Amide I modes of tripeptides: Hessian matrix reconstruction and isotope effects

Unnatural Amino Acids for Biological Spectroscopy and Microscopy

Due to advances in methods for site-specific incorporation of unnatural amino acids (UAAs) into proteins, a large number of UAAs with tailored chemical and/or physical properties have been developed and used in a wide array of biological applications. In particular, UAAs with specific spectroscopic characteristics can be used as external reporters to produce additional signals, hence increasing the information content obtainable in protein spectroscopic and/or imaging measurements. In this Review, we summarize the progress in the past two decades in the development of such UAAs and their applications in biological spectroscopy and microscopy, with a focus on UAAs that can be used as site-specific vibrational, fluorescence, electron paramagnetic resonance (EPR), or nuclear magnetic resonance (NMR) probes. Wherever applicable, we also discuss future directions.

Vibrational anisotropy decay resolves rare earth binding induced conformational change in DTPA

Elucidating the relationship between metal-ligand interactions and the associated conformational change of the ligand is critical for understanding the separation of lanthanides via ion binding. Here we examine DTPA, a multidentate ligand that binds lanthanides, in its free and metal bound conformations using ultrafast polarization dependent vibrational spectroscopy. The polarization dependent pump-probe spectra were analyzed to extract the isotropic and anisotropic response of DTPA's carbonyl groups in the 1550-1650 cm-1 spectral region. The isotropic response reports on the population relaxation of the carbonyl stretching modes. We find that the isotropic response is influenced by the identity of the metal ion. The anisotropy decay of the carbonyl stretching modes reveals a faster decay in the lanthanide-DTPA complexes than in the free DTPA ligand. We attribute the anisotropy decay to energy transfer among the different carbonyl sites - where the conformational change results in an increased coupling between the carbonyl sites of metal-bound DTPA complexes. DFT calculations and theoretical simulations of energy transfer suggest that the carbonyl sites are more strongly coupled in the metal-bound conformations compared to the free DTPA. The stronger coupling in the metal bound DTPA conformation leads to efficient energy transfer among the different carbonyl sites. Comparing the rate of anisotropy decay across the series of metal bound DTPA complexes we find that the anisotropy is sensitive to the charge density of the central metal ion, and thus can serve as a molecular scale reporter for lanthanide ion binding.

Refining protein amide I spectrum simulations with simple yet effective electrostatic models for local wavenumbers and dipole derivative magnitudes

Analysis of the amide I band of proteins is probably the most wide-spread application of bioanalytical infrared spectroscopy. Although highly desirable for a more detailed structural interpretation, a quantitative description of this absorption band is still difficult. This work optimized several electrostatic models with the aim to reproduce the effect of the protein environment on the intrinsic wavenumber of a local amide I oscillator. We considered the main secondary structures - α-helices, parallel and antiparallel β-sheets - with a maximum of 21 amide groups. The models were based on the electric potential and/or the electric field component along the CO bond at up to four atoms in an amide group. They were bench-marked by comparison to Hessian matrices reconstructed from density functional theory calculations at the BPW91, 6-31G** level. The performance of the electrostatic models depended on the charge set used to calculate the electric field and potential. Gromos and DSSP charge sets, used in common force fields, were not optimal for the better performing models. A good compromise between performance and the stability of model parameters was achieved by a model that considered the electric field at the positions of the oxygen, nitrogen, and hydrogen atoms of the considered amide group. The model describes also some aspects of the local conformation effect and performs similar on its own as in combination with an explicit implementation of the local conformation effect. It is better than a combination of a local hydrogen bonding model with the local conformation effect. Even though the short-range hydrogen bonding model performs worse, it captures important aspects of the local wavenumber sensitivity to the molecular surroundings. We improved also the description of the coupling between local amide I oscillators by developing an electrostatic model for the dependency of the dipole derivative magnitude on the protein environment.

Unpolarized laser method for infrared spectrum calculation of amide I CO bonds in proteins using molecular dynamics simulation

The investigation of the strong infrared (IR)-active amide I modes of peptides and proteins has received considerable attention because a wealth of detailed information on hydrogen bonding, dipole-dipole interactions, and the conformations of the peptide backbone can be derived from the amide I bands. The interpretation of experimental spectra typically requires substantial theoretical support, such as direct ab-initio molecular dynamics simulation or mixed quantum-classical description. However, considering the difficulties associated with these theoretical methods and their applications are limited in small peptides, it is highly desirable to develop a simple yet efficient approach for simulating the amide I modes of any large proteins in solution. In this work, we proposed a comprehensive computational method that extends the well-established molecular dynamics (MD) simulation method to include an unpolarized IR laser for exciting the CO bonds of proteins. We showed the amide I frequency corresponding to the frequency of the laser pulse which resonated with the CO bond vibration. At this frequency, the protein energy and the CO bond length fluctuation were maximized. Overall, the amide I bands of various single proteins and amyloids agreed well with experimental data. The method has been implemented into the AMBER simulation package, making it widely available to the scientific community. Additionally, the application of the method to simulate the transient amide I bands of amyloid fibrils during the IR laser-induced disassembly process was discussed in details.

Modeling the Infrared Spectroscopy of Oligonucleotides with 13C Isotope Labels

The carbonyl stretching modes have been widely used in linear and two-dimensional infrared (IR) spectroscopy to probe the conformation, interaction, and biological functions of nucleic acids. However, due to their universal appearance in nucleobases, the IR absorption bands of nucleic acids are often highly congested in the 1600-1800 cm^-1 region. Following the fruitful applications in proteins, ¹³C isotope labels have been introduced to the IR measurements of oligonucleotides to reveal their site-specific structural fluctuations and hydrogen bonding conditions. In this work, we combine recently developed frequency and coupling maps to develop a theoretical strategy that models the IR spectra of oligonucleotides with ¹³C labels directly from molecular dynamics simulations. We apply the theoretical method to nucleoside 5'-monophosphates and DNA double helices and demonstrate how elements of the vibrational Hamiltonian determine the spectral features and their changes upon isotope labeling. Using the double helices as examples, we show that the calculated IR spectra are in good agreement with experiments and the ¹³C isotope labeling technique can potentially be applied to characterize the stacking configurations and secondary structures of nucleic acids.

A comparative study of interfacial environments in lipid nanodiscs and vesicles

Membrane protein conformations and dynamics are driven by the protein-lipid interactions occurring within the local environment of the membrane. These environments remain challenging to accurately capture in structural and biophysical experiments using bilayers. Consequently, there is an increasing need for realistic cell-membrane mimetics for in vitro studies. Lipid nanodiscs provide certain advantages over vesicles for membrane protein studies. Nanodiscs are increasingly used for structural and spectroscopic characterization of membrane proteins. Despite the common use of nanodiscs, the interfacial environments of lipids confined to a ~10-nm diameter area have remained relatively underexplored. Here, we use ultrafast two-dimensional infrared spectroscopy and temperature-dependent infrared absorption measurements of the ester carbonyls to compare the interfacial hydrogen bond structure and dynamics in lipid nanodiscs of varying lipid compositions and sizes with ~100-nm vesicles. We examine the effects of lipid composition and nanodisc size. We found that nanodiscs and vesicles share largely similar lipid-water H-bond environments and interfacial dynamics. Differences in measured enthalpies of H-bonding suggest that H-bond dynamics in nanodiscs are modulated by the interaction between the annular lipids and the scaffold protein.

Segregation on the nanoscale coupled to liquid water polyamorphism in supercooled aqueous ionic-liquid solution

The most intriguing hypothesis explaining many water anomalies is a metastable liquid-liquid phase transition (LLPT) at high pressure and low temperatures, experimentally hidden by homogeneous nucleation. Recent infrared spectroscopic experiments showed that upon addition of hydrazinium trifluoroacetate to water, the supercooled ionic solution undergoes a sharp, reversible LLPT at ambient pressure, possible offspring of that in pure water. Here, we calculate the temperature-dependent signature of the OH-stretching band, reporting on the low/high density phase of water, in neat water and in the same experimentally investigated ionic solution. The comparison between the infrared signature of the pure liquid and that of the ionic solution can be achieved only computationally, providing insight into the nature of the experimentally observed phase transition and allowing us to investigate the effects of ionic compounds on the high to low density supercooled liquid water transition. We show that the experimentally observed crossover behavior in the ionic solution can be reproduced only if the phase transition between the low- and high-density liquid states of water is coupled to a mixing-unmixing transition between the water component and the ions: at low temperatures, water and ions are separated and the water component is a low density liquid. At high temperatures, water and ions get mixed and the water component is a high-density liquid. The separation at low temperatures into ion-rich and ion-poor regions allows unveiling the polyamorphic nature of liquid water, leading to a crossover behavior resembling that observed in supercooled neat water under high pressure.

A computational insight into the relationship between side chain IR line shapes and local environment in fibril-like structures

Infrared spectroscopy is a widely used technique to characterize protein structures and protein mediated processes. While the amide I band provides information on proteins' secondary structure, amino acid side chains are used as infrared probes for the investigation of protein reactions and local properties. In this paper, we use a hybrid quantum mechanical/classical molecular dynamical approach based on the perturbed matrix method to compute the infrared band due to the C=O stretching mode of amide-containing side chains. We calculate, at first, the infrared band of zwitterionic glutamine in water and obtain results in very good agreement with the experimental data. Then, we compute the signal arising from glutamine side chains in a microcrystal of the yeast prion Sup35-derived peptide, GNNQQNY, with a fibrillar structure. The infrared bands obtained by selective isotopic labeling of the two glutamine residues, Q4 and Q5, of each peptide were experimentally used to investigate the local hydration in the fibrillar microcrystal. The experimental spectra of the two glutamine residues, which experience different hydration environments, feature different spectral signals that are well reproduced by the corresponding calculated spectra. In addition, the analysis of the simulated spectra clarifies the molecular origin of the experimentally observed spectroscopic differences that arise from the different local electric field experienced by the two glutamine residues, which is, in turn, determined by a different hydrogen bonding pattern.

Computational IR Spectroscopy of Insulin Dimer Structure and Conformational Heterogeneity

We have investigated the structure and conformational dynamics of insulin dimer using a Markov state model (MSM) built from extensive unbiased atomistic molecular dynamics simulations and performed infrared spectral simulations of the insulin MSM to describe how structural variation within the dimer can be experimentally resolved. Our model reveals two significant conformations to the dimer: a dominant native state consistent with other experimental structures of the dimer and a twisted state with a structure that appears to reflect a ∼55° clockwise rotation of the native dimer interface. The twisted state primarily influences the contacts involving the C-terminus of insulin's B chain, shifting the registry of its intermolecular hydrogen bonds and reorganizing its side-chain packing. The MSM kinetics predict that these configurations exchange on a 14 μs time scale, largely passing through two Markov states with a solvated dimer interface. Computational amide I spectroscopy of site-specifically ¹³C¹⁸O labeled amides indicates that the native and twisted conformation can be distinguished through a series of single and dual labels involving the B24F, B25F, and B26Y residues. Additional structural heterogeneity and disorder is observed within the native and twisted states, and amide I spectroscopy can also be used to gain insight into this variation. This study will provide important interpretive tools for IR spectroscopic investigations of insulin structure and transient IR kinetics experiments studying the conformational dynamics of insulin dimer.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Tautomeric Effect of Histidine on β-Sheet Formation of Amyloid Beta 1-40: 2D-IR Simulations

Histidine state (protonated or δ or ε tautomer) has been considered the origin of abnormal misfolding and aggregation of β-amyloid (Aβ). Our previous studies reported that the δδδ isomer of Aβ (1-40) has a greater propensity for β-sheet conformation compared to other isomers. However, direct proof of the tautomeric effect has not been reported. In this context, we calculated histidine site-specific two-dimensional infrared spectroscopy of the δδδ, εεε, and πππ (all protonated histidine) systems within the framework of classical molecular dynamics simulations aiming at connecting our previous results with the current experimental observations. Our results showed that β-sheet formation is favored for the δδδ and πππ tautomers compared with the εεε tautomer, consistent with our previous studies. This result was further supported by contact map analyses and the strength of dipole coupling between the amide-I bonds of each residue. The two-dimensional infrared diagonal trace for each tautomer included three distinctive spectrally resolvable peaks near 1680, 1686, and 1693 cm^-1, as was also observed for histidine dipeptides. However, the peak positions at His6, His13, and His14 did not show a consensus trend with the histidine or protonation state but were instead affected by the presence of surrounding hydrogen bonds. Our study provides a deeper insight into the influence of tautomerism and protonation of histidine residues in Aβ (1-40) on amyloid misfolding and provides a connection between our previous simulations and experimental observations.

Modeling the vibrational couplings of nucleobases

Vibrational spectroscopy, in particular infrared spectroscopy, has been widely used to probe the three-dimensional structures and conformational dynamics of nucleic acids. As commonly used chromophores, the C=O and C=C stretch modes in the nucleobases exhibit distinct spectral features for different base pairing and stacking configurations. To elucidate the origin of their structural sensitivity, in this work, we develop transition charge coupling (TCC) models that allow one to efficiently calculate the interactions or couplings between the C=O and C=C chromophores based on the geometric arrangements of the nucleobases. To evaluate their performances, we apply the TCC models to DNA and RNA oligonucleotides with a variety of secondary and tertiary structures and demonstrate that the predicted couplings are in quantitative agreement with the reference values. We further elucidate how the interactions between the paired and stacked bases give rise to characteristic IR absorption peaks and show that the TCC models provide more reliable predictions of the coupling constants as compared to the transition dipole coupling scheme. The TCC models, together with our recently developed through-bond coupling constants and vibrational frequency maps, provide an effective theoretical strategy to model the vibrational Hamiltonian, and hence the vibrational spectra of nucleic acids in the base carbonyl stretch region directly from atomistic molecular simulations.

The Amide I Spectrum of Proteins-Optimization of Transition Dipole Coupling Parameters Using Density Functional Theory Calculations

The amide I region of the infrared spectrum is related to the protein backbone conformation and can provide important structural information. However, the interpretation of the experimental results is hampered because the theoretical description of the amide I spectrum is still under development. Quantum mechanical calculations, for example, using density functional theory (DFT), can be used to study the amide I spectrum of small systems, but the high computational cost makes them inapplicable to proteins. Other approaches that solve the eigenvalues of the coupled amide I oscillator system are used instead. An important interaction to be considered is transition dipole coupling (TDC). Its calculation depends on the parameters of the transition dipole moment. This work aims to find the optimal parameters for TDC in three major secondary structures: α-helices, antiparallel β-sheets, and parallel β-sheets. The parameters were suggested through a comparison between DFT and TDC calculations. The comparison showed a good agreement for the spectral shape and for the wavenumbers of the normal modes for all secondary structures. The matching between the two methods improved when hydrogen bonding to the amide oxygen was considered. Optimal parameters for individual secondary structures were also suggested.

Modeling amino-acid side chain infrared spectra: the case of carboxylic residues

Infrared (IR) spectroscopy is commonly utilized for the investigation of protein structures and protein-mediated processes.

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala-Ala-Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala-Ala-Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.

Development of Vibrational Frequency Maps for Nucleobases

Vibrational spectroscopy provides a powerful tool to probe the structure and dynamics of nucleic acids because specific normal modes, particularly the base carbonyl stretch modes, are highly sensitive to the hydrogen bonding patterns and stacking configurations in these biomolecules. In this work, we develop vibrational frequency maps for the C═O and C═C stretches in nucleobases that allow the calculations of their site frequencies directly from molecular dynamics simulations. We assess the frequency maps by applying them to nucleobase derivatives in aqueous solutions and nucleosides in organic solvents and demonstrate that the predicted infrared spectra are in good agreement with experimental measurements. The frequency maps can be readily used to model the linear and nonlinear vibrational spectroscopy of nucleic acids and elucidate the molecular origin of the experimentally observed spectral features.

Understanding the intramolecular vibrational energy transfer and structural dynamics of anionic ligands in a photo-catalytic CO2reduction catalyst

The knowledge of intramolecular vibrational energy redistribution (IVR) and structural dynamics of rhenium photo-catalysts is essential for understanding the mechanism of the photo-catalytic process of CO₂reduction.

The dynamics of peptide-water interactions in dialanine: An ultrafast amide I 2D IR and computational spectroscopy study

We present a joint experimental and computational study of the dynamic interactions of dialanine (Ala-Ala) with water, comparing the results of ultrafast 2D IR and infrared transient absorption spectroscopy of its amide I vibration with spectra modeled from molecular dynamics (MD) simulations. The experimental data are analyzed to describe vibrational frequency fluctuations, vibrational energy relaxation, and chemical exchange processes. The origin of these processes in the same underlying fluctuating forces allows a common description in terms of the fluctuations and conformational dynamics of the peptide and associated solvent. By comparing computational spectroscopy from MD simulations with multiple force fields and water models, we describe how the dynamics of water hydrogen bond fluctuations and switching processes act as a source of friction that governs the dephasing and vibrational relaxation, and provide a description of coupled water and peptide motions that give rise to spectroscopic exchange processes.

Computing infrared spectra of proteins using the exciton model

The ability to compute from first principles the infrared spectrum of a protein in solution phase representing a biological system would provide a useful connection to atomistic models of protein structure and dynamics. Indeed, such calculations are a vital complement to 2DIR experimental measurements, allowing the observed signals to be interpreted in terms of detailed structural and dynamical information. In this article, we have studied nine structurally and spectroscopically well-characterized proteins, representing a range of structural types. We have simulated the equilibrium conformational dynamics in an explicit point charge water model. Using the resulting trajectories based on MD simulations, we have computed the one and two dimensional infrared spectra in the Amide I region, using an exciton approach, in which a local mode basis of carbonyl stretches is considered. The role of solvent in shifting the Amide I band (by 30 to 50 cm-1 ) is clearly evident. Similarly, the conformational dynamics contribute to the broadening of peaks in the spectrum. The inhomogeneous broadening in both the 1D and 2D spectra reflects the significant conformational diversity observed in the simulations. Through the computed 2D cross-peak spectra, we show how different pulse schemes can provide additional information on the coupled vibrations. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

Three low-lying vibrational states of molecular systems are responsible for the signals of linear and third-order nonlinear vibrational spectroscopies. Theoretical studies based on mixed quantum/classical calculations provide a powerful way to analyze those experiments. A statistically meaningful result can be obtained from the calculations by solving the vibrational Schrödinger equation over many numbers of molecular configurations. The discrete variable representation (DVR) method is a useful technique to calculate vibrational eigenstates subject to an arbitrary anharmonic potential surface. Considering the large number of molecular configurations over which the DVR calculations are repeated, the calculations are desired to be optimized in balance between the cost and accuracy. We determine a dimension of the DVR method which appears to be optimum for the calculations of the three states of molecular vibrations with anharmonic strengths often found in realistic molecular systems. We apply the numerical technique to calculate the local OH stretching frequencies of liquid water, which are well known to be widely distributed due to the inhomogeneity in molecular configuration, and found that the frequencies of the 0-1 and 1-2 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.

Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results

The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

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.

Dissecting amide-I vibration in β-peptide helices

The vibrational properties of the amide-I modes of β-peptides in five helical conformations (8-helix, 10-helix, 12-helix, 14-helix, and 10/12-helix) from tetramer to heptamer were examined by ab initio calculations. The normal modes have been first decoupled into local modes, whose transition energies are found to be intrinsically sensitive to peptide structure and intramolecular hydrogen bonding interactions. By further removing the intramolecular hydrogen bonding interactions, pure local modes are obtained, whose transition energies still exhibit some conformational dependence in 8-helix and 10/12 hybrid helix, but not much in homogeneous 10-, 12-, and 14-helical conformations. This suggests that a set of nearly degenerated pure local-mode transitions can be specified when excitonic modeling the amide-I vibration in latter cases. The work provides important benchmark measurements for understanding the complexity of the amide-I absorption spectra of β-polypeptides.

Assessment of amide I spectroscopic maps for a gas-phase peptide using IR-UV double-resonance spectroscopy and density functional theory calculations

The spectroscopy of amide I vibrations has become a powerful tool for exploring protein structure and dynamics. To help with spectral interpretation, it is often useful to perform molecular dynamics (MD) simulations. To connect spectroscopic experiments to simulations in an efficient manner, several researchers have proposed "maps," which relate observables in classical MD simulations to quantum spectroscopic variables. It can be difficult to discern whether errors in the theoretical results (compared to experiment) arise from inaccuracies in the MD trajectories or in the maps themselves. In this work, we evaluate spectroscopic maps independently from MD simulations by comparing experimental and theoretical spectra for a single conformation of the α-helical model peptide Ac-Phe-(Ala)5-Lys-H(+) in the gas phase. Conformation-specific experimental spectra are obtained for the unlabeled peptide and for several singly and doubly (13)C-labeled variants using infrared-ultraviolet double-resonance spectroscopy, and these spectra are found to be well-modeled by density functional theory (DFT) calculations at the B3LYP/6-31G** level. We then compare DFT results for the deuterated and (13)C(18)O-labeled peptide with those from spectroscopic maps developed and used previously by the Skinner group. We find that the maps are typically accurate to within a few cm(-1) for both frequencies and couplings, having larger errors only for the frequencies of terminal amides.

PICVib: an accurate, fast and simple procedure to investigate selected vibrational modes and evaluate infrared intensities

The generalization of the PICVib approach for calculating selected infrared intensities is shown to be successful and to preserves its easiness of implementation and parallelization, flexibility and treatment of large systems and/or at high theoretical levels.

Conformational analysis of Gly-Ala-NHMe in D(2)O and DMSO solutions: a two-dimensional infrared spectroscopy study

A relevant number of experiments on short peptides has been performed in recent years. One of the major problems rises from the simultaneous presence of slightly different conformers at equilibrium in solution. In the present paper, the conformational characteristics of the Gly-l-Ala-Methyl amide dipeptide in D2O and DMSO solutions are investigated by nonlinear IR spectroscopy. The pump-probe scheme with ultrashort mid-infrared pulses, in the Amide I region, is used to determine the mutual orientation of the two C═O bonds and the dynamics due to solute-solvent interactions. The coupling between Amide I modes is evaluated from both linear and 2D spectra. The interconversion between the different conformations occurs on time scales longer than the vibrational lifetime, and the spectral diffusion observed in 2D spectra is attributed to the solvent dynamics. Quantum mechanical calculations and molecular dynamics simulations are performed to identify the most stable geometries. By comparing the experimental and the theoretical data, we establish the prevalence of β-like polar conformers in both water and DMSO solvents.

Electrostatic frequency shifts in amide I vibrational spectra: direct parameterization against experiment

The interpretation of protein amide I infrared spectra has been greatly assisted by the observation that the vibrational frequency of a peptide unit reports on its local electrostatic environment. However, the interpretation of spectra remains largely qualitative due to a lack of direct quantitative connections between computational models and experimental data. Here, we present an empirical parameterization of an electrostatic amide I frequency map derived from the infrared absorption spectra of 28 dipeptides. The observed frequency shifts are analyzed in terms of the local electrostatic potential, field, and field gradient, evaluated at sites near the amide bond in molecular dynamics simulations. We find that the frequency shifts observed in experiment correlate very well with the electric field in the direction of the C=O bond evaluated at the position of the amide oxygen atom. A linear best-fit mapping between observed frequencies and electric field yield sample standard deviations of 2.8 and 3.7 cm(-1) for the CHARMM27 and OPLS-AA force fields, respectively, and maximum deviations (within our data set) of 9 cm(-1). These results are discussed in the broader context of amide I vibrational models and the effort to produce quantitative agreement between simulated and experimental absorption spectra.

Parallel β-sheet vibrational couplings revealed by 2D IR spectroscopy of an isotopically labeled macrocycle: quantitative benchmark for the interpretation of amyloid and protein infrared spectra

Infrared spectroscopy is playing an important role in the elucidation of amyloid fiber formation, but the coupling models that link spectra to structure are not well tested for parallel β-sheets. Using a synthetic macrocycle that enforces a two stranded parallel β-sheet conformation, we measured the lifetimes and frequency for six combinations of doubly (13)C═(18)O labeled amide I modes using 2D IR spectroscopy. The average vibrational lifetime of the isotope labeled residues was 550 fs. The frequencies of the labels ranged from 1585 to 1595 cm(-1), with the largest frequency shift occurring for in-register amino acids. The 2D IR spectra of the coupled isotope labels were calculated from molecular dynamics simulations of a series of macrocycle structures generated from replica exchange dynamics to fully sample the conformational distribution. The models used to simulate the spectra include through-space coupling, through-bond coupling, and local frequency shifts caused by environment electrostatics and hydrogen bonding. The calculated spectra predict the line widths and frequencies nearly quantitatively. Historically, the characteristic features of β-sheet infrared spectra have been attributed to through-space couplings such as transition dipole coupling. We find that frequency shifts of the local carbonyl groups due to nearest neighbor couplings and environmental factors are more important, while the through-space couplings dictate the spectral intensities. As a result, the characteristic absorption spectra empirically used for decades to assign parallel β-sheet secondary structure arises because of a redistribution of oscillator strength, but the through-space couplings do not themselves dramatically alter the frequency distribution of eigenstates much more than already exists in random coil structures. Moreover, solvent exposed residues have amide I bands with >20 cm(-1) line width. Narrower line widths indicate that the amide I backbone is solvent protected inside the macrocycle. This work provides calculated and experimentally verified couplings for parallel β-sheets that can be used in structure-based models to simulate and interpret the infrared spectra of β-sheet containing proteins and protein assemblies, such as amyloid fibers.

Frequency distribution of the amide-I vibration sorted by residues in amyloid fibrils revealed by 2D-IR measurements and simulations

The infrared optical response of amyloid fibrils Aβ(1-40) is investigated. Simulations of two models corresponding to different protonation states are compared with experiment. The simulations reveal that vibrational frequency distributions inside the fibrils are dominated by side chain fluctuations. We further confirm earlier suggestions based on 2D-IR measurements that water molecules can be trapped inside the fibrils.

Determination of noncovalent docking by infrared spectroscopy of cold gas-phase complexes

Multidentate, noncovalent interactions between small molecules and biopolymer fragments are central to processes ranging from drug action to selective catalysis. We present a versatile and sensitive spectroscopic probe of functional groups engaged in hydrogen bonding in such contexts. This involves measurement of the frequency changes in specific covalent bonds upon complex formation, information drawn from otherwise transient complexes that have been extracted from solution and conformationally frozen near 10 kelvin in gas-phase clusters. Resonances closely associated with individual oscillators are easily identified through site-specific isotopic labeling, as demonstrated by application of the method to an archetypal system involving a synthetic tripeptide known to bind biaryl substrates through tailored hydrogen bonding to catalyze their asymmetric bromination. With such data, calculations readily converge on the plausible operative structures in otherwise computationally prohibitive, high-dimensionality landscapes.

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).

2DIR spectroscopy of human amylin fibrils reflects stable β-sheet structure

The aggregation of human amylin to form amyloid contributes to islet β-cell dysfunction in type 2 diabetes. Studies of amyloid formation have been hindered by the low structural resolution or relatively modest time resolution of standard methods. Two-dimensional infrared (2DIR) spectroscopy, with its sensitivity to protein secondary structures and its intrinsic fast time resolution, is capable of capturing structural changes during the aggregation process. Moreover, isotope labeling enables the measurement of residue-specific information. The diagonal line widths of 2DIR spectra contain information about dynamics and structural heterogeneity of the system. We illustrate the power of a combined atomistic molecular dynamics simulation and theoretical and experimental 2DIR approach by analyzing the variation in diagonal line widths of individual amide I modes in a series of labeled samples of amylin amyloid fibrils. The theoretical and experimental 2DIR line widths suggest a "W" pattern, as a function of residue number. We show that large line widths result from substantial structural disorder and that this pattern is indicative of the stable secondary structure of the two β-sheet regions. This work provides a protocol for bridging MD simulation and 2DIR experiments for future aggregation studies.