Two-dimensional vibrational spectroscopy. IV. Relationship between through-space vibrational coupling and intermolecular distance

In Situ Identification of Secondary Structures in Unpurified Bombyx mori Silk Fibrils Using Polarized Two-Dimensional Infrared Spectroscopy

The mechanical properties of biomaterials are dictated by the interactions and conformations of their building blocks, typically proteins. Although the macroscopic behavior of biomaterials is widely studied, our understanding of the underlying molecular properties is generally limited. Among the noninvasive and label-free methods to investigate molecular structures, infrared spectroscopy is one of the most commonly used tools because the absorption bands of amide groups strongly depend on protein secondary structure. However, spectral congestion usually complicates the analysis of the amide spectrum. Here, we apply polarized two-dimensional (2D) infrared spectroscopy (IR) to directly identify the protein secondary structures in native silk films cast from Bombyx mori silk feedstock. Without any additional peak fitting, we find that the initial effect of hydration is an increase of the random coil content at the expense of the helical content, while the β-sheet content is unchanged and only increases at a later stage. This paper demonstrates that 2D-IR can be a valuable tool for characterizing biomaterials.

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.

Chiroptical nature of two-exciton states of light-harvesting complex: Doubly resonant three-wave-mixing spectroscopy

Photosynthetic light-harvesting complex is a coupled multichromophore system. Due to electronic couplings between neighboring chlorophylls in the complex, the one- and two-exciton states are delocalized and they can be written as linear combinations of singly and doubly excited configurations, respectively. Despite that the chiroptical properties of one-exciton states in such a multichromophore system have been investigated by using linear optical activity measurement techniques; those of two-exciton states have not been studied before due to a lack of appropriate measurement methods. Here, we present a theoretical description on chiroptical chi((2)) spectroscopy and show that it can be used to investigate such properties of a photosynthetic light-harvesting system, which is the Fenna-Matthews-Olson complex, consisting of seven bacteriochlorophylls in its protein subunit. To simulate the doubly resonant sum- and difference-frequency-generation spectra of the complex, one- and two-exciton transition dipoles were calculated. Carrying out quantum chemistry calculations of electronically excited states of a model bacteriochlorophyll system and taking into account the dipole-induced dipole electronic transition processes between the ground state and two-exciton states, we could calculate the two-dimensional sum-frequency-generation spectra revealing dominant second-order chiroptical transition pathways and involved one- and two-exciton states. It is believed that the present computational scheme and the theoretically proposed doubly resonant two-dimensional three-wave-mixing spectroscopy would be of use to shed light on the chiroptical natures of two-exciton states of arbitrary coupled multichromophore systems.

Biological and biomedical applications of two-dimensional vibrational spectroscopy: proteomics, imaging, and structural analysis

In the last 10 years, several forms of two-dimensional infrared (2DIR) spectroscopy have been developed, such as IR pump-probe spectroscopy and photon-echo techniques. In this Account, we describe a doubly vibrationally enhanced four-wave mixing method, in which a third-order nonlinear signal is generated from the interaction of two independently tunable IR beams and an electron-polarizing visible beam at 790 nm. When the IR beams are independently in resonance with coupled vibrational transitions, the signal is enhanced and cross-peaks appear in the spectrum. This method is known as either DOVE (doubly vibrationally enhanced) four-wave mixing or EVV (electron-vibration-vibration) 2DIR spectroscopy. We begin by discussing the basis and properties of EVV 2DIR. We then discuss several biological and potential biomedical applications. These include protein identification and quantification, as well as the potential of this label-free spectroscopy for protein and peptide structural analysis. In proteomics, we also show how post-translational modifications in peptides (tyrosine phosphorylation) can be detected by EVV 2DIR spectroscopy. The feasibility of EVV 2DIR spectroscopy for tissue imaging is also evaluated. Preliminary results were obtained on a mouse kidney histological section that was stained with hematoxylin (a small organic molecule). We obtained images by setting the IR frequencies to a specific cross-peak (the strongest for hematoxylin was obtained from its analysis in isolation; a general CH(3) cross-peak for proteins was also used) and then spatially mapping as a function of the beam position relative to the sample. Protein and hematoxylin distribution in the tissue were measured and show differential contrast, which can be entirely explained by the different tissue structures and their functions. The possibility of triply resonant EVV 2DIR spectroscopy was investigated on the retinal chromophore at the centre of the photosynthetic protein bacteriorhodopsin (bR). By putting the visible third beam in resonance with an electronic transition, we were able to enhance the signal and increase the sensitivity of the method by several orders of magnitude. This increase in sensitivity is of great importance for biological applications, in which the number of proteins, metabolites, or drug molecules to be detected is low (typically pico- to femtomoles). Finally, we present theoretical investigations for using EVV 2DIR spectroscopy as a structural analysis tool for inter- and intramolecular interaction geometries.

Exploring a free energy landscape by means of multidimensional infrared and terahertz spectroscopies

A model for the dipolar crystal system is employed to explore a role of free energy landscape (FEL), in which dipolar molecules are posted on two-dimensional lattice sites with two-state libratinal dynamics. All dipole-dipole interactions are included to have frustrated interactions among the dipoles. For the regular and distorted lattice cases, the FEL is calculated from the interaction energies and the total polarizations for all possible dipolar states at various temperatures. At high temperatures, the shape of the calculated FEL is smooth and parabolic, while it becomes bumpy at low temperatures exhibiting multiple local minima. To study dynamical aspects of the system, the single flip dynamics and the single-double mixed flips dynamics of dipoles are examined from a master equation approach. As the observables of linear absorption and two-dimensional (2D) infrared, far infrared, and terahertz spectroscopies, the first- and third-order response functions of polarization are calculated for different physical conditions characterized by the FEL. While the linear absorption signals decay in time in a similar manner regardless of the FEL profiles, the 2D signals exhibit prominent differences for those profiles. This indicates that we may differentiate the FEL profiles by changing two-time valuables in 2D spectroscopy. As illustrated in the single-double flips case, the FEL study by means of 2D spectroscopy, however, relies on the dynamics which is set independently from the FEL. The Smoluchowski equation is applied to examine the description of the collective dynamics on the microscopically calculated FEL. We found that the one-dimensional and 2D signals calculated from the Smoluchowski equation agree with those from master equation only at temperatures where the FEL becomes parabolic shape.

Doubly resonant three-wave-mixing spectroscopy of a chiral coupled-chromophore system in solution: coherent two-dimensional optical activity spectroscopy

Theoretical descriptions of doubly resonant two-dimensional (2D) sum-frequency-generation (SFG) and difference-frequency-generation (DFG) spectroscopies of coupled-chromophore systems are presented. Despite that each electronic or vibrational chromophore is achiral, the interaction-induced chirality of a coupled multichromophore system in solution can be measured by using the doubly resonant 2D three-wave-mixing (3WM) spectroscopic method. An electronically coupled dimer, where each monomer is modeled as a simple two-level system, can have nonvanishing SFG (or DFG) properties, e.g., susceptibility in frequency domain or nonlinear response function in time domain, if the induced dipole vector of the dimer is not orthogonal to the vector product of the two monomer electronic transition dipole vectors. In order to demonstrate that these 2D 3WM spectroscopic methods can be used to determine the solution structure of a polypeptide, the authors carried out quantum chemistry calculations for an alanine dipeptide and obtained first- and second-order dipole derivatives associated with the amide I vibrational transitions of the dipeptide. It is shown that the numerically simulated 2D IR-IR SFG spectrum is highly sensitive to the dipeptide secondary structure and provides rich information on the one- and two-exciton states. It is believed that the theoretically proposed doubly resonant 2D 3WM spectroscopy, which can be considered to be an optical activity spectroscopy, will be of use in studying both structural and dynamical aspects of coupled multichromophore systems, such as proteins, nucleic acids, nanoparticle aggregates etc.

A phosphoryl transfer intermediate in the GTPase reaction of Ras in complex with its GTPase-activating protein

The hydrolysis of nucleoside triphosphates by enzymes is used as a regulation mechanism in key biological processes. Here, the GTP hydrolysis of the protein complex of Ras with its GTPase-activating protein is monitored at atomic resolution in a noncrystalline state by time-resolved FTIR spectroscopy. At 900 ms, after the attack of water at the gamma-phosphate, there appears a H2PO4- intermediate that is shown to be hydrogen-bonded in an eclipsed conformation to the beta-phosphate of GDP. The H2PO4- intermediate is in a position where it can either reform GTP or be released from the protein in 7 s in the rate-limiting step of the GTPase reaction. We propose that such an intermediate also occurs in other GTPases and ATPases.

Two-dimensional Raman spectra of atomic solids and liquids

We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.

Heterodyned fifth-order two-dimensional IR spectroscopy: Third-quantum states and polarization selectivity

A heterodyned fifth-order two-dimensional (2D) IR spectrum of a model coupled oscillator system, Ir(CO)(2)(C(5)H(7)O(2)), is reported. The spectrum is generated by a pulse sequence that probes the eigenstate energies up to the second overtone and combination bands, providing a more rigorous potential-energy surface of the coupled carbonyl local modes than can be obtained with third-order spectroscopy. Furthermore, the pulse sequence is designed to generate and then rephase a two-quantum coherence so that the spectrum is line narrowed and the resolution improved for inhomogeneously broadened systems. Features arising from coherence transfer processes are identified, which are more pronounced than in third-order 2D IR spectroscopy because the transition dipoles of the second overtone and combination states are not rigorously orthogonal, relaxing the polarization constraints on the signal intensity for these features. The spectrum provides a stringent test of cascading signals caused by third-order emitted fields and no cascading is observed. In the Appendix, formulas for calculating the signal intensities for resonant fifth-order spectroscopies with arbitrarily polarized pulses and transition dipoles are reported. These relationships are useful for interpreting and designing polarization conditions to enhance specific spectral features.

Higher-order optical correlation spectroscopy in liquids

Linear optical spectroscopies have long been used to study the behavior of liquids. Laser technology has progressed to the point that it has become possible to perform nonlinear optical experiments that probe higher-order correlation functions in liquids, opening a new window into our understanding of the microscopic details of solution-phase processes. Here we review advances that have been made in recent years in employing higher-order electronic and vibrational spectroscopies to study liquid-state dynamics and structure.

Two-dimensional infrared spectroscopy: a promising new method for the time resolution of structures

Recently, new methods for determining time-evolving structures using infrared analogs of NMR spectroscopy have been introduced that have outstanding potential in structural biology. Already, within the past two years, structures of dipeptides, tripeptides and pentapeptides have been determined on much faster timescales than the conformational dynamics. Also, two-dimensional infrared correlation spectra of some proteins and isotopically edited alanine-rich helices have been examined.