


Figure 8. Anisotropic Raman band, IR band, and VCD couplet of amide I′ of a 20-resiude peptide simulated with ∆i,i(1 ) 7 cm-1, ϑ ) -96° (solid black), ∆i,i(1 ) 9 cm-1, ϑ ) -96° (dash-dash), ∆i,i(1 ) 12 cm-1, ϑ ) -96°(dash-dot-dot), ∆i,i(1 ) 7 cm-1, ϑ ) -86° (solid blue), and ∆i,i(1 ) 7 cm-1, ϑ ) -106° (dash blue). IR-absorption and VCD spectra were calculated in units of M-1 cm-1.

estimation. Generally, the respective RR shifts of the isotropic and anisotropic Raman profiles is less pronounced than that of the IR profile. Interestingly, the depolarization ratio dispersion curves are significantly different only for small n values, i.e., n ) 9, 6, and 4. This suggests that their measurement can serve as a very useful tool to monitor the last phase of helix unfolding. Our simulations yielded a significant noncoincidence for the corresponding bands of the unfolded state, which is characteristic for the assumed PPII conformation. For more extended and randomized structures the anisotropic peak would be close to the IR peak position. Thus far, all band profiles of RR were simulated with a nearest neighbor coupling constant of 7 cm-1, as suggested by the DFT calculation of Choi et al.14 This value is substantially lower than the 12 cm-1, which Torii and Tasumi obtained from their ab initio calculations of a blocked diglycine peptide5. To check the influence of the excitonic coupling parameters on position and shape of the band profiles of the RR-helical peptide, we performed calculations for a n ) 20 residue peptide using ∆j,j(1 values of 7, 9, and 12 cm-1. As shown in Figure 8, this causes a significant broadening and asymmetry of both the IR and the anisotropic Raman band profile. For ∆i,i(1 ) 12 cm-1 a second peak emerges at lower wavenumbers. This is close to what Bour et al. simulated for the IR-band profile of a A9-peptide.10 The VCD changes dramatically; a negative couplet is created for 9 cm-1 and an inversed W-shape for 12 cm-1. In a next step we investigated the influence of the second and third neighbor coupling by changing the direction of the transition dipole moment by (10°. ∆i,i(1 ) 7 cm-1 was used for these simulations. Even though these changes involved substantial changes of the corresponding coupling constants, the

J. Phys. Chem. B, Vol. 108, No. 43, 2004 16973 band shapes were only slightly affected (Figure 8, blue curves). An orientational change by +10° causes a narrowing of the IR band, whereas the anisotropic Raman band shifts up and becomes asymmetric toward the lower wavenumber region. On the contrary, a change by -10° causes an asymmetric IR band and a downshift of the anisotropic band. In both cases the VCD spectrum depicts a positive couplet. The symmetric amide I′ profiles in the IR spectra of alanine-based peptides35,36,44 suggest that that ∆i,i(1 ) 7 cm-1 is a more appropriate approach than the higher coupling values. However, the available experimental data do not allow identifying the most appropriate choice for the average transition dipole moment orientation. Our laboratory is planning detailed Raman, IR, and VCD measurements on alanine-based peptides to clarify this issue. The simulations reveal that VCD should be particularly useful for an exact determination of coupling parameters. Selective labeling of the carbonyl carbon with 13C shifts the respective IR band to significantly lower wavenumbers. The intensity of the shifted band depends on the excitonic coupling strength. Keiderling, Decatur, and their respective associates have carried out various IR and VCD studies on isotopically labeled alanine-based helix-forming peptides.44,46 We selected the amide I′ bands of the IR and VCD spectra of Ac(A4K)3A4Y-NH2) (nL) and of its four isotopically labeled derivatives AcA4K(A4K)2A3Y-NH2 (L1), AcA4KA4KA4KA4YNH2 (L2), Ac(A4K)2A4KA4Y-NH2 (L3), and Ac(A4K)3A4YNH2 (L4) reported by Silva et al.44 The 13C labeled residues are underscored. Since the authors provided evidence for the C-terminal residues to be nonhelical, we carried out a simulation for a 20-residue peptide, the first 17 residues of which were RR helical, whereas the last three residues were assumed to adopt PPII. As shown in Figure 9, our simulation yields band profiles that are slightly asymmetric toward higher wavenumbers. The IR band profile nicely compares with the experimental one reported by Silva et al.44 The spectra of the L1-L3 clearly display a second maximum at 1598 cm-1. For the IR spectrum the relative peak intensities are close to what Silva et al. observed experimentally.44 The 1598 cm-1 IR band of L4 emerged as only half as intense as the corresponding L2 and L3 band. This is again in excellent agreement with the experimental data and reflects the fact that the C-terminal residues were assumed to adopt PPII rather than RR. The calculated VCD signals compare less well with the experimental spectra. For the unlabeled peptide our calculation yielded the classical positive couplet with an minimum at 1650 cm-1 and a maximum at 1625 cm-1, while the authors obtained a W-shaped signal with minima at 1650 cm-1 and 1620 cm-1 and a maximum at 1630 cm-1. For L1, we obtained a positive couplet that appears redshifted with respect to signal of the unlabled species, which does not coincide well with the experimental spectrum. For L2, however, we obtained a W-shaped signal with a relatively strong lobe at 1600 cm-1, which was also observed experimentally. However, the corresponding lobe is less pronounced for L3 and absent for L1, whereas the experimental VCD spectrum of L2 is comparable with that of L1 and L3. For L4, we again reproduced the minimum at 1650 cm-1, but the calculated maximum at 1615 cm-1 is at variance with the experimentally observed maximum at 1630 cm-1 and the minimum at 1625 cm-1. Interestingly, the calculated VCD spectra are closer to the DFT-based simulations by Silva et al.44 who also do not reproduce the W-shaped signal from the unlabeled parts of L0-L4. As shown above, the VCD signal of RR helices is very sensitive to changes of coupling constants and transition dipole


Schweitzer-Stenner

Figure 9. Isotropic Raman band, anisotropic Raman band, IR band, depolarization ratio dispersion and VCD couplet of amide I′ simulated for a 20 residue peptide. Residues 1-17 were assumed to be RR-helical, the residues 18, 19, and 20 were assumed to adopt a polyproline II conformation. IR-absorption and VCD spectra were calculated in units of M-1 cm-1. The simulation was carried out for an unlabeled peptide (solid) and the isotopically labeled derivatives L1 (dash long), L2 (dash-dot-dot), L3 (dash medium), and L4 (dash dot).

moments. The differences between the simulations obtained for the differently labeled peptides indicate that we did not identify the ideal set of coupling constants and transition dipole moments for a robust VCD calculation. Another likely source for the obtained instability is our use of a degenerate set of vibrational eigenstates for a distinct structure, which makes the individual amplitudes aij susceptible to small changes of coupling constants. An analysis of the aij values reveals a significant delocalization of the excitonic states, in agreement with ref 38. Equation 15 reveals that this must have a serious impact on the VCD signal. This is less a problem for the extended conformations in the upper left square of the Ramachandran plot, since the respective coupling constants are smaller particularly for nonnearest neighbor interactions. Summary We have developed an algorithm by means of which we simulated the amide I′ band profiles of the IR, isotropic, and anisotropic Raman spectra of polypeptides of various length.

The approach is based on an excitonic coupling model, which considers coupling between first, second, third, and fourth neighbors. In addition, we developed and employed a formalism to simulate the corresponding VCD signals. Our simulations reveal that different secondary structures (i.e., PPII, parallel and antiparallel β-strand, extended β-strand) assignable to the upper left quadrant of the Ramachandran plot can be distinguished particularly by their different anisotropic Raman and VCD spectra. This is particularly important for spectroscopic investigations of the unfolded state of peptides. For right-handed helices we found that the combined use of IR and Raman spectroscopy provides a suitable tool to discriminate between RR and 310 helices. For short helices (n

Secondary Structure Analysis of Polypeptides Based on an Excitonic

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