Theoretical Study of Internal Field Effects on Peptide Amide I Modes

Infrared, vibrational circular dichroism, and Raman spectral simulations for β-sheet structures with various isotopic labels, interstrand, and stacking arrangements using density functional theory

Infrared (IR), Raman, and vibrational circular dichroism (VCD) spectral variations for different β-sheet structures were studied using simulations based on density functional theory (DFT) force field and intensity computations. The DFT vibrational parameters were obtained for β-sheet fragments containing nine-amides and constrained to a variety of conformations and strand arrangements. These were subsequently transferred onto corresponding larger β-sheet models, normally consisting of five strands with ten amides each, for spectral simulations. Further extension to fibril models composed of multiple stacked β-sheets was achieved by combining the transfer of DFT parameters for each sheet with dipole coupling methods for interactions between sheets. IR spectra of the amide I show different splitting patterns for parallel and antiparallel β-sheets, and their VCD, in the absence of intersheet stacking, have distinct sign variations. Isotopic labeling by (13)C of selected residues yields spectral shifts and intensity changes uniquely sensitive to relative alignment of strands (registry) for antiparallel sheets. Stacking of multiple planar sheets maintains the qualitative spectral character of the single sheet but evidences some reduction in the exciton splitting of the amide I mode. Rotating sheets with respect to each other leads to a significant VCD enhancement, whose sign pattern and intensity is dependent on the handedness and degree of rotation. For twisted β-sheets, a significant VCD enhancement is computed even for sheets stacked with either the same or opposite alignments and the inter-sheet rotation, depending on the sense, can either further increase or weaken the enhanced VCD intensity. In twisted, stacked structures (without rotation), similar VCD amide I patterns (positive couplets) are predicted for both parallel and antiparallel sheets, but different IR intensity distributions still enable their differentiation. Our simulation results prove useful for interpreting experimental vibrational spectra in terms of β-sheet and fibril structure, as illustrated in the accompanying paper.

VCD spectroscopic properties of the beta-hairpin forming miniprotein CLN025 in various solvents

Electronic and vibrational circular dichroism are often used to determine the secondary structure of proteins, because each secondary structure has a unique spectrum. Little is known about the vibrational circular dichroic spectroscopic features of the beta-hairpin. In this study, the VCD spectral features of a decapeptide, YYDPETGTWY (CLN025), which forms a stable beta-hairpin that is stabilized by intramolecular weakly polar interactions and hydrogen bonds were determined. Molecular dynamics simulations and ECD spectropolarimetry were used to confirm that CLN025 adopts a beta-hairpin in water, TFE, MeOH, and DMSO and to examine differences in the secondary structure, hydrogen bonds, and weakly polar interactions. CLN025 was synthesized by microwave-assisted solid phase peptide synthesis with N(alpha)-Fmoc protected amino acids. The VCD spectra displayed a (-,+,-) pattern with bands at 1640 to 1656 cm(-1), 1667 to 1687 cm(-1), and 1679 to 1686 cm(-1) formed by the overlap of a lower frequency negative couplet and a higher frequency positive couplet. A maximum IR absorbance was observed at 1647 to 1663 cm(-1) with component bands at 1630 cm(-1), 1646 cm(-1), 1658 cm(-1), and 1675 to 1680 cm(-1) that are indicative of the beta-sheet, random meander, either random meander or loop and turn, respectively. These results are similar to the results of others, who examined the VCD spectra of beta-hairpins formed by (D)Pro-Xxx turns and indicated that observed pattern is typical of beta-hairpins.

Two-dimensional vibrational spectroscopy of rotaxane-based molecular machines

It has recently become possible to synthesize mechanical devices the size of a single molecule. Although it is tempting to regard such molecular machines as nanoscale versions of their macroscopic analogs, many notions from macroscopic mechanics no longer apply at a molecular level. For instance, the concept of viscous friction is meaningless for a molecular machine because the size of the solvent molecules that cause the friction is comparable to that of the machine itself. Furthermore, in many cases, the interactions between a molecular machine and its surroundings are comparable to the force driving the machine. As a result, a certain amount of intrinsic randomness exists in the motion of molecular machines, and the details of their mechanics are largely unknown. For a detailed understanding of the mechanical behavior of molecular machines, experiments that probe their motion on an ultrafast time scale, such as two-dimensional (2D) vibrational spectroscopy, are essential. This method uses coupling between vibrational modes in a molecule to investigate the molecular conformation. The coupling shows up as off-diagonal peaks in a 2D graph of the vibrational response of the molecule, analogous to the spin coupling observed in multidimensional NMR spectroscopy. Both spin coupling and vibrational coupling are sensitive probes of the molecular conformation, but 2D vibrational spectroscopy shows orders of magnitude better time resolution than NMR. In this Account, we use 2D vibrational spectroscopy to study molecular machines based on rotaxanes. These devices consist of a linear thread and a macrocycle that is noncovalently locked onto the thread. In the rotaxanes we study, the macrocycle and the thread both contain CO and NH groups. By determining the coupling between the stretching modes of these goups from the cross peaks in the 2D spectrum, we directly and quantitatively probe the relative position and orientation of the macrocycle and the thread for both a small model rotaxane and a rotaxane-based molecular shuttle. Our results demonstrate the feasibility of using time-resolved 2D-IR experiments to measure externally triggered structural changes of molecular devices with subpicosecond time resolution. We can observe each of the elementary events that underlie the mechanical motion separately. With this ability to investigate the nature of the mechanical motions at the molecular level and with unprecedented time resolution, we expect that 2D-IR spectroscopy on molecular machines will lead to new insights into their function.

A polarizable force field for computing the infrared spectra of the polypeptide backbone

The shapes of the amide bands in the infrared (IR) spectra of proteins and peptides are caused by electrostatically coupled vibrations within the polypeptide backbone and code the structures of these biopolymers. A structural decoding of the amide bands has to resort to simplified models because the huge size of these macromolecules prevents the application of accurate quantum mechanical methods such as density functional theory (DFT). Previous models employed transition-dipole coupling methods that are of limited accuracy. Here we propose a concept for the computation of protein IR spectra, which describes the molecular mechanics (MM) of polypeptide backbones by a polarizable force field of "type II". By extending the concepts of conventional polarizable MM force fields, such a PMM/II approach employs field-dependent parameters not only for the electrostatic signatures of the molecular components but also for the local potentials modeling the stiffness of chemical bonds with respect to elongations, angle deformations, and torsions. Using a PMM/II force field, the IR spectra of the polypeptide backbone can be efficiently calculated from the time dependence of the backbone's dipole moment during a short (e.g., 100 ps) MD simulation by Fourier transformation. PMM/II parameters are derived for harmonic bonding potentials of amide groups in polypeptides from a series of DFT calculations on the model molecule N-methylacetamide (NMA) exposed to homogeneous external electric fields. The amide force constants are shown to vary by as much as 20% for relevant field strengths. As a proof of principle, it is shown that the large solvatochromic effects observed in the IR spectra of NMA upon transfer from the gas phase into aqueous solution are not only excellently reproduced by DFT/MM simulations but are also nicely modeled by the PMM/II approach. The tasks remaining for a proof of practice are specified.

Two-Dimensional Vibrational Lineshapes of Amide III, II, I and A Bands in a Helical Peptide

An effective exciton Hamiltonian for all amide bands is used to calculate the linear absorption and photon echo spectra of a 17 residue helical peptide (YKKKH17). The cross peak bandshapes are sensitive to the inter-band couplings. Fluctuations of the local amide frequencies of the all amide fundamental and their overtone and combination states are calculated using the multipole electric field induced by environment employing the electrostatic DFT map of N-methyl acetamide. Couplings between neighboring peptide units are obtained using the anharmonic vibrational Hamiltonian of glycine dipeptide (GLDP) at the BPW91/6-31G(d,p) level. Electrostatic couplings between non-neighboring units are calculated by the fourth rank transition multipole coupling (TMC) expansion including 1/R(3) (dipole-dipole), 1/R(4) (quadrupole-dipole), and 1/R(5) (quadrupole-quadrupole and octapole-dipole) interactions.

Vibrational-exciton couplings for the amide I, II, III, and A modes of peptides

The couplings between all amide fundamentals and their overtones and combination vibrational states are calculated. Combined with the level energies reported previously (Hayashi, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. A 2005, 109, 9747), we obtain a complete effective vibrational Hamiltonian for the entire amide system. Couplings between neighboring peptide units are obtained using the anharmonic vibrational Hamiltonian of glycine dipeptide (GLDP) at the BPW91/6-31G(d,p) level. Electrostatic couplings between non-neighboring units are calculated by the fourth rank transition multipole coupling (TMC) expansion, including 1/R3 (dipole-dipole), 1/R4 (quadrupole-dipole), and 1/R5 (quadrupole-quadrupole and octapole-dipole) interactions. Exciton delocalization length and its variation with frequency in the various amide bands are calculated. The simulated infrared amide I and II absorptions and CD spectra of 24 residue alpha-helical motifs (SPE3) are in good agreement with experiment.

Infrared and vibrational CD spectra of partially solvated alpha-helices: DFT-based simulations with explicit solvent

Theoretical simulations are used to investigate the effects of aqueous solvent on the vibrational spectra of model alpha-helices, which are only partly exposed to solvent to mimic alpha-helices in proteins. Infrared absorption (IR) and vibrational circular dichroism (VCD) amide I' spectra for 15-amide alanine alpha-helices are simulated using density functional theory (DFT) calculations combined with the property transfer method. The solvent is modeled by explicit water molecules hydrogen bonded to the solvated amide groups. Simulated spectra for two partially solvated model alpha-helices, one corresponding to a more exposed and the other to a more buried structure, are compared to the fully solvated and unsolvated (gas phase) simulations. The dependence of the amide I spectra on the orientation of the partially solvated helix with respect to the solvent and effects of solvation on the amide I' of 13C isotopically substituted alpha-helices are also investigated. The partial exposure to solvent causes significant broadening of the amide I' bands due to differences in the vibrational frequencies of the explicitly solvated and unsolvated amide groups. The different degree of partial solvation is reflected primarily in the frequency shifts of the unsolvated (buried) amide group vibrations. Depending on which side of the alpha-helix is exposed to solvent, the simulated IR band-shapes exhibit significant changes, from broad and relatively featureless to distinctly split into two maxima. The simulated amide I' VCD band-shapes for the partially solvated alpha-helices parallel the broadening of the IR and exhibit more sign variation, but generally preserve the sign pattern characteristic of the alpha-helical structures and are much less dependent on the alpha-helix orientation with respect to the solvent. The simulated amide I' IR spectra for the model peptides with explicitly hydrogen-bonded water are consistent with the experimental data for small alpha-helical proteins at very low temperatures, but overestimate the effects of solvent on the protein spectra at ambient temperatures, where the peptide-water hydrogen bonds are weakened by thermal motion.

Geometry and Solvent Dependence of the Electronic Spectra of the Amide Group and Consequences for Peptide Circular Dichroism

The influence of geometry variations and solvent environment of N-methylacetamide on its energies and absorption intensities was systematically analyzed with the aid of the time-dependent density functional theory (TD DFT). Selective and often complicated reactions of individual electronic levels on the perturbations were found important for the resultant spectral profile. For example, the n-pi band position varied by tens of nanometers due to the C=O bond length oscillations, while it was rather unaffected by surrounding water. On the contrary, pi-pi type transition energies and intensities were broadly dispersed by the aqueous environment but exhibited a modest coordinate dependence. A simple electrostatic model used previously for absorption in the IR region (J. Chem. Phys. 2005, 122, 144501) explained these changes only partially. Additionally, electronic transfer between the solute and the solvent had to be considered for faithful modeling of the ultraviolet light absorption. The inclusion of the environment and dynamics in the modeling then provided more accurate positions, intensities, and realistic inhomogeneous widths of spectral lines. These factors were found important for absorption and circular dichroism spectra of larger peptides and proteins. This was demonstrated with a combined DFT/coupled oscillator model providing principal features observed in electronic circular dichroism spectra of standard peptide conformations.

Vibrational Spectral Simulation for Peptides of Mixed Secondary Structure: Method Comparisons with the Trpzip Model Hairpin

Infrared absorption and vibrational circular dichroism (IR and VCD) spectra of model fragments of TrpZip-style beta-hairpin structures are simulated using density functional theory (DFT) methods to estimate the influence of fragment size, end effects, conformational irregularities, peptide side chains, and solvent. Different fragmentation schemes, computing the strands and turn segments separately, were tested by varying the sizes of each and their respective overlaps. For suitably overlapping fragments, atomic property tensors were found to be reliably transferable, as tested by their ability to generate simulated spectra in good agreement with results from ab initio DFT computations for the entire peptide. This fragment approach significantly reduces computational times and opens up a wider range of systems that can be studied with a DFT-based approach as compared to previous methods based on uniform repeating sequences. However, vacuum calculations do not adequately represent the frequency dispersion of solvated molecules, and thus, some alternate strategies for solvation correction are explored for improving the simulation accuracy. Unlike for regular periodic secondary structure, the solvent significantly impacts the spectral shapes of hairpins, due to the different degrees of hydration of individual amide groups, which can be exposed to or shielded from water due to external vs internal hydrogen bonding. This is amplified by the shielding of selected amides from the solvent due to bulky side chains. The peptide plus solvent was structurally modeled with molecular dynamics methods, and then an electrostatic field-based parametrization correction was added to the force field and intensity tensors to compensate for the solvent dipolar field. The effect of the shielding and subsequent reordering of modes has a larger impact on VCD than IR band shapes.

Simulation Studies of Amide I IR Absorption and Two-Dimensional IR Spectra of β Hairpins in Liquid Water

Amide I IR absorption and two-dimensional (2D) IR photon echo spectra of a model beta hairpin in aqueous solution are theoretically studied and simulated by combining semiempirical quantum chemistry calculations and molecular dynamics simulation methods. The instantaneous normal-mode analysis of the beta hairpin in solution is performed to obtain the density of states and the inverse participation ratios of the one-exciton states. The motional and exchange narrowing processes are taken into account by employing the time-correlation function theory for the linear and nonlinear response functions. Numerically simulated IR absorption and 2D spectra are then found to be determined largely by the amide I normal modes delocalized on the peptides in the two strands. The site-specific isotope-labeling effects on the IR and 2D IR spectra are discussed. The simulation results for the ideal (A17) beta hairpin are directly compared with those of the realistic 16-residue (GB1) beta hairpin from an immunoglobulin G-binding protein. It was found that the characteristic features in IR and 2D spectra of both the ideal (A17) beta hairpin and the GB1 beta hairpin are the same. The simulated IR spectrum of the GB1 beta hairpin is found to be in good agreement with experiment, which demonstrates that the present computational method is quantitatively reliable.