Ultrafast vibrational spectroscopy of water and aqueous N-methylacetamide: Comparison of different electronic structure/molecular dynamics approaches

A new computational methodology for the characterization of complex molecular environments using IR spectroscopy: bridging the gap between experiments and computations

The molecular interactions and dynamics of complex liquid solutions are now routinely measured using IR and 2DIR spectroscopy. In particular, the use of the latter allows the determination of the frequency fluctuation correlation function (FFCF), while the former provides us with the average frequency. In turn, the FFCF can be used to quantify the vibrational dynamics of a molecule in a solution, and the center frequency provides details about the chemical environment, solvatochromism, of the vibrational mode. In simple solutions, the IR methodology can be used to unambiguously assign the interactions and dynamics observed by a molecule in solution. However, in complex environments with molecular heterogeneities, this assignment is not simple. Therefore, a method that allows for such an assignment is essential. Here, a parametrization free method, called Instantaneous Frequencies of Molecules or IFM, is presented. The IFM method, when coupled to classical molecular simulations, can predict the FFCF of a molecule in solutions. Here, N-methylacetamide (NMA) in seven different chemical environments, both simple and complex, is used to test this new method. The results show good agreement with experiments for the NMA solvatochromism and FFCF dynamics, including characteristic times and amplitudes of fluctuations. In addition, the new method shows equivalent or improved results when compared to conventional frequency maps. Overall, the use of the new method in conjunction with molecular dynamics simulations allows unlocking the full potential of IR spectroscopy to generate molecular maps from vibrational observables, capable of describing the interaction landscape of complex molecular systems.

Chasing weakly-bound biological water in aqueous environment near the peptide backbone by ultrafast 2D infrared spectroscopy

There has been a long-standing debate as to how many hydrogen bonds a peptide backbone amide can form in aqueous solution. Hydrogen-bonding structural dynamics of N-ethylpropionamide (a β-peptide model) in water was examined using infrared (IR) spectroscopy. Two amide-I sub bands arise mainly from amide C=O group that forms strong H-bonds with solvent water molecules (SHB state), and minorly from that involving one weak H-bond with water (WHB state). This picture is supported by molecular dynamics simulations and ab-initio calculations. Further, thermodynamics and kinetics of the SHB and WHB species were examined mainly by chemical-exchange two-dimensional IR spectroscopy, yielding an activation energy for the SHB-to-WHB exchange of 13.25 ± 0.52 kJ mol‒1, which occurs in half picosecond at room temperature. Our results provided experimental evidence of an unstable water molecule near peptide backbone, allowing us to gain more insights into the dynamics of the protein backbone hydration.

Theoretical basis for interpreting heterodyne chirality-selective sum frequency generation spectra of water

Chirality-selective vibrational sum frequency generation (chiral SFG) spectroscopy has emerged as a powerful technique for the study of biomolecular hydration water due to its sensitivity to the induced chirality of the first hydration shell. Thus far, water O-H vibrational bands in phase-resolved heterodyne chiral SFG spectra have been fit using one Lorentzian function per vibrational band, and the resulting fit has been used to infer the underlying frequency distribution. Here, we show that this approach may not correctly reveal the structure and dynamics of hydration water. Our analysis illustrates that the chiral SFG responses of symmetric and asymmetric O-H stretch modes of water have opposite phase and equal magnitude and are separated in energy by intramolecular vibrational coupling and a heterogeneous environment. The sum of the symmetric and asymmetric responses implies that an O-H stretch in a heterodyne chiral SFG spectrum should appear as two peaks with opposite phase and equal amplitude. Using pairs of Lorentzian functions to fit water O-H stretch vibrational bands, we improve spectral fitting of previously acquired experimental spectra of model β-sheet proteins and reduce the number of free parameters. The fitting allows us to estimate the vibrational frequency distribution and thus reveals the molecular interactions of water in hydration shells of biomolecules directly from chiral SFG spectra.

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.

Ultrafast Spectroscopy Reveals Slow Water Dynamics in Biocondensates

Cells achieve high spatiotemporal control over biochemical processes through compartmentalization to membrane-bound as well as membraneless organelles that assemble by liquid-liquid phase separation. Characterizing the balance of forces within these environments is essential to understanding their stability and function, and water is an integral part of the condensate, playing an important role in mediating electrostatic and hydrogen-bonding interactions. Here, we investigate the ultrafast, picosecond hydrogen-bond dynamics of a model biocondensate consisting of a peptide poly-l-arginine (Poly-R) and the nucleic acid adenosine monophosphate (AMP) using coherent two-dimensional infrared (2D IR) spectroscopy. We investigated three vibrational modes: the arginine side-chain C═N stretches, an AMP ring mode, and the amide backbone carbonyl stretching modes. Dynamics slow considerably between the dilute phase and the condensate phase for each vibrational probe. For example, the arginine side-chain C═N modes slow from 0.38 to 2.26 ps due to strong electrostatic interactions. All-atom molecular dynamics simulations provide an atomistic interpretation of the H-bond network disruption resulting from electrostatic contributions as well as collapse within the condensate. Simulations predict that a fraction of water molecules are highly constrained within the condensate, explaining the observed slowdown in the H-bond dynamics.

Asymmetry of the Electrostatic Environment as the Origin of the Symmetry Breaking Effect of the Nitrate Ion in Aqueous Solution

Elucidating the mechanism of how vibrational modes are affected by intermolecular interactions is important for a better understanding of the nature of the former as probes of the latter. Here, such an analysis is carried out for the N-O stretching modes of the nitrate ion interacting with water, with an emphasis on the symmetry breaking effect. On the basis of theoretical calculations on the structural, vibrational, and electrostatic properties of molecular clusters and spectral simulations for an aqueous solution, a transparent view is demonstrated on the mechanism that modulations of spatially local electrostatic environment give rise to structural and spectroscopic symmetry breaking effect. The electrostatic interaction model constructed here is a seven-parameter model; the use of a single electrostatic parameter, such as the electric field on a single atomic site, is found to be insufficient for quantitative evaluation. It is also shown that the frequency modulations of the N-O stretching modes in aqueous solution occur on a time scale much shorter than 0.1 ps.

Design of an Electrostatic Frequency Map for the NH Stretch of the Protein Backbone and Application to Chiral Sum Frequency Generation Spectroscopy

We develop an electrostatic map for the vibrational NH stretch (amide A) of the protein backbone with a focus on vibrational chiral sum frequency generation spectroscopy (chiral SFG). Chiral SFG has been used to characterize protein secondary structure at interfaces using the NH stretch and to investigate chiral water superstructures around proteins using the OH stretch. Interpretation of spectra has been complicated because the NH stretch and OH stretch overlap spectrally. Although an electrostatic map for water OH developed by Skinner and co-workers was used previously to calculate the chiral SFG response of water structures around proteins, a map for protein NH that is directly responsive to biological complexity has yet to be developed. Here, we develop such a map, linking the local electric field to vibrational frequencies and transition dipoles. We apply the map to two protein systems and achieve much better agreement with experiment than was possible in our previous studies. We show that couplings between NH and OH vibrations are crucial to the line shape, which informs the interpretation of chiral SFG spectra, and that the chiral NH stretch response is sensitive to small differences in structure. This work increases the utility of the NH stretch in biomolecular spectroscopy.

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.

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.

Testing the Limitations of MD-Based Local Electric Fields Using the Vibrational Stark Effect in Solution: Penicillin G as a Test Case

Noncovalent interactions underlie nearly all molecular processes in the condensed phase from solvation to catalysis. Their quantification within a physically consistent framework remains challenging. Experimental vibrational Stark effect (VSE)-based solvatochromism can be combined with molecular dynamics (MD) simulations to quantify the electrostatic forces in solute-solvent interactions for small rigid molecules and, by extension, when these solutes bind in enzyme active sites. While generalizing this approach toward more complex (bio)molecules, such as the conformationally flexible and charged penicillin G (PenG), we were surprised to observe inconsistencies in MD-based electric fields. Combining synthesis, VSE spectroscopy, and computational methods, we provide an intimate view on the origins of these discrepancies. We observe that the electric fields are correlated to conformation-dependent effects of the flexible PenG side chain, including both the local solvation structure and solute conformational sampling in MD. Additionally, we identified that MD-based electric fields are consistently overestimated in three-point water models in the vicinity of charged groups; this cannot be entirely ameliorated using polarizable force fields (AMOEBA) or advanced water models. This work demonstrates the value of the VSE as a direct method for experiment-guided refinements of MD force fields and establishes a general reductionist approach to calibrating vibrational probes for complex (bio)molecules.

Multiresolution continuous wavelet transform for studying coupled solute-solvent vibrations via ab initio molecular dynamics

Vibrational analysis in solution and the theoretical determination of infrared and Raman spectra are of key importance in many fields of chemical interest. Vibrational band dynamics of molecules and their sensitivity to the environment can also be captured by these spectroscopies in their time dependent version. However, it is often difficult to provide an interpretation of the experimental data at the molecular scale, such as molecular mechanisms or the processes hidden behind them. In this work, we present a theoretical-computational protocol based on ab initio molecular dynamics simulations and a combination of normal-like (generalized) mode analysis of solute-solvent clusters with a wavelet transform, for the first time. The case study is the vibrational dynamics of N-methyl-acetamide (NMA) in water solution, a well-known model of hydration of peptides and proteins. Amide modes are typical bands of peptide and protein backbone, and their couplings with the environment are very challenging in terms of the accurate prediction of solvent induced intensity and frequency shifts. The contribution of water molecules surrounding NMA to the composition of generalized and time resolved modes is introduced in our vibrational analysis, showing unequivocally its influence on the amide mode spectra. It is also shown that such mode compositions need the inclusion of the first shell solvent molecules to be accurately described. The wavelet analysis is proven to be strongly recommended to follow the time evolution of the spectra, and to capture vibrational band couplings and frequency shifts over time, preserving at the same time a well-balanced time-frequency resolution. This peculiar feature also allows one to perform a combined structural-vibrational analysis, where the different strengths of hydrogen bond interactions can quantitatively affect the amide bands over time at finite temperature. The proposed method allows for the direct connection between vibrational modes and local structural changes, providing a link from the spectroscopic observable to the structure, in this case the peptide backbone, and its hydration layouts.

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.

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.

IR Spectroscopy Can Reveal the Mechanism of K+ Transport in Ion Channels

Ion channels like KcsA enable ions to move across cell membranes at near diffusion-limited rates and with very high selectivity. Various mechanisms have been proposed to explain this phenomenon. Broadly, there is disagreement among the proposed mechanisms about whether ions occupy adjacent sites in the channel during the transport process. Here, using a mixed quantum-classical approach to calculate theoretical infrared spectra, we propose a set of infrared spectroscopy experiments that can discriminate between mechanisms with and without adjacent ions. These experiments differ from previous ones in that they independently probe specific ion binding sites within the selectivity filter. When ions occupy adjacent sites in the selectivity filter, the predicted spectra are significantly redshifted relative to when ions do not occupy adjacent sites. Comparisons between theoretical and experimental peak frequencies will therefore discriminate the mechanisms.

Modelling vibrational relaxation in complex molecular systems

In this paper we show how it is possible to treat the quantum vibrational relaxation of a chromophore, embedded in a complex atomic-molecular environment, via the explicit solution of the time-dependent Schroedinger equation once using a proper separation between quantum and semiclassical degrees of freedom. The rigorous theoretical framework derived, based on first principles and making use of well defined approximations/assumptions, is utilized to construct a general model for the kinetics of the vibrational relaxation as obtained by the direct evaluation of the density matrix for all the relevant quantum state transitions. Application to (deuterated) N-methylacetamide (the typical benchmark used as a model for the amino acids) shows that the obtained theoretical-computational approach captures the essential features of the experimental process, unveiling the basic relaxation mechanism involving several vibrational state transitions.

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.

Temperature dependence of the ultrafast vibrational echo spectroscopy of OD modes in liquid water from first principles simulations

The temperature dependence of the vibrational spectral diffusion of OD modes in liquid water is investigated through calculations of vibrational echo spectral observables from first principles molecular dynamics.

A Direct, Quantitative Connection between Molecular Dynamics Simulations and Vibrational Probe Line Shapes

A quantitative connection between molecular dynamics simulations and vibrational spectroscopy of probe-labeled systems would enable direct translation of experimental data into structural and dynamical information. To constitute this connection, all-atom molecular dynamics (MD) simulations were performed for two SCN probe sites (solvent-exposed and buried) in a calmodulin-target peptide complex. Two frequency calculation approaches with substantial nonelectrostatic components, a quantum mechanics/molecular mechanics (QM/MM)-based technique and a solvatochromic fragment potential (SolEFP) approach, were used to simulate the infrared probe line shapes. While QM/MM results disagreed with experiment, SolEFP results matched experimental frequencies and line shapes and revealed the physical and dynamic bases for the observed spectroscopic behavior. The main determinant of the CN probe frequency is the exchange repulsion between the probe and its local structural neighbors, and there is a clear dynamic explanation for the relatively broad probe line shape observed at the "buried" probe site. This methodology should be widely applicable to vibrational probes in many environments.

Hydrophobic Collapse in N-Methylacetamide-Water Mixtures

Aqueous N-methylacetamide solutions were investigated by polarization-resolved pump-probe and 2D infrared spectroscopy (2D IR), using the amide I mode as a reporter. The 2D IR results are compared with molecular dynamics simulations and spectral calculations to gain insight into the molecular structures in the mixture. N-Methylacetamide and water molecules tend to form clusters with "frozen" amide I dynamics. This is driven by a hydrophobic collapse as the methyl groups of the N-methylacetamide molecules cluster in the presence of water. Since the studied system can be considered as a simplified model for the backbone of proteins, the present study forms a convenient basis for understanding the structural and vibrational dynamics in proteins. It is particularly interesting to find out that a hydrophobic collapse as the one driving protein folding is observed in such a simple system.

Strategy for Modeling the Electrostatic Responses of the Spectroscopic Properties of Proteins

For better understanding and more efficient use of the spectroscopic probes (vibrational and NMR) of the local electrostatic situations inside proteins, appropriate modeling of the properties of those probes is essential. The present study is devoted to examining the strategy for constructing such models. A more well-founded derivation than the ones in previous studies is given in constructing the models. Theoretical analyses are conducted on two representative example cases related to proteins, i.e., the peptide group of the main chains and the CO and NO ligands to the Fe²⁺ ion of heme, with careful treatment of the behavior of electrons in the electrostatic responses and with verification of consistency with observable quantities. It is shown that, for the stretching frequencies and NMR chemical shifts, it is possible to construct reasonable electrostatic interaction models that encompass the situations of hydration and uniform electric field environment and thus are applicable also to the cases of nonuniform electrostatic situations, which are highly expected for inside of proteins.

Revealing the Solvation Structure and Dynamics of Carbonate Electrolytes in Lithium-Ion Batteries by Two-Dimensional Infrared Spectrum Modeling

Carbonate electrolytes in lithium-ion batteries play a crucial role in conducting lithium ions between two electrodes. Mixed solvent electrolytes consisting of linear and cyclic carbonates are commonly used in commercial lithium-ion batteries. To understand how the linear and cyclic carbonates introduce different solvation structures and dynamics, we performed molecular dynamics simulations of two representative electrolyte systems containing either linear or cyclic carbonate solvents. We then modeled their two-dimensional infrared (2DIR) spectra of the carbonyl stretching mode of these carbonate molecules. We found that the chemical exchange process involving formation and dissociation of lithium-ion/carbonate complexes is responsible for the growth of 2DIR cross peaks with increasing waiting time. In addition, we also found that cyclic carbonates introduce faster dynamics of dissociation and formation of lithium-ion/carbonate complexes than linear carbonates. These findings provide new insights into understanding the lithium-ion mobility and its interplay with solvation structure and ultrafast dynamics in carbonate electrolytes used in lithium-ion batteries.

Watching Proteins Wiggle: Mapping Structures with Two-Dimensional Infrared Spectroscopy

Proteins exhibit structural fluctuations over decades of time scales. From the picosecond side chain motions to aggregates that form over the course of minutes, characterizing protein structure over these vast lengths of time is important to understanding their function. In the past 15 years, two-dimensional infrared spectroscopy (2D IR) has been established as a versatile tool that can uniquely probe proteins structures on many time scales. In this review, we present some of the basic principles behind 2D IR and show how they have, and can, impact the field of protein biophysics. We highlight experiments in which 2D IR spectroscopy has provided structural and dynamical data that would be difficult to obtain with more standard structural biology techniques. We also highlight technological developments in 2D IR that continue to expand the scope of scientific problems that can be accessed in the biomedical sciences.

Electrostatic frequency maps for amide-I mode of β-peptide: Comparison of molecular mechanics force field and DFT calculations

The spectroscopy of amide-I vibrations has been widely utilized for the understanding of dynamical structure of polypeptides. For the modeling of amide-I spectra, two frequency maps were built for β-peptide analogue (N-ethylpropionamide, NEPA) in a number of solvents within different schemes (molecular mechanics force field based, GM map; DFT calculation based, GD map), respectively. The electrostatic potentials on the amide unit that originated from solvents and peptide backbone were correlated to the amide-I frequency shift from gas phase to solution phase during map parameterization. GM map is easier to construct with negligible computational cost since the frequency calculations for the samples are purely based on force field, while GD map utilizes sophisticated DFT calculations on the representative solute-solvent clusters and brings insight into the electronic structures of solvated NEPA and its chemical environments. The results show that the maps' predicted amide-I frequencies present solvation environmental sensitivities and exhibit their specific characters with respect to the map protocols, and the obtained vibrational parameters are in satisfactory agreement with experimental amide-I spectra of NEPA in solution phase. Although different theoretical schemes based maps have their advantages and disadvantages, the present maps show their potentials in interpreting the amide-I spectra for β-peptides, respectively.

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.

Solvent-Independent Anharmonicity for Carbonyl Oscillators

The physical origins of vibrational frequency shifts have been extensively studied in order to understand noncovalent intermolecular interactions in the condensed phase. In the case of carbonyls, vibrational solvatochromism, MD simulations, and vibrational Stark spectroscopy suggest that the frequency shifts observed in simple solvents arise predominately from the environment's electric field due to the vibrational Stark effect. This is contrary to many previously invoked descriptions of vibrational frequency shifts, such as bond polarization, whereby the bond's force constant and/or partial nuclear charges are altered due to the environment, often illustrated in terms of favored resonance structures. Here we test these hypotheses using vibrational solvatochromism as measured using 2D IR to assess the solvent dependence of the bond anharmonicity. These results indicate that the carbonyl bond's anharmonicity is independent of solvent as tested using hexanes, DMSO, and D₂O and is supported by simulated 2D spectra. In support of the linear vibrational Stark effect, these 2D IR measurements are consistent with the assertion that the Stark tuning rate is unperturbed by the electric field generated by both hydrogen and non-hydrogen bonding environments and further extends the general applicability of carbonyl probes for studying intermolecular interactions.

Probing the dynamics of N-methylacetamide in methanol via ab initio molecular dynamics

Two-dimensional infrared (2D IR) spectroscopy of amide 1 vibrational bands provides a valuable probe of proteins as well as molecules such as N-methylacetamide (NMA), which present peptide-like H-bonding possibilities to a solvent.

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.

Refining Disordered Peptide Ensembles with Computational Amide I Spectroscopy: Application to Elastin-Like Peptides

The characterization of intrinsically disordered protein (IDP) ensembles is complicated both by inherent heterogeneity and by the fact that many common experimental techniques function poorly when applied to IDPs. For this reason, the development of alternative structural tools for probing IDP ensembles has attracted considerable attention. Here we describe our recent work in developing experimental and computational tools for characterizing IDP ensembles using Amide I (backbone carbonyl stretch) vibrational spectroscopy. In this approach, the infrared (IR) absorption frequencies of isotope-labeled amide bonds probe their local electrostatic environments and structures. Empirical frequency maps allow us to use this spectroscopic data as a direct experimental test of atomistic structural models. We apply these methods to a family of short elastin-like peptides (ELPs), fragments of the elastin protein based around the Pro-Gly turn motif characteristic of the elastomeric segments of the full protein. Using a maximum entropy analysis that applies constraints from experimental spectra to weighting predicted spectra from molecular dynamics (MD) ensembles, we find that peptides with Ala or Val side chains preceding the Pro-Gly turn unit exhibit a stronger tendency toward extended structures than do Gly-Pro-Gly motifs, suggesting an important role for steric interactions in tuning the molecular properties of elastin.

Two-Dimensional Infrared Study of Vibrational Coupling between Azide and Nitrile Reporters in a RNA Nucleoside

The vibrations in the azide, N3, asymmetric stretching region and nitrile, CN, symmetric stretching region of 2'-azido-5-cyano-2'-deoxyuridine (N3CNdU) are examined by two-dimensional infrared (2D IR) spectroscopy. At earlier waiting times, the 2D IR spectrum shows the presence of both vibrational transitions along the diagonal and off-diagonal cross peaks indicating vibrational coupling. The coupling strength is determined from the off-diagonal anharmonicity to be 66 cm(-1) for the intramolecular distance of ∼7.9 Å, based on a structural map generated for this model system. In addition, the frequency-frequency correlation decay is detected, monitoring the solvent dynamics around each individual probe position. Overall, these vibrational reporters can be utilized in tandem to simultaneously track global structural information and fast structural fluctuations.

Communication: Quantitative multi-site frequency maps for amide I vibrational spectroscopy

An accurate method for predicting the amide I vibrational spectrum of a given protein structure has been sought for many years. Significant progress has been made recently by sampling structures from molecular dynamics simulations and mapping local electrostatic variables onto the frequencies of individual amide bonds. Agreement with experiment, however, has remained largely qualitative. Previously, we used dipeptide fragments and isotope-labeled constructs of the protein G mimic NuG2b as experimental standards for developing and testing amide I frequency maps. Here, we combine these datasets to test different frequency-map models and develop a novel method to produce an optimized four-site potential (4P) map based on the CHARMM27 force field. Together with a charge correction for glycine residues, the optimized map accurately describes both experimental datasets, with average frequency errors of 2-3 cm(-1). This 4P map is shown to be convertible to a three-site field map which provides equivalent performance, highlighting the viability of both field- and potential-based maps for amide I spectral modeling. The use of multiple sampling points for local electrostatics is found to be essential for accurate map performance.

Roles of the scalar and vector components of the solvation effects on the vibrational properties of hydrogen- or halogen-bond accepting stretching modes

Solvation-induced vibrational frequency shifts and infrared (IR) intensity changes of the hydrogen- or halogen-bond accepting stretching modes, especially their dependence on the angular position of the hydrogen- or halogen-bond donating molecule, are examined theoretically. Calculations are carried out for some modes of hydrogen- or halogen-bonding molecular complexes, including the S[double bond, length as m-dash]O stretch of dimethyl sulfoxide-(13)C2H2O, the C[triple bond, length as m-dash]N stretch of acetonitrileH2O, and the amide I' mode of the N-methylacetamide-d1BrNC 1 : 1 complex. It is shown that, in all the example cases dealt with in this study, the frequency shift depends rather strongly on the hydrogen- or halogen-bond angle (e.g., S[double bond, length as m-dash]OH angle), with a larger low-frequency shift as the hydrogen or halogen bond becomes more bent, indicating the generality of the results obtained for the amide I' mode of the N-methylacetamide-d1(2)H2O 1 : 1 complex in a previous study. Contrary to our vague expectation, the frequency shift is not well correlated to the hydrogen- or halogen-bond distance or strength, but nevertheless, it is well reproduced by an electrostatic interaction model if it is carefully constructed by considering the scalar and vector components separately in a reasonable way. On the basis of this electrostatic interaction model, the reason why our vague expectation is not realized is clarified, and a unified understanding is achieved on the hydration-induced high-frequency shift of the C[triple bond, length as m-dash]N stretch and the low-frequency shifts of the S[double bond, length as m-dash]O stretch and amide I'. With regard to the IR intensity, it is shown that, in some of the example cases, it also has rather strong angular position dependence. The mechanism of the IR intensity changes is estimated by analyzing the dipole derivative vector, especially its angular relation with the hydrogen or halogen bond.

Isotope-enriched protein standards for computational amide I spectroscopy

We present a systematic isotope labeling study of the protein G mutant NuG2b as a step toward the production of reliable, structurally stable, experimental standards for amide I infrared spectroscopic simulations. By introducing isotope enriched amino acids into a minimal growth medium during bacterial expression, we induce uniform labeling of the amide bonds following specific amino acids, avoiding the need for chemical peptide synthesis. We use experimental data to test several common amide I frequency maps and explore the influence of various factors on map performance. Comparison of the predicted absorption frequencies for the four maps tested with empirical assignments to our experimental spectra yields a root-mean-square error of 6-12 cm(-1), with outliers of at least 12 cm(-1) in all models. This means that the predictions may be useful for predicting general trends such as changes in hydrogen bonding configuration; however, for finer structural constraints or absolute frequency assignments, the models are unreliable. The results indicate the need for careful testing of existing literature maps and shed light on possible next steps for the development of quantitative spectral maps.

General Applicable Frequency Map for the Amide-I Mode in β-Peptides

In this work, a general applicable amide-I vibrational frequency map (GA map) for β-peptides in a number of common solvents was constructed, based on a peptide derivative, N-ethylpropionamide (NEPA). The map utilizes force fields at the ab initio computational level to accurately describe molecular structure and solute-solvent interactions, and also force fields at the molecular mechanics level to take into account long-range solute-solvent interactions. The results indicate that the GA map works reasonably for mapping the vibrational frequencies of the amide-I local-modes for β-peptides, holding promises for understanding the complicated infrared spectra of the amide-I mode in β-polypeptides.

Understanding and Manipulating Electrostatic Fields at the Protein-Protein Interface Using Vibrational Spectroscopy and Continuum Electrostatics Calculations

Biological function emerges in large part from the interactions of biomacromolecules in the complex and dynamic environment of the living cell. For this reason, macromolecular interactions in biological systems are now a major focus of interest throughout the biochemical and biophysical communities. The affinity and specificity of macromolecular interactions are the result of both structural and electrostatic factors. Significant advances have been made in characterizing structural features of stable protein-protein interfaces through the techniques of modern structural biology, but much less is understood about how electrostatic factors promote and stabilize specific functional macromolecular interactions over all possible choices presented to a given molecule in a crowded environment. In this Feature Article, we describe how vibrational Stark effect (VSE) spectroscopy is being applied to measure electrostatic fields at protein-protein interfaces, focusing on measurements of guanosine triphosphate (GTP)-binding proteins of the Ras superfamily binding with structurally related but functionally distinct downstream effector proteins. In VSE spectroscopy, spectral shifts of a probe oscillator's energy are related directly to that probe's local electrostatic environment. By performing this experiment repeatedly throughout a protein-protein interface, an experimental map of measured electrostatic fields generated at that interface is determined. These data can be used to rationalize selective binding of similarly structured proteins in both in vitro and in vivo environments. Furthermore, these data can be used to compare to computational predictions of electrostatic fields to explore the level of simulation detail that is necessary to accurately predict our experimental findings.