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.

Second-Order Vibrational Lineshapes from the Air/Water Interface.

We explore by means of modeling how absorptive-dispersive mixing between the second- and third-order terms modifies the imaginary χtotal(2) responses from air/water interfaces under conditions of varying charge densities and ionic strength. To do so, we use published Im(χ(2)) and χ(3) spectra of the neat air/water interface that were obtained either from computations or experiments. We find that the χtotal(2) spectral lineshapes corresponding to experimentally measured spectra contain significant contributions from both interfacial χ(2) and bulk χ(3) terms at interfacial charge densities equivalent to less than 0.005% of a monolayer of water molecules, especially in the 3100 to 3300 cm-1 frequency region. Additionally, the role of short-range static dipole potentials is examined under conditions mimicking brine. Our results indicate that surface potentials, if indeed present at the air/water interface, manifest themselves spectroscopically in the tightly bonded H-bond network observable in the 3200 cm-1 frequency range.

Water Dynamics in Gyroid Phases of Self-Assembled Gemini Surfactants.

Water-mediated ion transport through functional nanoporous materials depends on the dynamics of water confined within a given nanostructured morphology. Here, we investigate H-bonding dynamics of interfacial water within a "normal" (Type I) lyotropic gyroid phase formed by a gemini dicarboxylate surfactant self-assembly using a combination of 2DIR spectroscopy and molecular dynamics simulations. Experiments and simulations demonstrate that water dynamics in the normal gyroid phase is 1 order of magnitude slower than that in bulk water, due to specific interactions between water, the ionic surfactant headgroups, and counterions. Yet, the dynamics of water in the normal gyroid phase are faster than those of water confined in a reverse spherical micelle of a sulfonate surfactant, given that the water pool in the reverse micelle and the water pore in the gyroid phase have roughly the same diameters. This difference in confined water dynamics likely arises from the significantly reduced curvature-induced frustration at the convex interfaces of the normal gyroid, as compared to the concave interfaces of a reverse spherical micelle. These detailed insights into confined water dynamics may guide the future design of artificial membranes that rapidly transport protons and other ions.

Reparametrized E3B (Explicit Three-Body) Water Model Using the TIP4P/2005 Model as a Reference.

In this study, we present the third version of a water model that explicitly includes three-body interactions. The major difference between this version and the previous two is in the two-body water model we use as a reference potential; here we use the TIP4P/2005 model (previous versions used the TIP4P water model). We alter four parameters from our previous version of the model by fitting to the diffusion coefficient of the ambient liquid, the liquid and ice densities, and the melting point. We evaluate the performance of this version by calculating many other microscopic and thermodynamic static and dynamic properties as a function of temperature and near the critical point and comparing to experiment, the TIP4P/2005 model and the previous version of our three-body model.

Theoretical Sum Frequency Generation Spectroscopy of Peptides.

Vibrational sum frequency generation (SFG) has become a very promising technique for the study of proteins at interfaces, and it has been applied to important systems such as anti-microbial peptides, ion channel proteins, and human islet amyloid polypeptide. Moreover, so-called "chiral" SFG techniques, which rely on polarization combinations that generate strong signals primarily for chiral molecules, have proven to be particularly discriminatory of protein secondary structure. In this work, we present a theoretical strategy for calculating protein amide I SFG spectra by combining line-shape theory with molecular dynamics simulations. We then apply this method to three model peptides, demonstrating the existence of a significant chiral SFG signal for peptides with chiral centers, and providing a framework for interpreting the results on the basis of the dependence of the SFG signal on the peptide orientation. We also examine the importance of dynamical and coupling effects. Finally, we suggest a simple method for determining a chromophore's orientation relative to the surface using ratios of experimental heterodyne-detected signals with different polarizations, and test this method using theoretical spectra.

Structural motif of polyglutamine amyloid fibrils discerned with mixed-isotope infrared spectroscopy.

Polyglutamine (polyQ) sequences are found in a variety of proteins, and mutational expansion of the polyQ tract is associated with many neurodegenerative diseases. We study the amyloid fibril structure and aggregation kinetics of K2Q24K2W, a model polyQ sequence. Two structures have been proposed for amyloid fibrils formed by polyQ peptides. By forming fibrils composed of both (12)C and (13)C monomers, made possible by protein expression in Escherichia coli, we can restrict vibrational delocalization to measure 2D IR spectra of individual monomers within the fibrils. The spectra are consistent with a ß-turn structure in which each monomer forms an antiparallel hairpin and donates two strands to a single ß-sheet. Calculated spectra from atomistic molecular-dynamics simulations of the two proposed structures confirm the assignment. No spectroscopically distinct intermediates are observed in rapid-scan 2D IR kinetics measurements, suggesting that aggregation is highly cooperative. Although 2D IR spectroscopy has advantages over linear techniques, the isotope-mixing strategy will also be useful with standard Fourier transform IR spectroscopy.

Dynamics of water confined in reversed micelles: multidimensional vibrational spectroscopy study.

Here we perform a comprehensive study of ultrafast molecular and vibrational dynamics of water confined in small reversed micelles (RMs). The molecular picture is elucidated with two-dimensional infrared (2D IR) spectroscopy of water OH stretch vibrations and molecular dynamics simulations, bridged by theoretical calculations of linear and 2D IR vibrational spectra. To investigate the effects of intermolecular coupling, experiments and modeling are performed for isotopically diluted (HDO in D2O) and undiluted (H2O) water. We put a separation of water inside RMs into two subensembles (water-bound and surfactant-bound molecules), observed by many before, on a solid theoretical basis. Water molecules fully attached to the lipid interface ("shell" water) are decoupled from one another and from the central water nanopool ("core" water). The environmental fluctuations are largely "frozen" for the shell water, while the core waters demonstrate much faster dynamics but still not as fast as in the bulk case. A substantial nanoconfinement effect on the dynamics of the core water is observed after disentanglement of the shell water contribution, which is fully confirmed by the simulations of 2D IR spectra. Current results provide new insights into interaction between biological objects like membranes or proteins with the surrounding aqueous bath, and highlight peculiarities in vibrational energy redistribution near the lipid surface.

Slow hydrogen-bond switching dynamics at the water surface revealed by theoretical two-dimensional sum-frequency spectroscopy.

Using our newly developed explicit three-body (E3B) water model, we simulate the surface of liquid water. We find that the timescale for hydrogen-bond switching dynamics at the surface is about three times slower than that in the bulk. In contrast, with this model rotational dynamics are slightly faster at the surface than in the bulk. We consider vibrational two-dimensional (2D) sum-frequency generation (2DSFG) spectroscopy as a technique for observing hydrogen-bond rearrangement dynamics at the water surface. We calculate the nonlinear susceptibility for this spectroscopy for two different polarization conditions, and in each case we see the appearance of cross-peaks on the timescale of a few picoseconds, signaling hydrogen-bond rearrangement on this timescale. We thus conclude that this 2D spectroscopy will be an excellent experimental technique for observing slow hydrogen-bond switching dynamics at the water surface.

Parallel ß-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 ß-sheets. Using a synthetic macrocycle that enforces a two stranded parallel ß-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 ß-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 ß-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 ß-sheets that can be used in structure-based models to simulate and interpret the infrared spectra of ß-sheet containing proteins and protein assemblies, such as amyloid fibers.

Thermally induced protein unfolding probed by isotope-edited IR spectroscopy.

Infrared (IR) spectroscopy has been widely utilized for the study of protein folding, unfolding, and misfolding processes. We have previously developed a theoretical method for calculating IR spectra of proteins in the amide I region. In this work, we apply this method, in combination with replica-exchange molecular dynamics simulations, to study the equilibrium thermal unfolding transition of the villin headpiece subdomain (HP36). Temperature-dependent IR spectra and spectral densities are calculated. The spectral densities correctly reflect the unfolding conformational changes in the simulation. With the help of isotope labeling, we are able to capture the feature that helix 2 of HP36 loses its secondary structure before global unfolding occurs, in agreement with experiment.

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

The aggregation of human amylin to form amyloid contributes to islet ß-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 ß-sheet regions. This work provides a protocol for bridging MD simulation and 2DIR experiments for future aggregation studies.

Hydrogen bonding at the water surface revealed by isotopic dilution spectroscopy.

The air-water interface is perhaps the most common liquid interface. It covers more than 70 per cent of the Earth's surface and strongly affects atmospheric, aerosol and environmental chemistry. The air-water interface has also attracted much interest as a model system that allows rigorous tests of theory, with one fundamental question being just how thin it is. Theoretical studies have suggested a surprisingly short 'healing length' of about 3 ångströms (1 Å = 0.1 nm), with the bulk-phase properties of water recovered within the top few monolayers. However, direct experimental evidence has been elusive owing to the difficulty of depth-profiling the liquid surface on the ångström scale. Most physical, chemical and biological properties of water, such as viscosity, solvation, wetting and the hydrophobic effect, are determined by its hydrogen-bond network. This can be probed by observing the lineshape of the OH-stretch mode, the frequency shift of which is related to the hydrogen-bond strength. Here we report a combined experimental and theoretical study of the air-water interface using surface-selective heterodyne-detected vibrational sum frequency spectroscopy to focus on the 'free OD' transition found only in the topmost water layer. By using deuterated water and isotopic dilution to reveal the vibrational coupling mechanism, we find that the free OD stretch is affected only by intramolecular coupling to the stretching of the other OD group on the same molecule. The other OD stretch frequency indicates the strength of one of the first hydrogen bonds encountered at the surface; this is the donor hydrogen bond of the water molecule straddling the interface, which we find to be only slightly weaker than bulk-phase water hydrogen bonds. We infer from this observation a remarkably fast onset of bulk-phase behaviour on crossing from the air into the water phase.

Surface of liquid water: three-body interactions and vibrational sum-frequency spectroscopy.

Phase-sensitive vibrational sum-frequency experiments on the water surface, using isotopic mixtures of water and heavy water, have recently been performed. The experiments show a positive feature at low frequency in the imaginary part of the susceptibility, which has been difficult to interpret, and impossible to reproduce using two-body (pairwise-additive) water simulation models. We have reparameterized a new three-body simulation model for liquid water, and with this model we calculate the imaginary part of the sum-frequency susceptibility, finding good agreement with experiment for dilute HOD in D(2)O. Theoretical analysis provides a molecular-level structural interpretation of these new and exciting experiments. In particular, we do not find evidence of any special ice-like ordering at the surface of liquid water.

Stable and metastable states of human amylin in solution.

Patients with type II diabetes exhibit fibrillar deposits of human amylin protein in the pancreas. It has been proposed that amylin oligomers arising along the aggregation or fibril-formation pathways are important in the genesis of the disease. In a step toward understanding these aggregation pathways, in this work we report the conformational preferences of human amylin monomer in solution using molecular simulations and infrared experiments. In particular, we identify a stable conformer that could play a key role in aggregation. We find that amylin adopts three stable conformations: one with an α-helical segment comprising residues 9-17 and a short antiparallel ß-sheet comprising residues 24-28 and 31-35; one with an extended antiparallel ß-hairpin with the turn region comprising residues 20-23; and one with no particular structure. Using detailed calculations, we determine the relative stability of these various conformations, finding that the ß-hairpin conformation is the most stable, followed by the α-helical conformation, and then the unstructured coil. To test our predicted structure, we calculate its infrared spectrum in the amide I stretch regime, which is sensitive to secondary structure through vibrational couplings and linewidths, and compare it to experiment. We find that theoretically predicted spectra are in good agreement with the experimental line shapes presented herein. The implications of the monomer secondary structures on its aggregation pathway and on its interaction with cell membranes are discussed.

2D IR line shapes probe ovispirin peptide conformation and depth in lipid bilayers.

We report a structural study on the membrane binding of ovispirin using 2D IR line shape analysis, isotope labeling, and molecular dynamics simulations. Ovispirin is an antibiotic polypeptide that binds to the surfaces of membranes as an alpha-helix. By resolving individual backbone vibrational modes (amide I) using 1-(13)C=(18)O labeling, we measured the 2D IR line shapes for 15 of the 18 residues in this peptide. A comparison of the line shapes reveals an oscillation in the inhomogeneous line width that has a period equal to that of an alpha-helix (3.6 amino acids). The periodic trend is caused by the asymmetric environment of the membrane bilayer that exposes one face of the alpha-helix to much stronger environmental electrostatic forces than the other. We compare our experimental results to 2D IR line shapes calculated using the lowest free energy structure identified from molecular dynamics simulations. These simulations predict a periodic trend similar to the experiment and lead us to conclude that ovispirin lies in the membrane just below the headgroups, is tilted, and may be kinked. Besides providing insight into the antibiotic mechanism of ovispirin, our procedure provides an infrared method for studying peptide and protein structures that relies on the natural vibrational modes of the backbone. It is a complementary method to other techniques that utilize line shapes, such as fluorescence, NMR, and ESR spectroscopies, because it does not require mutations, the spectra can be quantitatively simulated using molecular dynamics, and the technique can be applied to difficult-to-study systems like ion channels, aggregated proteins, and kinetically evolving systems.

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

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