Progress towards understanding protein structure and folding requires sensitive experimental methods for probing the conformation of proteins and model peptides. Optical spectroscopic techniques, especially electronic circular dichroism (ECD) and vibrational spectroscopies, infrared absorption (IR) and Raman, are well established methods that are sensitive to specific structural types in peptides and proteins and have inherently fast time scales making them capable of monitoring fast conformational interconversions. Vibrational circular dichroism (VCD) spectroscopy unites the advantages of the frequency resolution of vibrational spectroscopies with the signed bandshape resolution of the ECD. However, as a consequence of the inherent low resolution of optical spectroscopies, structural interpretation of spectral data is often problematic and can be further complicated by other sources of spectral signals unrelated to the structure.
Theoretical simulations of vibrational spectra can provide an insight into spectral features characteristic of different structures as well as features due to the non-structural effects. Modern quantum mechanical methods, especially those based on the density functional theory (DFT), allow IR and VCD spectral simulations for relatively large peptide segments. Simulations of vibrational spectra for even larger oligopeptides are possible using transferred, ab initio calculated spectral parameters for the smaller molecules. In this thesis, theoretical simulations are applied to study the IR and VCD spectra of model peptides and are then compared to experimental data to provide understanding and interpretation of various effects on the peptide and protein vibrational spectra. The first part of the thesis focuses on helical conformations. Experimental VCD spectra show distinct amide I and amide II bandshapes characteristic for the -helical, 310-helical and 31-(poly Pro II) helical structures. Theoretical spectral simulations for model peptides constrained to these three helical conformations were carried out to examine the effects of peptide size, hydrogen-bonding and solvent on the IR and VCD spectra. The simulations were based on DFT BPW91/6-31G* level ab initio calculations of harmonic force fields (FF), atomic polar (APT) and axial (AAT) tensors. The simulated spectra for diamide models reproduce the basic characteristic VCD experimental bandshapes and thus demonstrate local conformational origin of the VCD bandshapes. The agreement with experiment improves with increasing oligopeptide size. Solvent, modeled as explicit, hydrogen bonded water molecules, causes large shifts in vibrational frequencies, but has only a minor impact on the VCD spectral intensities and bandshapes. The local nature of the interactions that give rise to the characteristic VCD bandshapes was further evident in the simulated spectra for large, 20-mer peptide models, using the transfer of ab initio calculated spectral parameters from the smaller structures. In general, corrections for long-range coupling terms in the transferred FF caused only small changes in spectral bandshapes. Isolated molecule calculations and the transfer method were shown to be valid approximations for the simulations of VCD spectra for large peptides in solution.
Selective 13C isotopic substitution (on C=O) introduces site-specific resolution into vibrational spectroscopies via frequency shifts of vibrations. Temperature-dependent IR and VCD experiments for a series of 13C isotopically labeled Ala-rich 20-mer oligopeptides demonstrated that the -helix unwinds from the termini through a multi-state transition. In addition, the experimental spectra indicated a complex character of isotopic spectral patterns. Significant enhancement of the 13C band VCD intensity with respect to the fraction of 13C labels, was observed for low-temperature (-helical) samples. Theoretical simulations of the IR and VCD spectra were performed for the 13C isotopically labeled model Ala 20-mer peptides, using FF, APT and AAT transferred from DFT BPW91/6-31G* calculations on smaller molecules. Simulated spectra for -helical and 31-helical (pseudo-random coil) models evidenced very good correspondence with experimental spectral patterns for different peptide isotopomers at low and high temperatures, respectively. The coupling between the labeled and unlabeled peptide -helical segments seems to be responsible for the enhancement of the 13C VCD. Thus, theoretical simulations proved to be a valuable tool in the structural interpretation of the vibrational spectra of isotopically labeled peptides.
Although VCD spectra have consistently shown distinct amide I and amide II patterns that allow for discrimination between - and 310-helices, to date, all experimentally studied model 310-helical peptides contain some fraction of C,-dialkylated residues, while the -helical models are typically based on natural amino acids. The effects of -methylation on the 310- and -helical bandshapes were investigated by DFT BPW91/6-31G* based simulations of IR and VCD spectra for model peptides containing varying fractions of Aib (-amino isobutyric acid). Some dependence of the VCD bandshapes on the content of -methylated amino acids was predicted, in agreement with experimental data. However, the fundamental qualitative characteristic of the -helical and 310-helical VCD that provides spectral discrimination between the - and 310-helices, i.e., the ratio of the amide I to amide II VCD intensities, is not altered by the effects of -methylation.
The second major part of the work presented here is aimed at the spectral characteristics of -sheet structures. While the VCD is most sensitive to helical conformations, the IR amide I appears to be specifically sensitive to -sheet conformations. However, the split amide I band, often seen for -sheet polypeptides and regarded as "characteristic" for the -sheet, may be only due to large, extended aggregated peptide strands. DFT BPW91/6-31G**-based simulations of IR and VCD spectra were performed for several model peptide -sheets, corresponding to polypeptide as well as protein -sheet structures. Characteristic -sheet amide I IR spectra and weak amide I VCD were predicted for large, extended antiparallel -sheets in agreement with experimental results for polypeptide models. Characteristic distinctions between planar (polypeptide-like) and twisted (protein-like) antiparallel -sheets were predicted in both IR and VCD. However, the parallel -sheet does not seem to have a specific signature in either IR or VCD and yields similar spectra to twisted, protein-like antiparallel -sheets.
The 13C isotopic substitution has been shown to have dramatic effects on the IR spectra of -sheet structures. In certain isotopically labeled positions, the 13C band exhibits strong intensity enhancement with respect to the proportion of the labeled residues. The IR spectra of a series of 13C isotopically labeled -sheet models K2(LA)6 were also studied by theoretical simulations, using DFT BPW91/6-31G*-level spectral parameters. The comparison between experiment and simulation, in particular the "anomalous" intensity enhancement of the 13C labeled IR amide I band, suggests that large multi-stranded -sheets are formed by these model peptides. The results further indicate that the relative 13C band intensity phenomenon is dependent on the relative positions of the isotopic labels and could, for example, be used to distinguish parallel associated strands from antiparallel ones.
The -sheets in proteins are not isolated but accompanied by turn and loop segments, forming super-secondary structure elements, such as -hairpins. Recently, model -hairpins, based on DPro-Gly turns have been experimentally studied in our laboratory. Using transfer of ab initio DFT BPW91/6-31G** calculated parameters for the -sheet and connecting turn segments, IR and VCD spectral simulations were performed for DPro-Gly model -turns and -hairpins. In addition, the spectra for a -hairpin and a three-stranded -sheet segment from a protein were simulated. The -turn VCD amide I bandshape is predicted to be similar to that of the 31-helix. The DPro-containing -turn and -hairpin models show distinct amide I patterns with low frequency components arising from the tertiary amide of the X-Pro linkage. These simulations show good agreement with experimental amide I spectra for model DPro-Gly and protein derived -hairpins.
The final chapter of this thesis examines methods for calculating amide vibrational frequencies corresponding to those measured in solution. It is shown for a model amide, N-methyl acetamide (NMA), that DFT BPW91/6-31G* calculated amide I, II and III frequencies are in very good agreement with experimental gas phase values, but are very sensitive to the solvent environment. Frequencies comparable to the experiment in aqueous solution are obtained when both explicit water molecules as well as implicit solvent model are employed. A modified 6-31G* basis set with smaller Gaussian exponent of the polarization (d) function is proposed and tested as a computationally efficient means of approximating the solvent effects on amide vibrational frequencies.