Quantum-classical description of the amide I vibrational spectrum of trialanine

Theoretical Sum Frequency Generation Spectra of Protein Amide with Surface-Specific Velocity-Velocity Correlation Functions

Vibrational sum frequency generation (vSFG) spectroscopy is widely used to probe the protein structure at interfaces. Because protein vSFG spectra are complex, they can only provide detailed structural information if combined with computer simulations of protein molecular dynamics and spectra calculations. We show how vSFG spectra can be accurately modeled using a surface-specific velocity-velocity scheme based on ab initio normal modes. Our calculated vSFG spectra show excellent agreement with the experimental sum frequency spectrum of LTα14 peptide and provide insight into the origin of the characteristic α-helical amide I peak. Analysis indicates that the peak shape can be explained largely by two effects: (1) the uncoupled response of amide groups located on opposite sides of the α-helix will have different orientations with respect to the interface and therefore different local environments affecting the local mode vibrations and (2) vibrational splitting from nearest neighbor coupling evaluated as inter-residue vibrational correlation. The conclusion is consistent with frequency mapping techniques with an empirically based ensemble of peptide structures, thus showing how time correlation approaches and frequency mapping techniques can give independent yet complementary molecular descriptions of protein vSFG. These models reveal the sensitive relationship between protein structure and their amide I response, allowing exploitation of the complicated molecular vibrations and their interference to derive the structures of proteins under native conditions at interfaces.

Forbidden Secondary Structures Found in Gel-Forming Fibrils of Glycylphenylalanylglycine

The zwitterionic l-tripeptide glycylphenylalanylglycine self-assembles into very long crystalline fibrils in an aqueous solution, which causes the formation of an exceptionally strong gel phase (G' ∼ 5 × 10⁶ Pa). The Rietveld refinement analysis of its powder X-ray diffraction (PXRD) pattern reveals a unit cell with four peptides forming a P2₁2₁2₁ space group and adopting an inverse polyproline II conformation, that is, a right-handed helical structure that occupies the "forbidden" region of the Ramachandran plot. This unusual structure is stabilized by a plethora of intermolecular interactions facilitated by the large number of different functional groups of the unblocked tripeptide. Comparisons of simulated and experimental Fourier transform infrared and vibrational circular dichroism (VCD) amide I' profiles corroborate the PXRD structure. Our experimental setup reduces the sample to a quasi-two-dimensional network of fibrils. We exploited the influence of this reduced dimensionality on the amide I VCD to identify the main fibril axis. We demonstrate that PXRD, vibrational spectroscopy, and amide I simulations provide a powerful toolset for secondary structure and fibril axis determination.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Distinct electrostatic frequency tuning rates for amide I and amide I' vibrations

Amide I spectroscopy probes the backbone C=O stretch vibrations of peptides and proteins. Amide I spectra are often collected in deuterated water (D₂O) since this provides a cleaner background in the amide I frequency range; such data are often referred to as amide I' spectra since deuteration induces changes in the mode structure, including a roughly ∼10 cm^-1 redshift. For biological samples, however, deuteration is often not possible. As amide I frequency maps are increasingly applied to quantitative protein structural analysis, this raises the interesting challenge of drawing direct connections between amide I and amide I' data. We here analyze amide I and amide I' peak frequencies for a series of dipeptides and related compounds. Changes in protonation state induce large electrostatic shifts in the peak frequencies, allowing us to amass a sizable library of data points for direct amide I/amide I' comparison. While we find an excellent linear correlation between amide I and amide I' peak frequencies, the deuteration-induced shift is smaller for more red-shifted vibrations, indicating different electrostatic tuning rates in the two solvents. H₂O/D₂O shifts were negligible for proline-containing dipeptides that lack exchangeable amide hydrogens, indicating that the intrinsic properties of the solvent do not strongly influence the H/D shift. These findings indicate that the distinct tuning rates observed for the two vibrations arise from modifications to the intrinsic properties of the amide bond and provide (at least for solvated dipeptides) a simple, linear "map" for translating between amide I and amide I' frequencies.

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.

Multipolar Force Fields for Amide-I Spectroscopy from Conformational Dynamics of the Alanine Trimer

The dynamics and spectroscopy of N-methyl-acetamide (NMA) and trialanine in solution are characterized from molecular dynamics simulations using different energy functions, including a conventional point charge (PC)-based force field, one based on a multipolar (MTP) representation of the electrostatics, and a semiempirical DFT method. For the 1D infrared spectra, the frequency splitting between the two amide-I groups is 10 cm^-1 from the PC, 13 cm^-1 from the MTP, and 47 cm^-1 from self-consistent charge density functional tight-binding (SCC-DFTB) simulations, compared with 25 cm^-1 from experiment. The frequency trajectory required for the frequency fluctuation correlation function (FFCF) is determined from individual normal mode (INM) and full normal mode (FNM) analyses of the amide-I vibrations. The spectroscopy, time-zero magnitude of the FFCF C(t = 0), and the static component Δ₀² from simulations using MTP and analysis based on FNM are all consistent with experiments for (Ala)₃. Contrary to this, for the analysis excluding mode-mode coupling (INM), the FFCF decays to zero too rapidly and for simulations with a PC-based force field, the Δ₀² is too small by a factor of two compared with experiments. Simulations with SCC-DFTB agree better with experiment for these observables than those from PC-based simulations. The conformational ensemble sampled from simulations using PCs is consistent with the literature (including P_II, β, α_R, and α_L), whereas that covered by the MTP-based simulations is dominated by P_II with some contributions from β and α_R. This agrees with and confirms recently reported Bayesian-refined populations based on 1D infrared experiments. FNM analysis together with a MTP representation provides a meaningful model to correctly describe the dynamics of hydrated trialanine.

Triglycine (GGG) Adopts a Polyproline II (pPII) Conformation in Its Hydrated Crystal Form: Revealing the Role of Water in Peptide Crystallization

Polyproline II (pPII) is a left-handed 31-helix conformation, which has been observed to be the most abundant secondary structure in unfolded peptides and proteins compared to α-helix and β-sheet. Although pPII has been reported as the most stable conformation for several unfolded short chain peptides in aqueous solution, it is rarely observed in their solid state. Here, we show for the first time a glycine homopeptide (gly-gly-gly) adopting the pPII conformation in its crystalline dihydrate structure. The single crystal X-ray structure with molecular dynamic simulation suggests that a network of water and the charged carboxylate group is critical in stabilizing the pPII conformation in solid state, offering an insight into the structures of unfolded regions of proteins and the role of water in peptide crystallization.

Conformational sampling of metastable states: Tq-REM as a novel replica exchange method

Although the replica exchange methods (REMs) were developed as efficient conformational sampling methods for bio-molecular simulations, their application to very large bio-systems is somewhat limited. We propose a new replica exchange scheme (Tq-REM) created by combining the conventional temperature-REM (T-REM) and one of the Hamiltonian-REMs, q-REM, using the effective potential with reduced barriers. In the proposed Tq-REM scheme, high temperature replicas in T-REM are substituted with q-replicas. This combined scheme is expected to exploit advantages of the T-REM and q-REM resulting in improved sampling efficiency while minimizing the drawbacks of both approaches. We investigated the performance of Tq-REM compared with T-REM by performing all-atom MD simulations on Met-enkephalin, (AAQAA)₃, and Trpzip2. It was found that convergence of the free energy surfaces was improved by Tq-REM over the conventional T-REM. In particular, the trajectories of Tq-REM were able to sample the relevant conformations for all of the metastable folding intermediates, while some of the local minimum structures are poorly represented by T-REM. The results of the present study suggest that Tq-REM can provide useful tools to investigate systems where metastable states play important roles.

A weight averaged approach for predicting amide vibrational bands of a sphingomyelin bilayer

Infrared (IR) and Raman spectra of a sphingomyelin (SM) bilayer have been calculated for the amide I, II and A modes and the double-bonded CC stretching mode by a weight averaged approach, based on an all-atom molecular dynamics (MD) simulation and a vibrational structure calculation. Representative structures and statistical weights of SM clusters connected by hydrogen bonds (HBs) are observed in MD trajectories. After constructing smaller fragments from the SM clusters, the vibrational spectra of the target modes were calculated by normal mode analysis with a correction for anharmonicity, using density functional theory. The final IR and Raman spectra of a SM bilayer were obtained as the weight averages over all SM clusters. The calculated Raman spectrum is in excellent agreement with a recent measurement, providing a clear assignment of the peak in question observed at 1643 cm(-1) to the amide I modes of a SM bilayer. The analysis of the IR spectrum has also revealed that the amide bands are sensitive to the water content inside the membrane, since their band positions are strongly modulated by the HB between SM and water molecules. The present study suggests that the amide I band serves as a marker to identify the formation of SM clusters, and opens a new way to detect lipid rafts in the biological membrane.

The interplay of aggregation, fibrillization and gelation of an unexpected low molecular weight gelator: glycylalanylglycine in ethanol/water

Hydrogels formed by polypeptides could be much-favored tools for drug delivery because their main ingredients are generally biodegradable. However, the gelation of peptides in aqueous solution generally requires a minimal length of the peptide as well as distinct sequences of hydrophilic and hydrophobic residues. The aggregation of short peptides like tripeptides, which are relatively cheap and offer a high degree of biodegradability, are generally thought to require a high hydrophobicity of their residues. We found that contrary to this expectation cationic glycylalanylglycine in 55 mol% ethanol/45 mol% water forms a gel below a melting temperature of ca. 36 °C. A pure hydrogel state can be obtained after allowing the ethanol component to evaporate. The gel phase consists of crystalline fibrils of several 100 μm, which form a sample-spanning network. Rheological data reveal a soft elastic solid gel. We investigated the kinetics of the various processes that lead to the final gel state of the ternary mixture by a unique combination of UV circular dichroism, infrared, vibrational circular dichroism (VCD) and rheological measurements. A mathematical analysis of our data show that gelation is preceded by the formation of peptide β-sheet like tapes or ribbons, which give rise to a significant enhancement of the amide I' VCD signal, and the subsequent formation of rather thick and long fibrils. The VCD signals indicate that the tapes exhibit a right-handed helicity at temperatures above 16 °C and a left-handed helicity below. The tapes'/ribbons' helicity change occurs at a temperature where the UVCD data reflect a relatively long nucleation process. The kinetics of gel formation probed by the storage and loss moduli are composed of a fast process that follows tape/ribbon/fibril formation and is clearly identifiable in a movie that shows the gelation process and a slow process that causes an additional gel stabilization. The rheological data indicate that left-handed fibrils observed at low temperatures form a more solid-like structure than their right-handed counterparts formed at higher temperatures. Taken together our data reveal GAG as an unexpected gelator, the formation of which is underlied by a set of distinguishable kinetic processes.

Application of two-dimensional infrared spectroscopy to benchmark models for the amide I band of proteins

In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinations of molecular dynamics force fields, vibrational frequency mappings, and coupling models. We find that two-dimensional infrared spectra provide a much stronger test of the models than linear absorption does. The best modelling approach in the present study still leaves significant room for future improvement. The presented benchmarking scheme, thus, provides a way of validating future protocols for modelling the amide I band in proteins.

Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode

Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechano-energetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

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.

pH-Independence of trialanine and the effects of termini blocking in short peptides: a combined vibrational, NMR, UVCD, and molecular dynamics study

Several lines of evidence now well establish that unfolded peptides in general, and alanine in specific, have an intrinsic preference for the polyproline II (pPII) conformation. Investigation of local order in the unfolded state is, however, complicated by experimental limitations and the inherent dynamics of the system, which has in some cases yielded inconsistent results from different types of experiments. One method of studying these systems is the use of short model peptides, and specifically short alanine peptides, known for predominantly sampling pPII structure in aqueous solution. Recently, He et al. ( J. Am. Chem. Soc. 2012 , 134 , 1571 - 1576 ) proposed that unblocked tripeptides may not be suitable models for studying conformational propensities in unfolded peptides due to the presence of end effect, that is, electrostatic interactions between investigated amino acid residues and terminal charges. To determine whether changing the protonation states of the N- and C-termini influence the conformational manifold of the central amino acid residue in tripeptides, we have examined the pH-dependence of unblocked trialanine and the conformational preferences of alanine in the alanine dipeptide. To this end, we measured and globally analyzed amide I' band profiles and NMR J-coupling constants. We described conformational distributions as the superposition of two-dimensional Gaussian distributions assignable to specific subspaces of the Ramachandran plot. Results show that the conformational ensemble of trialanine as a whole, and the pPII content (χpPII = 0.84) in particular, remains practically unaffected by changing the protonation state. We found that compared to trialanine, the alanine dipeptide has slightly lower pPII content (χpPII = 0.74) and an ensemble more reminiscent of the unblocked Gly-Ala-Gly model peptide. In addition, a two-state thermodynamic analysis of the conformational sensitive Δε(T) and (3)J(H(N)H(α))(T) data obtained from electronic circular dichroism and H NMR spectra indicate that the free energy landscape of trialanine is similar in all protonation states. MD simulations for the investigated peptides corroborate this notion and show further that the hydration shell around unblocked trialanine is unaffected by the protonation/deprotonation of the C-terminal group. In contrast, the alanine dipeptide shows a reduced water density around the central residue as well as a less ordered hydration shell, which decreases the pPII propensity and reduces the lifetime of sampled conformations.

Structure analysis of unfolded peptides I: vibrational circular dichroism spectroscopy

Vibrational circular dichroism (VCD) spectroscopy is an invaluable spectroscopic techniques utilized to exploit the optical strength of vibrational transitions for structure analysis. In this chapter, we describe the protocol for measuring and self-consistently analyzing VCD and the corresponding FT-IR spectra of short peptides. This process involves the decomposition of the IR spectrum as well as simulations of the amide I band profiles in both spectra based on structural models of the peptides investigated. This type of spectral analysis should be complemented with similar investigations of Raman spectra, which are described in the subsequent chapter. The structural analysis of short, unfolded peptides described in this chapter can easily be extended for the analysis of longer unfolded peptides or even proteins. This is particularly important in view of the demonstrated biological relevance of intrinsically disordered peptides and proteins (IDPs).

Development and validation of transferable amide I vibrational frequency maps for peptides

Infrared (IR) spectroscopy of the amide I band has been widely utilized for the analysis of peptides and proteins. Theoretical modeling of IR spectra of proteins requires an accurate and efficient description of the amide I frequencies. In this paper, amide I frequency maps for protein backbone and side chain groups are developed from experimental spectra and vibrational lifetimes of N-methylacetamide and acetamide in different solvents. The frequency maps, along with established nearest-neighbor frequency shift and coupling schemes, are then applied to a variety of peptides in aqueous solution and reproduce experimental spectra well. The frequency maps are designed to be transferable to different environments; therefore, they can be used for heterogeneous systems, such as membrane proteins.

UV resonance Raman investigation of the conformations and lowest energy allowed electronic excited states of tri- and tetraalanine: charge transfer transitions

UV resonance Raman excitation profiles and Raman depolarization ratios were measured for trialanine and tetraalanine between 198 and 210 nm. Excitation within the pi --> pi* electronic transitions of the peptide bond results in UVRR spectra dominated by amide peptide bond vibrations. In addition to the resonance enhancement of the normal amide vibrations, we find enhancement of the symmetric terminal COO(-) vibration. The Ala(3) UVRR AmIII(3) band frequencies indicate that poly-proline II and 2.5(1) helix conformations and type II turns are present in solution. We also find that the conformation of the interior peptide bond of Ala(4) is predominantly poly-proline-II-like. The Raman excitation profiles of both Ala(3) and Ala(4) reveal a charge transfer electronic transition at 202 nm, where electron transfer occurs from the terminal nonbonding carboxylate orbital to the adjacent peptide bond pi* orbital. Raman depolarization ratio measurements support this assignment. An additional electronic transition is found in Ala(4) at 206 nm.

Solution structures of rat amylin peptide: simulation, theory, and experiment

Amyloid deposits of amylin in the pancreas are an important characteristic feature found in patients with Type-2 diabetes. The aggregate has been considered important in the disease pathology and has been studied extensively. However, the secondary structures of the individual peptide have not been clearly identified. In this work, we present detailed solution structures of rat amylin using a combination of Monte Carlo and molecular dynamics simulations. A new Monte Carlo method is presented to determine the free energy of distinct biomolecular conformations. Both folded and random-coil conformations of rat amylin are observed in water and their relative stability is examined in detail. The former contains an alpha-helical segment comprised of residues 7-17. We find that at room temperature the folded structure is more stable, whereas at higher temperatures the random-coil structure predominates. From the configurations and weights we calculate the alpha-carbon NMR chemical shifts, with results that are in reasonable agreement with experiments of others. We also calculate the infrared spectrum in the amide I stretch regime, and the results are in fair agreement with the experimental line shape presented herein.

Signatures of coherent vibrational energy transfer in IR and Raman line shapes for liquid water

We calculate theoretical IR and Raman line shapes for the OH stretch region of liquid water, using mixed quantum/classical and electronic-structure/molecular-dynamics methods. Our approach improves upon the time-averaging approximation used earlier for the same problem, and our results are in excellent agreement with experiment. Previous analysis of theoretical results for this problem considered the extent of delocalization (over local OH stretch excitations) of the instantaneous vibrational eigenstates. In this work we present a complementary analysis in the time-domain, by decomposing the appropriate response functions into diagonal and off-diagonal contributions (in the local mode basis). Our analysis indicates that all vibrational spectra show signatures of coherent vibrational energy transfer. This is manifest in different (IR, isotropic and depolarized Raman) experiments to different extents, because of the competition between coherent energy transfer and rotational disorder.

Computational vibrational spectroscopy of peptides and proteins in one and two dimensions

Vibrational spectroscopy provides direct information on molecular environment and motions but, its interpretation is often hampered by band broadening. Over the past decade, two-dimensional (2D) vibrational spectroscopy has emerged as a promising technique to overcome a number of difficulties associated with linear spectroscopy and provided significantly detailed information on the structure and dynamics of complex molecules in condensed phases. This Account reviews recently developed computational methods used to simulate 1D and 2D vibrational spectra. The central quantity to calculate in computational spectroscopy is the spectroscopic response function, which is the product of many contributing factors such as vibrational transition energies, transition moments, and their modulations by fluctuating local environment around a solute. Accurate calculations of such linear and nonlinear responses thus require a concerted effort employing a wide range of methods including electronic structure calculation (ESC) and molecular dynamics (MD) simulation. The electronic structure calculation can provide fundamental quantities such as normal-mode frequencies and transition multipole strengths. However, since the treatable system size is limited with this method, classical MD simulation has also been used to account for the dynamics of the solvent environment. To achieve chemical accuracy, these two results are combined to generate time series of fluctuating transition frequencies and transition moments with the distributed multipole analysis, and this particular approach has been known as the hybrid ESC/MD method. For coupled multichromophore systems, vibrational properties of each chromophore such as a peptide are individually calculated by electronic structure methods and the Hessian matrix reconstruction scheme was used to obtain local mode frequencies and couplings of constituting anharmonic oscillators. The spectra thus obtained, especially for biomolecules including polypeptides and proteins, have proven to be reliable and in good agreement with experimental spectra. An alternative to the hybrid method has also been developed, where the classical limit of the vibrational response function was considered. Its main attraction is the capability to obtain the spectra directly from a set of MD trajectories. A novel development along this direction has been achieved by using quantum mechanical/molecular mechanical (QM/MM) force fields for the accurate description of vibrational anharmonicity and chromophore polarization effects. The latter aspects are critical in the 2D case because classical force fields employing harmonic intramolecular potential cannot produce reliable 2D signal. We anticipate that the computational methods presented here will continue to evolve along with experimental advancements and will be of use to further elucidate ultrafast dynamics of chemical and biological systems.

Amide I Raman optical activity of polypeptides: fragment approximation

Vibrational optical activity (VOA) is an important property used to determine the absolute configuration of a chiral molecule in condensed phases. In particular, vibrational circular dichroism and Raman optical activity (ROA) are two representative VOA measurement techniques that have been extensively used to study structures and dynamics of biomolecules. Recently, the amide I vibrational circular dichroism of polypeptides was theoretically described by using fragment approximation methods, which are based on the assumption that amide I VOA can be described as a linear combination of those of constituent fragment peptide units. Here, we develop a fragment approximation theory applicable to numerical simulations of Raman and Raman optical activity spectra for the amide I vibrations in polypeptides. For an alanine dipeptide and pentapeptide analogs, we carried out density functional theory calculations of polarizability, magnetic dipole-, and electric quadrupole-ROA tensors. Numerically simulated spectra using the fragment approximation are directly compared to density functional theory results. Furthermore, the simulated ROA spectra of alanine-based right-handed alpha-helix and polyproline II polypeptides are directly compared to the previously reported experimental results. The agreements were found to be excellent, which suggests that the fragment approximation method developed for the numerical simulation of ROA spectrum of polypeptide in solution is valid and useful.