Theoretical Study of Internal Field Effects on Peptide Amide I Modes

J. Phys. Chem. B 2005, 109, 5331-5340

5331

Theoretical Study of Internal Field Effects on Peptide Amide I Modes Hochan Lee, Seong-Soo Kim, Jun-Ho Choi, and Minhaeng Cho* Department of Chemistry and Center for Multidimensional Spectroscopy, DiVision of Chemistry and Molecular Engineering, Korea UniVersity, Seoul 136-701, Korea ReceiVed: August 26, 2004; In Final Form: January 10, 2005

Charged terminal groups or polar side chains of amino acids create spatially nonuniform electrostatic potential around intramolecular peptide bonds and induce amide I mode frequency shifts in polypeptides. By carrying out a series of quantum chemistry calculation studies of various ionic di- and tripeptides as well as dipeptides of 20 different amino acids, these internal field effects on vibrational properties are theoretically investigated. The amide I local and normal mode frequencies and dipole and rotational strengths determining IR and vibrational circular dichroism intensities, respectively, are found to depend on the polar nature of side chains, whereas the vibrational coupling strength weakly does so. The empirical correction and fragment analysis methods were used to theoretically calculate the amide I local mode frequencies and dipole and rotational strengths. These values were directly compared with ab initio and density functional theory calculation results, and the agreements were found to be quantitative.

I. Introduction Amide I infrared absorption spectrum of polypeptide has been found to be strongly dependent on its three-dimensional (3D) structure so that the structure-spectrum relationship has been extensively studied.1-14 Although a number of examples already exist in the literature that aim at extracting critical information on the secondary structure content of a given polypeptide from its amide I IR band,15-24 one still needs a refined theoretical method that is capable of predicting amide I local mode frequencies and coupling constants of any arbitrary polypeptides. Recently, we have developed an empirical correlation method for calculating an amide I local mode frequency shift when the target peptide is surrounded by other peptides or solvent molecules.25,26 When a peptide bond is exposed to a spatially nonuniform electrostatic potential, its electronic structure of the peptide bond changes, molecular structure is slightly distorted, peptide vibrational potential energy surface also changes, and thus, peptide vibrational frequencies shift. It was shown that the amide I mode frequency of the mth peptide bond can be expressed as a multivariate linear equation with respect to the electrostatic potentials at four different sites of a given peptide bond26 4

ν˜ m ) ν˜ 0 +

lj(m)φj(m) ∑ j)1

(1)

where ν˜ 0 is the reference amide I mode frequency of an isolated peptide bond without other peptides or solvent molecules around it. The Coulombic electrostatic potential at the jth site of the mth peptide bond was denoted as φj(m). The four sites of a peptide bond are C(dO), O(dC), N, and H(-N) atoms. The electrostatic potential is created by partial charges of surrounding peptides and solvent molecules. In ref 26, we have determined the four partial charges of a peptide bond. To quantitatively describe solvatochromic amide I mode frequency shift of an * Author to whom correspondence should be addressed. E-mail address: [email protected].

N-methylacetamide (NMA) in liquid water, the partial charges of the three atoms of a water molecule were obtained by carrying out Hartree-Fock calculation of a single water molecule. The expansion coefficients, lj, in eq 1 were already determined by fitting numerous ab initio-calculated amide I mode frequencies for NMA-water clusters,25 NMA-methanol clusters,27 dipeptides,26 tripeptides,28 and polypeptides.29 Although we have demonstrated that the four-site model, eq 1, works well in describing amide I mode frequency shift, fluctuation, and dephasing in solutions, the peptides considered before were electrically neutral, and the constituent amino acid was either glycine or alanine. Therefore, before the four-site model is used to calculate amide I normal mode frequencies, eigenvectors, transition dipoles, and rotational strengths of any arbitrary protein, one more critical issue, which is internal (electrostatic) field effects, should be studied. Here, the two internal field effects from (1) the intramolecular ionic field and (2) the amino acid side chain on the amide I mode frequencies will be studied in detail by carrying out systematic quantum chemistry calculations for a variety of mono- and dipeptides. The former issue is related to experimental studies of amide I IR-band analysis for varying pH.30-33 A brief discussion will be presented in section II. The second goal of this paper is to elucidate the side-chain effects on the vibrational coupling constants. To construct the vibrational exciton Hamiltonians for amide I modes of a given protein and to numerically calculate various one-dimensional (1D) IR and vibrational circular dichroism (VCD) spectra as well as two-dimensional (2D) IR pump-probe or photon-echo spectra, it is necessary to determine the vibrational coupling constants between any two neighboring peptides. In ref 34, we suggested that the coupling constant map, J(φ, ψ), obtained from the high-level ab initio calculation results of glycine or alanine dipeptide analogues, where φ and ψ are the two dihedral angles determining the polypeptide backbone structure, can be directly used for such a purpose. However, since the model dipeptide used to obtain the J(φ, ψ) contour map was either glycine or alanine dipeptide, the side-chain effects on the vibrational coupling constants were not fully

10.1021/jp0461302 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/26/2005

5332 J. Phys. Chem. B, Vol. 109, No. 11, 2005

Lee et al. After the structures of neutral dialanines were determined, we carried out HF/6-311++G** geometry optimizations of three different ionic (cationic, anionic, and zwitterionic) dialanines in each constrained secondary structure. However, except for the ionic groups, such as amino and carboxyl groups, not only the two dihedral angles φ and ψ but also all other bond lengths and angles were fixed so that the backbone structures of cationic, anionic, and zwitterionic dialanines were identical to that of the neutral dialanine, which is the reference molecule. These additional constraints were deliberately used to specifically investigate the intramolecular ionic field effect only. To calculate the electrostatic potentials at four sites of the peptide bond, the partial charges of the NH3+ and COO- groups should be determined first. Since we are interested in the net amide I mode frequency shift of cationic, anionic, or zwitterionic dialanines from that of the neutral dialanine,

Figure 1. Molecular structures of di- and trialanine. The cationic, anionic, and zwitterionic di- and trialanines have (NH3+, COOH), (NH2, COO-), and (NH3+, COO-) terminal groups. For the deuterated diand trialanines, all amide N-H, COOH, NH2, and NH3+ groups are replaced with N-D, COOD, ND2, and ND3+, respectively. The peptide close to the amino (carboxyl)-terminus is denoted as the peptide 1(2).

explored yet. Therefore, whether the same contour map of J(φ, ψ) from glycine or alanine dipeptides can still be used to predict the coupling constants of any arbitrary proteins having various amino acids other than glycine or alanine has not been theoretically addressed before. In the present paper, we will show that the side-chain effects on amide I mode coupling strengths are not important, which is quite crucial because the J(φ, ψ) contour map can be of use for any combination of two neighboring peptides in a given polypeptide. Finally, the third goal of this paper is to examine whether the fragment analysis method for calculating dipole and rotational strengths, which determine the amide I IR and VCD intensities, respectively, is still useful even for those dipeptides having different side chains. As will be shown in this paper, the fragment analysis method works very well and reproduces both signs and magnitudes of rotational strengths of amide I normal modes of various dipeptides. II. Intramolecular Ionic Field Effect On Amide I Mode Frequency Shift To study both intramolecular ionic field and side-chain effects on the amide I mode frequencies of polypeptides, we have performed ab initio molecular orbital calculations with the Gaussian 98 program.35 Geometry optimization and vibrational frequency analysis were performed at the RHF/6-311++G** or B3LYP/6-31G* levels. The scaling factors used to make corrections to the harmonic vibrational frequencies thus calculated are 0.8929 and 0.9613, respectively.36 A. Dialanine. We first consider the dialanine molecule in Figure 1 to study the intramolecular ionic field effect. The dialanine contains a single peptide bond, and the free amino and carboxyl groups are in close proximity to the peptide bond. For a neutral dialanine with NH2 and COOH groups, we considered three different conformations, i.e., right-handed R helix (RHH), antiparallel β sheet (APB), and polyproline II (PII), where the two dihedral angles (φ, ψ) are fixed to be (-57, -47), (-139, 135), and (-78, 149), respectively. Other than these dihedral angles, all other degrees of freedom are relaxed during the geometry optimization process. Then, these three optimized structures, neutral RHH, APB, and PII dialanines, will be considered to be the reference molecules.

4

ν˜ ionic ) ν˜ neutral +

ljδφj ∑ j)1

(2)

, the partial charges of the three hydrogen and one nitrogen atoms of the ammonium cation were obtained by taking the differences of the partial charges of the four atoms in the NH3+ of the cationic dialanine from those of the NH2 group of the neutral dialanine. Similarly, the partial atomic charges of the COO- were determined. These partial charge differences were used to numerically calculate the electrostatic potential differences, δφj, in eq 2. The amide I local mode frequencies obtained from the HF calculations are found to be linearly proportional to the corresponding CdO bond lengths, which confirms that the linear relationship (see fig 3 of ref 29) between the two is still valid for ionic di- and trialanines (including other dipeptides with varying side chains studied below). The bar charts of ab initiocalculated amide I mode frequencies are shown in Figure 2 for the sake of comparison. The internal ionic field-induced amide I mode frequency shift can be as large as tens of wavenumbers. The intramolecular ionic field-induced frequency shifts are strongly dependent on the secondary structure simply because the relative distance and orientation of the peptide bond with respect to the centers of NH3+ and COO- are determined by the 3D conformation of a given dialanine. When the dipeptide is in the APB structure, the amide I mode frequency is slightly blue-shifted when the NH2 group becomes positively charged. On the other hand, the negative (COO-) ionic field induces a strong red-shift of the amide I mode frequency. In the case of zwitterionic dialanine, these two effects induced by NH3+ and COO- groups add up together to make the amide I mode frequency overall red-shifted. This additive effect is also found in the other two cases of PII and RHH dialanines. B. Trialanine. We next consider trialanines shown in Figure 1. This model trialanine has two peptide bonds so that not only the intramolecular ionic field but also the intramolecular peptide-peptide interaction could induce amide I mode frequency shift. Again, three representative secondary structures, RHH, APB, and PII, are considered and the same constraints used in the geometry optimization of dialanine are used. Although the two amide I normal mode frequencies are affected by the presence of the intramolecular ionic fields, the local mode picture is much easier and more useful for quantitatively describing the amide I local mode frequency shifts induced by the intramolecular ionic fields. Since the ab initio vibrational analysis does not directly provide us the amide I local mode frequencies nor coupling constants, the Hessian matrix recon-

Internal Field Effects on Peptide Amide I Modes

J. Phys. Chem. B, Vol. 109, No. 11, 2005 5333

Figure 2. (a) Local amide I mode frequencies of deuterated neutral, cationic, anionic, and zwitterionic dialanines are compared with one another. (b) Local amide I mode frequencies of deuterated trialanines.

struction method26,28 was used to obtain the two amide I local mode frequencies (diagonal Hessian matrix elements) and coupling constant (off-diagonal Hessian matrix elements). In Figure 2b, the two amide I local mode frequencies are plotted for different ionic forms of trialanines. For all these cases, the amide I local mode frequencies of zwitterionic trialanines are close to the average values of those of anionic and cationic trialanines, indicating that the internal field effects are again additive. This fact that the cationic and anionic field effects, i.e., electrostatic potentials created by the positive and negative ionic groups, are additive can be a circumstantial evidence supporting the simple model of eq 1 (note that eq 1 can be written as a sum of contributions from the cationic group (NH3+) and the anionic group (COO-)). Now, we directly compare these ab initio-calculated amide I local mode frequencies of di- and trialanines with those obtained by using eq 1. Using the net partial charges of ionic groups, we calculated the net frequency shifts of three ionic (cationic, anionic, and zwitterionic) di- and trialanines in a given secondary structure. Then, by adding these net frequency shifts to the amide I local mode frequencies of the neutral (reference) di- and trialanines, the shifted amide I mode frequencies are predicted with eq 2 and are compared with the ab initio calculation results in Figure 3a and c. The agreement appears to be acceptable, and this confirms that the four-site model in eq 1 with properly adjusted parameters and partial charges can be of use in describing intramolecular ionic field effects on the amide I mode frequency shift. Although we have considered normal di- and trialanines to study the internal ionic field effects on the amide I frequency, it would also be useful to carry out the same series of calculations for deuterated peptides. In an aqueous solution of peptides, it is well-known that the amide I vibrational mode is coupled to the HOH bending mode. To overcome this additional complexity, amide I′ band, where the N-H is replaced with an N-D group, has been studied instead. Therefore, to make the present calculation results useful for comparison with experimental observations, we have also carried out quantum chemistry calculations of deuterated di- and trialanines, where all NH2, NH3+, N-H, and COOH groups are replaced with ND2, ND3+, N-D, and COOD, respectively. In Figure 3b, the amide I local mode frequencies of deuterated di- and trialanines (filled squares) are directly compared with those of normal peptides (open circles). Not only the general trends with respect to the internal ionic field but also their absolute magnitudes do not depend on the deuterium isotope exchange. We have also examined how strongly the NH2 and ND2 bending modes as

well as COO- antisymmetric stretching modes are coupled to the amide I vibration. It is found that the NH2 and NH3+ bending modes are coupled to the amide I mode when the secondary structure is either APB or PII because the NH2 and NH3+ groups are spatially close to the peptide CdO group. However, the RHH peptides do not exhibit any notable coupling between NH2 bending and amide I mode. For deuterated di- and trialanines, the ND2 and ND3+ bending modes are not coupled to the amide I vibration, as expected. For all cases, the antisymmetric COO stretching mode does not couple to the amide I vibration, which is consistent with the experimental finding in ref 31. Although our quantum chemistry calculation results suggest that the amide I mode frequency shifts can be as large as tens of wavenumbers when the terminal amine or carboxyl groups become ionic, the pD-dependence of amide I IR peak frequency of dipeptide in liquid water was found to be relatively small (approximately a few wavenumbers). Varying solution pH, Schweitzer-Stenner and co-workers measured both polarized visible Raman and Fourier transform infrared (FTIR) spectra of cationic, zwitterionic, and anionic alanylalanines (AA) in liquid water.37 They found that the amide I peak position of the cationic AA is almost identical to that of the zwitterionic AA but that of anionic AA is about 20 cm-1 red-shifted from that of the zwitterionic AA. In ref 38, it was also found that the deprotonation of the ammonium ion in a diglycine notably downshifts the amide I sub-band.38 These results suggest that the N-terminal charge strongly affects the amide I mode frequency of neighboring peptides in liquid water, whereas the C-terminal charge does not. However, we found that the ionic field effect on the amide I frequency is large both when the C-terminal is negatively charged and when the secondary structures are either APB or PII (extended structures). However, if the AA conformation is RHH, the cationic group at the N-terminal induces a strong blue-shift in comparison to the neutral NH2 group. Therefore, the present calculation results are to some extent in contrast with the previous experimental studies reported in refs 37 and 38. Nevertheless, it should be emphasized that a direct comparison of the present quantum chemistry calculation results with experiments above is not possible because of the following reasons. First of all, the solvation effects such as hydrogen bonding interaction-induced frequency shift, structuring of surrounding water molecules around the ammonium ion, charge screening (reduction of Coulombic interaction potential) by liquid water, etc., were not taken into account in the present calculations for isolated AAs. Second, the experimental finding that the protonation of the N-terminal significantly influences the amide I frequency,


Lee et al.

Figure 4. A schematic picture of fragmentation method. Twenty amino acids differ by the chemical group R. The origin of the molecular coordinate system is assumed to be at the R-carbon. The molecular z-axis is on the CR-N(-H) bond, and the three atoms, (H-)N-CRC(dO), are on the (x,z) plane. The fragments 1 and 2 both have a single peptide group, and the peptide group is connected to a chiral R-carbon. To carry out the fragment analysis, DFT calculations of fragments 1 and 2 were performed.

Figure 3. (a) Theoretically calculated local amide I mode frequencies of deuterated di- and trialanines by using eq 2 are directly compared with the ab initio (HF/6-311++G**) calculation results. (b) The same data in a are compared with normal di- and trialanines with H atoms instead of D atoms. (c) Equation 1 is used to numerically calculate the local amide I mode frequencies of di- and trialanines in Figure 1 and various dipeptides having 20 different side chains (plus five ionic side chains), and they are compared with the ab initio results.

whereas the C-terminal (negative) charge weakly does might be compared with the present ab initio calculation results only when the structures of AA in solution do not change with respect to the ionic states of the N- and C-terminal groups. However, there is no conclusive evidence that the absolute configurations of cationic, anionic, and zwitterionic di- and tripepetides remain the same in solution regardless of their ionic states.39,40 In fact, Eker et al.31 showed that the vibrational coupling constant of anionic AAA (trialanine) is different from those of cationic and zwitterionic AAA. This indicates that the anionic AAA might adopt a different 3D structure in highly alkaline aqueous solution in comparison to those of cationic and zwitterionic AAA’s. Third, the liquid water molecules have been known to form various stable hydrogen bonding networks with the peptides. Consequently, the solvation structure can strongly depend on the ionic state of the small peptides, particularly around the cationic ammonium. Therefore, it is not straightforward to make

comparisons of the present ab initio calculation results with experiments not only because the conformations of small peptides can be altered by changing pH but also because we could not correctly take into account various solvation-induced effects on amide I mode frequency. Only after one carries out appropriate molecular dynamics simulation studies to elucidate the structural variations of small peptides at acid, neutral, and alkaline pH solutions will it be possible to make concrete comparisons with experiments. Despite that, we could not provide a clear description on what the underlying physics of the amide I band frequency shifts is with respect to the ionic states for different pHs. The initial goal of the present work, which is to demonstrate that the empirical correction method mentioned in the Introduction is potentially useful to quantitatively predict the intramolecular ionic field effect on the amide I frequency shifts, was achieved for the gas-phase di- and tri-alanines in this section. III. Side-Chain Effects On Amide I Frequency and IR And VCD Intensities Twenty natural amino acids differ from one another by the chemical structures of the side chains. Although there exist IR absorption spectroscopic studies to elucidate the side-chain effects on the amide I IR band shape and frequency shift,41-43 because of the complication originating from conformational variation of the peptide backbone as the side-chain changes, it is not clear whether the spectral line shape change is solely due to the side-chain effect. In the present quantum chemistry calculation studies, the dipeptide backbone structures are constrained to be RHH, APB, or PII conformations so that it becomes possible to selectively study the side-chain effects only. The model dipeptides having different side chains are shown in Figure 4. Note that each amino acid is capped by either the acetyl or methylamine groups. In the cases of five amino acids, i.e., lysine, arginine, histidine, aspartate, and glutamate, their side chains can be ionized, either cationic or anionic. Therefore, in addition to the neutral dipeptides, we also considered cationic lysine, arginine, and histidine and anionic aspartate and glutamate



Figure 5. (a-c) Amide I local mode frequencies of 20 different neutral and 5 ionic dipeptides when they are APB, PII, or RHH conformations. (d-f) The coupling constants (off-diagonal Hessian matrix element) are plotted for the 25 dipeptides. Those cases when the side chains are ionic are particularly shown in the small box of each figure. Except for a few cases, the coupling constants do not strongly depend on side chains (see the main context for a detailed discussion).

peptides. The geometry-optimized structures of 75 amino acid dipeptides (three conformations for all 25 either neutral or charged dipeptides) are given in the Supporting Information. A. Amide I Local Mode Frequency Shifts. By using the Hessian matrix reconstruction and ab initio (HF/6-311++G**) calculation methods, the amide I local mode frequencies for all 25 different dipeptides in one of the three representative conformations were obtained. The amide I local mode frequencies are plotted in Figure 5a-c. The amide I local mode frequency of peptide 1 in the proline dipeptide is notably small in comparison to the other cases because the chemical structure of proline peptide is different from the others. For the dipeptides shown in Figure 6, the molecular structures are stabilized by intramolecular hydrogen bonds, and thus, the corresponding amide I local mode frequencies become notably small. Other than these exceptional cases, the amide I local mode frequencies are largely determined by their secondary structures not by their side chains. The average amide I frequencies of APB, PII, and

RHH dipeptides are about 1700, 1715, and 1730 cm-1, respectively. The principal reason the average amide I mode frequency of RHH dipeptides is much larger than that of APB dipeptides is because the interpeptide interaction in a given RHH dipeptide is repulsive so that the CdO bond lengths decrease and, consequently, amide I local mode frequencies increase.26 To use the four-site model, it is necessary to determine partial charges of each site of the side chain. One can use a variety of different ways to do this, but we will use the partial charges in the AMBER program44 because this program has been and will be used to quantitatively describe amide I mode frequency shift, fluctuation, dephasing, and dynamics of polypeptides. B. Vibrational Coupling Constants. Recent quantum chemistry calculations of small polypeptides proved that the vibrational coupling constants, the off-diagonal Hessian matrix elements, do not depend on polypeptide chain length but strongly depend on their secondary structure, i.e., relative orientation and distance between a pair of peptides.28,29 To study how strongly


Lee et al.

Figure 6. Six notable (neutral) dipeptide structures having one or two intramolecular hydrogen bonds. Also, the three cationic dipeptide structures are shown. The number in each figure corresponds to the hydrogen bond length in Å.

the vibrational coupling strength depends on side chains, we examined the reconstructed Hessian matrix, and the coupling constants are plotted in Figure 5d-f. The vibrational coupling strengths do not strongly depend on the nature of side chains except for a few cases of dipeptides having intramolecular hydrogen bonds or the APB proline dipeptide. The 3D conformations of serine, asparagine, and arginine RHH dipeptides, arginine and histidine APB dipeptides, and arginine PII dipeptide are depicted in Figure 6. The reason the coupling constants of these dipeptides having intramolecular hydrogen bonds deviate from the average values is not because the coupling mechanism changes but because the amide I vibrations of the two peptide groups mix with the side-chain vibrational degrees of freedom such as O-H bending in the serine, another amide I vibration of the CONH2 group in the asparagine, and NH2 bending of the arginine side chain. A directly related experimental result was presented in ref 31. Eker et al. used polarized Raman, FTIR, and VCD spectroscopies to study structures of tripeptides constituting alanine, valine, serine, or lysine at acidic, neutral, and alkaline pD. They showed that different tripeptides adopt stable but different structures in water. Regardless of pD, all the spectra of AAA in water are characteristic for an extended structure. They estimated local mode frequencies, vibrational coupling constants, and angles between the two local mode transition

dipoles. They found that the stable structures of tripeptides in liquid water are different from one another, depending on the side chain. However, since the detailed structures of side chains of these tripeptides in liquid water (D2O) were not determined, it is not straightforward to make comparisons with their experimental results. Note that the dipeptides with varying side chains considered in the present paper do not have free amine or carboxylic acid groups, and a given series of dipeptides are structurally constrained to be one of the three conformations, APB, PII, or RHH. Therefore, more detailed molecular dynamics simulation studies, including explicit D2O solvents, are desired to fully address the side-chain effects on amide I vibrational frequency shifts in these cases. For those dipeptides containing ionic side chains, the amide I local mode frequency shifts are notably large in comparison to those for the neutral dipeptides (see the data points in the small boxes of Figure 5a-c). To explain these large frequency shifts, the three structures of cationic histidine APB dipeptide, arginine PII dipeptide, and lysine RHH dipeptide are shown in Figure 6 (see the three structures in the bottom row). They all form intramolecular electrostatic interactions with either peptide 1 or 2 so that the electronic structure of the corresponding peptide bond would be greatly perturbed by these interactions that cause frequency shifts. All other cases of dipeptides having ionic side chains have similar nonbonding intramolecular



interactions (see the Supporting Information for optimized molecular structures). Then, does the same intramolecular electrostatic interaction induce changes of vibrational coupling constants? In Figure 5d-f, the calculated vibrational coupling constants when the dipeptides contain ionic side chains are plotted in the small boxes. For the anionic aspartate and glutamate PII dipeptides (see Figure 5e) and cationic lysine RHH dipeptide (see Figure 5f), the estimated coupling constants deviate from the average values. After examining the corresponding eigenvector elements, we found that the interactions between the peptide bond and side-chain ionic groups in these cases are strong enough to make the associated amide I local mode uncoupled from the other amide I local mode, which makes the coupling constant very small. However, the other 12 dipeptides containing ionic side chains have coupling constants that are close to the corresponding average values. Therefore, on the basis of the present calculation results for both neutral and charged dipeptides with varying side chains, we found that the Vibrational coupling strength between the two nearest neighboring peptides does not strongly depend on the side chain except for a few cases mentioned aboVe. C. Fragment Analyses. The band intensities in IR and VCD spectra are linearly proportional to the dipole and rotational strengths of the corresponding vibrational degree of freedom, respectively. In the present cases of dipeptides in Figure 4, because of the amide I vibrational coupling between the two local modes, the symmetric and asymmetric amide I normal modes are formed, which are denoted as Qs and Qa and are written as34

( ) () (

)( )

Qs q cos θ sin θ q1 ˜ q1 ) Qa ) U -sin θ cos θ q2 2

(3)

where the normal mode transformation matrix and the mixing angle were denoted as U ˜ and θ, respectively. The mixing angle can be determined by the two amide I local mode frequencies and the coupling constant. We carried out the DFT (B3LYP/6-31G*) calculations to obtain dipole and rotational strengths of the two amide I normal modes for all 20 different dipeptides when they are RHH, PII, or APB conformations. It should be noted that the electron correlation effects play a role in the quantum chemistry calculation of magnetic dipole moment so that the DFT method instead of Hartree-Fock was used in these calculations.45 Here, the dipole and rotational strengths are defined as, for m ) s or a,

Dm ) |(∂µ/∂Qm)0|2 Rm ) Im[(∂µ/∂Qm)0(∂m/∂Qm)0]

asymmetric mode rotational strengths for the PII dipeptides are positive and negative, respectively. These results are in close agreement with recent observations made from recent DFT studies of an alanine dipeptide analogue with fragment analysis. Unlike the cases of APB dipeptides, the PII or RHH dipeptides exhibit some dependencies of their rotational strengths on the detailed structures of side chains, but overall, the side-chain effect on the rotational strength is not large. Nevertheless, the more important issue is whether it is possible to theoretically predict the rotational strength of any arbitrary dipeptide. We will show that the fragment analysis method, where the two monopeptides (instead of oligopeptides) shown in Figure 4 are treated as two unit peptides, can be of use for such a purpose. For the sake of completeness, the fragment analysis method presented in ref 34 will be briefly outlined here. The alanine dipeptide analogue (ADA) was dissected into two unit peptides, fragments 1 and 2, and they both have a chiral carbon covalently bonded to each peptide group. These two unit monopeptides were considered to be the minimal building blocks for quantitatively determining various vibrational spectroscopic properties, including transition magnetic dipole and rotational strength of ADA in any arbitrary conformation. Nevertheless, the ADA has a simple side chain of a methyl group. Thus, whether the same fragment analysis method is useful, even for dipeptides having different side chains, has not been studied. To perform the fragment analysis, we first assume that the transition electric and magnetic dipoles can be written as linear combinations of transition electric and magnetic dipoles of these two fragments as, for the symmetric and asymmetric amide I normal modes,

Ds ) |(∂µ/∂Qs)0|2 ) |(∂µf1/∂q1)0|2 cos2 θ + |(∂µf2/∂q2)0|2 sin 2 θ + 2(∂µf1/∂q1)0(∂µf2/∂q2)0 cos θ sin θ ) Df1 cos2 θ + Df2 sin2 θ + Dcross cos θ sin θ Da ) |(∂µ/∂Qa)0|2 ) |(∂µf1/∂q1)0|2 sin2 θ + |(∂µf2/∂q2)0|2 cos2 θ - 2(∂µf1/∂q1)0(∂µf2/∂q2)0 cos θ sin θ ) Df1 sin2 θ + Df2 cos2 θ - Dcross cos θ sin θ Rs ) Im[(∂µ/∂Qs)0(∂m/∂Qs)0] = Im[(∂µf1/∂q1)0(∂mf1/∂q1)0 cos2 θ + (∂µf2/∂q2)0(∂mf2/∂q2)0 sin2 θ + {(∂µf1/∂q1)0(∂mf2/∂q2)0 +

(4)

where µ and m are the electric and magnetic dipole moments, respectively. Since the transition magnetic dipole moment depends on the origin of the molecular coordinate system, we used the gauge-invariant magnetic field perturbation (MFP) theory46 to calculate the rotational strengths of the symmetric and asymmetric amide I normal modes. In Figures 7 and 8, the DFT-calculated dipole and rotational strengths are summarized. Overall, the rotational strengths of APB dipeptides are an order of magnitude smaller than those of PII or RHH dipeptides regardless of side chains. Also, the rotational strengths of the symmetric (high-frequency) and asymmetric (low-frequency) amide I normal modes of RHH dipeptides are negative and positive, respectively. In contrast, the signs of symmetric and

(∂µf2/∂q2)0(∂mf1/∂q1)0} cos θ sin θ] ) Rf1 cos2 θ + Rf2 sin2 θ + Rcross cos θ sin θ Ra ) Im[(∂µ/∂Qa)0(∂m/∂Qa)0] = Im[(∂µf1/∂q1)0(∂mf1/∂q1)0 sin2 θ + (∂µf2/∂q2)0(∂mf2/∂q2)0 cos2 θ - {(∂µf1/∂q1)0(∂mf2/∂q2)0 + (∂µf2/∂q2)0(∂mf1/∂q1)0} cos θ sin θ] ) Rf1 sin2 θ + Rf2 cos2 θ - Rcross cos θ sin θ

(5)

Here, the transition electric and magnetic dipoles of the jth fragment were denoted as (∂µfj/∂qj)0 and (∂mfj/∂qj)0, respectively,


Lee et al.

Dfj ) |(∂µfj/∂qj)0|2 Rfj ) Im[(∂µfj/∂qj)0(∂mfj/∂qj)0]

Figure 7. Dipole strengths of all 25 dipeptides, which were obtained by using the fragment analysis method, are directly compared with the DFT calculation results.

and the dipole and rotational strengths of the jth fragment are, respectively,

(6)

Note that (∂µfj/∂qj)0 and (∂mfj/∂qj)0 depend on the 3D structures of each fragment not on the overall conformation of the dipeptide. However, the relative orientation and distance between the two fragments will affect (1) the mixing angle via changing the coupling strength and vibrational frequencies of the two fragments and (2) the cross terms, Dcross and Rcross. Since detailed discussions on the VCD spectra of seven representative secondary structure diepeptides were given in ref 34, we shall not provide any further discussion on the major differences among APB, PII, and RHH dipeptides. Using the fragment approximations in eq 5, the rotational strengths are numerically calculated with the transition electric and magnetic dipole moments of the two fragments for each dipeptide. In Figure 7, the fragment-approximated dipole strengths are plotted with respect to the DFT results of

Figure 8. Rotational strengths of the two amide I normal modes. The DFT (B3LYP/6-31G*) calculation results are plotted as the filled squares, and the fragment-approximated rotational strengths (open squares) calculated by using eq 5 are plotted for the sake of comparison.

Internal Field Effects on Peptide Amide I Modes dipeptides. In Figure 8, the DFT calculated rotational strengths are directly compared with fragment-approximated values for each individual dipeptide (see the open squares). The agreements are excellent, which confirms that the fragment analysis method works quantitatively well regardless of the nature of side chains. The ultimate use of the fragment analysis method is to quantitatively predict various vibrational properties such as normal mode frequencies, dipole and rotational strengths, and coupling constants of polypeptides and proteins. In general, because of the limitations of the high-level ab initio or DFT calculations, it is still not possible to directly calculate these properties of long polypeptides or natural proteins by using quantum calculation methods. Therefore, the fragment analysis method, which requires a minimal amount of high-level quantum chemistry calculations for a few fragments, will be of critical use. Before we close this section, a limitation of the constrained ab initio geometry optimization and vibrational analysis needs to be mentioned. We have used constraints that make the model di- and tripeptides form one of the three secondary structures and partially optimized molecular structures to obtain vibrational properties such as transition electric and magnetic dipoles, local mode frequencies, vibrational coupling constants, etc. However, in these cases, the molecular structures are nonstationary so that there are nonvanishing forces along the amide I vibrational degrees of freedom.47 This issue is keenly related to what properties one is really interested in. If one wants to study vibrational properties of an isolated (gas-phase) molecule without interacting with any other bath molecules, one should consider the global (or local) minimum structure. However, at finite temperature, the instantaneous molecular structures of polypeptides in solution would never be identical to the local minimum structure found in the gas-phase calculation. The ensemble of solute molecules has a broad distribution of structures and vibrational properties. Therefore, the constrained vibrational analysis, which is much like the instantaneous normal mode calculations of liquids, could be a useful method to explore a much wider range of vibrational properties of various structures that are not necessarily identical to the local minimum structures of the same molecule in a gas phase. Nevertheless, because of the structural constraints, the ab initio vibrational analysis might provide imaginary frequency modes. Examining the ab initio vibrational analysis results, we confirmed that all four criteria for a converged (stationary) geometry optimization were satisfied when the default values implemented in the Gaussian 98 program were used. This indicates that the optimized geometry with the structural constraints is very close to the energy minimum (stationary) structure. Nevertheless, we found that there is one unstable mode for APB and PII dialanines and their (imaginary) frequencies are -35 and -24 cm-1, respectively (here the negative sign means that the frequency is an imaginary number); note that the RHH dialanine does not have any imaginary frequency (unstable) mode. The imaginary frequencies are relatively small, indicating that the corresponding potential energy surface associated with these unstable modes is a slowly varying function with respect to the corresponding coordinate, i.e., the force (first-order derivative of the potential surface with respect to the unstable mode coordinate) is relatively small. However, this does not guarantee that the influence of unstable mode on amide I frequency is small because the absolute magnitudes of frequency shifts induced by structure changes, for example from RHH to APB dipeptide, are about or less than a few tens of wavenumbers. Therefore, it is not completely clear whether one can indeed ignore influences

J. Phys. Chem. B, Vol. 109, No. 11, 2005 5339 of imaginary frequency modes, which originate from vibrational mixing of the unstable and amide I local modes, on the amide I mode frequency. Nevertheless, it is believed that this issue is beyond the scope of this paper and that it be left for future investigations. IV. Summary In the present paper, two internal field effects, which originate from intramolecular charged terminal groups and from polar amino acid side chains, on the amide I vibrational properties were theoretically investigated by carrying out a series of HF and DFT calculations for a variety of short peptides. The amide I local mode frequencies were found to be strongly dependent on the polar natures of the side chains and neighboring charged groups, though these effects are likely to be less significant because of the screening effect when the peptides are dissolved in liquid water. The four-site model, eq 1, developed by using electronic structure calculations, was found to be useful for quantitatively describing these internal field effects. For dipeptides with 20 different side chains, it was shown that the vibrational coupling constants are not strongly dependent on the side-chain structures so that the coupling constant map, J(φ, ψ), obtained before will be of use in quantitatively constructing an amide I Hessian matrix for any arbitrary polypeptide. Also, the rotational strengths of these dipeptides were found to be weakly dependent on an amino acid side chain. In addition, the fragment analysis method presented in ref 34 was used to predict dipole and rotational strengths of dipeptides, and the fragmentapproximated values were found to be in quantitative agreement with the DFT calculation results. Currently, the correction and fragment approximation methods are used to numerically simulate one- and two-dimensional vibrational spectra of proteins in solutions. Acknowledgment. This work was supported by the Creative Research Initiatives Program of KOSEF (MOST, Korea). M.C. is thankful to Prof. R. Schweitzer-Stenner for helpful discussions. Supporting Information Available: Geometry-optimized structures of 75 amino acid dipeptides (3 conformations for all 25 either neutral or charged dipeptides). This material is available free of charge via the Internet at http://pus.acs.org. References and Notes (1) Mantsch, H. H.; Casal, H. L.; Jones, R. N. In Spectroscopy of Biological Systems, AdVances in Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Wiley: New York, 1986; Vol. 13, p 1. (2) Surewicz, W. K.; Mantsch, H. H. In Spectroscopic Methods for Determining Protein Structure in Solution; Havel, H. A., Ed.; VCH: New York, 1996; p 135. (3) Infrared and Raman Spectroscopy of Biological Materials; Gremlich, H.-U., Yan, B., Eds.; Marcel Dekker: New York, 2000. (4) Byler, D. M.; Susi, H. Biopolymers 1986, 25, 469. (5) Susi, H.; Byler, D. M. Biochem. Biophys. Res. Commun. 1983, 115, 391. (6) Jackson, M.; Haris, P. I.; Chapman, D. J. Mol. Struct. 1989, 214, 329. (7) Arrondo, J. L. R.; Goni, F. M. Prog. Biophys. Mol. Biol. 1999, 72, 367. (8) Prestrelski, S. J.; Byler, D. M.; Thompson, M. P. Biochemistry 1991, 30, 8797. (9) Torii, H.; Tasumi, M. In Infrared Spectroscopy of Biomolecules; Wiley-Liss: New York, 1996; p 1. (10) Krimm, S.; Bandekar, J. AdV. Protein Chem. 1986, 38, 181. (11) Krimm, S.; Abe, Y. Proc. Natl. Acad. Sci. U.S.A. 1972, 69, 2788. Moore, W. H.; Krimm, S. Proc. Natl. Acad. Sci. U.S.A. 1975, 72, 4933. (12) Moritz, R.; Fabian, H.; Hahn, U.; Diem, M.; Naumann, D. J. Am. Chem. Soc. 2002, 124, 6259.

5340 J. Phys. Chem. B, Vol. 109, No. 11, 2005 (13) Mix, G.; Schweitzer-Stenner, R.; Asher, S. A. J. Am. Chem. Soc. 2000, 122, 9028. (14) Asher, S. A.; Mikhonin, A. V.; Bykov, S. J. Am. Chem. Soc. 2004, 126, 8433. (15) Hilario, J.; Kubelka, J.; Keiderling, T. A. J. Am. Chem. Soc. 2003, 125, 7562. (16) Huang, R.; Kubelka, J.; Barber-Armstrong, W.; Silva, R. A. G. D.; Decatur, S. M.; Keiderling, T. A. J. Am. Chem. Soc. 2004, 126, 2346. (17) Dong, A.; Huang, P.; Caughey, W. S. Biochemstry 1990, 29, 3303. (18) Simonetti, M.; Bello, C. D. Biopolymers 2001, 62, 95. (19) Wi, S.; Pancoska, P.; Keiderling, T. A. Biospectroscopy 1998, 4, 93. (20) Kubelka, J.; Keiderling, T. A. J. Am. Chem. Soc. 2001, 123, 12048. (21) Kubelka, J.; Keiderling, T. A. J. Am. Chem. Soc. 2001, 123, 6142. (22) Kubelka, J.; Silva, R. A. G. D.; Keiderling, T. A. J. Am. Chem. Soc. 2002, 124, 5325. (23) Decatur, S. M.; Antonic, J. J. Am. Chem. Soc. 1999, 121, 11914. (24) Barber-Armstrong, W.; Donaldson, T.; Wijesooriya, H.; Silva, R. A. G. D.; Decatur, S. M. J. Am. Chem. Soc. 2004, 126, 2339. (25) Ham, S.; Kim, J.-H.; Lee, H.; Cho, M. J. Chem. Phys. 2002, 118, 3491. (26) Ham, S.; Cho, M. J. Chem. Phys. 2003, 118, 6915. (27) Kwac, K.; Lee, H.; Cho, M. J. Chem. Phys. 2004, 120, 1477. (28) Ham, S.; Cha, S.; Choi, J.-H.; Cho, M. J. Chem. Phys. 2003, 119, 1451. (29) Choi, J.-H.; Ham, S.; Cho, M. J. Phys. Chem. B 2003, 107, 9132. (30) Schweitzer-Stenner, R.; Eker, F.; Huang, Q.; Griebenow, K. J. Am. Chem. Soc. 2001, 123, 9628. (31) Eker, F.; Cao, X.; Nafie, L.; Schweitzer-Stenner, R. J. Am. Chem. Soc. 2002, 124, 14330. (32) Eker, F.; Cao, X.; Nafie, L.; Huang, Q.; Schweitzer-Stenner, R. J. Phys. Chem. B 2003, 107, 358. (33) Eker, F.; Griebenow, K.; Cao, X.; Nafie, L.; Schweitzer-Stenner, R. Biochemistry 2004, 43, 613.

Lee et al. (34) Choi, J.-H.; Cho, M. J. Chem. Phys. 2004, 120, 4383. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (36) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (37) Schweitzer-Stenner, R.; Eker, F.; Huang, Q.; Griebenow, K.; Mroz, P. A.; Kozlowski, P. M. J. Phys. Chem. B 2002, 106, 4294. (38) Sieler, G.; Schweitzer-Stenner, R.; Holtz, J. S. W.; Pajcini, V.; Asher, S. A. J. Phys. Chem. B 1999, 103, 372. (39) Tajkhorshid, E.; Jalkanen, K. J.; Suhai, S. J. Phys. Chem. B 1998, 102, 5899. (40) Han, W.; Jalkanen, K. J.; Elstner, M.; Suhai, S. J. Phys. Chem. B 1998, 102, 2587. (41) Xie, P.; Zhou, Q.; Diem, M. J. Am. Chem. Soc. 1995, 117, 9502. (42) Xie, P.; Diem, M. J. Am. Chem. Soc. 1995, 117, 429. (43) Rao, C. P.; Nagaraj, R.; Rao, C. N. R.; Balaram, P. Biochemistry. 1980, 19, 425. (44) Case, D. A.; Pearlman, D. A.; Caldwell, J. W. et al. AMBER 7; University of California: San Francisco, 2002. (45) Cheeseman, J. R.; Frisch, M. J.; Devlin, F. J.; Stephens, P. J. Chem. Phys. Lett. 1996, 252, 211. (46) Stephens, P. J. J. Phys. Chem. 1987, 91, 1712. (47) Fogarasi, G.; Zhou, X.; Taylor, P. W.; Pulay, P. J. Am. Chem. Soc. 1992, 114, 8191.

Theoretical Study of Internal Field Effects on Peptide Amide I Modes

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