Vibrational solvatochromism. III. Rigorous treatment of the dispersion interaction contribution

Ground-state heterogeneity and vibrational energy redistribution in bacterial phytochrome observed with femtosecond 2D IR spectroscopy

Phytochromes belong to a group of photoreceptor proteins containing a covalently bound biliverdin chromophore that inter-converts between two isomeric forms upon photoexcitation. The existence and stability of the photocycle products are largely determined by the protein sequence and the presence of conserved hydrogen-bonding interactions in the vicinity of the chromophore. The vibrational signatures of biliverdin, however, are often weak and obscured under more intense protein bands, limiting spectroscopic studies of its non-transient signals. In this study, we apply isotope-labeling techniques to isolate the vibrational bands from the protein-bound chromophore of the bacterial phytochrome from Deinococcus radiodurans. We elucidate the structure and ultrafast dynamics of the chromophore with 2D infra-red (IR) spectroscopy and molecular dynamics simulations. The carbonyl stretch vibrations of the pyrrole rings show the heterogeneous distribution of hydrogen-bonding structures, which exhibit distinct ultrafast relaxation dynamics. Moreover, we resolve a previously undetected 1678 cm^-1 band that is strongly coupled to the A- and D-ring of biliverdin and demonstrate the presence of complex vibrational redistribution pathways between the biliverdin modes with relaxation-assisted measurements of 2D IR cross peaks. In summary, we expect 2D IR spectroscopy to be useful in explaining how point mutations in the protein sequence affect the hydrogen-bonding structure around the chromophore and consequently its ability to photoisomerize to the light-activated states.

Frequency Changes in Terminal Alkynes Provide Strong, Sensitive, and Solvatochromic Raman Probes of Biochemical Environments

The C≡C stretching frequencies of terminal alkynes appear in the "clear" window of vibrational spectra, so they are attractive and increasingly popular as site-specific probes in complicated biological systems like proteins, cells, and tissues. In this work, we collected infrared (IR) absorption and Raman scattering spectra of model compounds, artificial amino acids, and model proteins that contain terminal alkyne groups, and we used our results to draw conclusions about the signal strength and sensitivity to the local environment of both aliphatic and aromatic terminal alkyne C≡C stretching bands. While the IR bands of alkynyl model compounds displayed surprisingly broad solvatochromism, their absorptions were weak enough that alkynes can be ruled out as effective IR probes. The same solvatochromism was observed in model compounds' Raman spectra, and comparisons to published empirical solvent scales (including a linear regression against four meta-aggregated solvent parameters) suggested that the alkyne C≡C stretching frequency mainly reports on local electronic interactions (i.e., short-range electron donor-acceptor interactions) with solvent molecules and neighboring functional groups. The strong solvatochromism observed here for alkyne stretching bands introduces an important consideration for Raman imaging studies based on these signals. Raman signals for alkynes (especially those that are π-conjugated) can be exceptionally strong and should permit alkynyl Raman signals to function as probes at very low concentrations, as compared to other widely used vibrational probe groups like azides and nitriles. We incorporated homopropargyl glycine into a transmembrane helical peptide via peptide synthesis, and we installed p-ethynylphenylalanine into the interior of the Escherichia coli fatty acid acyl carrier protein using a genetic code expansion technique. The Raman spectra from each of these test systems indicate that alkynyl C≡C bands can act as effective and unique probes of their local biomolecular environments. We provide guidance for the best possible future uses of alkynes as solvatochromic Raman probes, and while empirical explanations of the alkyne solvatochromism are offered, open questions about its physical basis are enunciated.

Machine Learning Approach for Describing Water OH Stretch Vibrations

A machine learning approach employing neural networks is developed to calculate the vibrational frequency shifts and transition dipole moments of the symmetric and antisymmetric OH stretch vibrations of a water molecule surrounded by water molecules. We employed the atom-centered symmetry functions (ACSFs), polynomial functions, and Gaussian-type orbital-based density vectors as descriptor functions and compared their performances in predicting vibrational frequency shifts using the trained neural networks. The ACSFs perform best in modeling the frequency shifts of the OH stretch vibration of water among the types of descriptor functions considered in this paper. However, the differences in performance among these three descriptors are not significant. We also tried a feature selection method called CUR matrix decomposition to assess the importance and leverage of the individual functions in the set of selected descriptor functions. We found that a significant number of those functions included in the set of descriptor functions give redundant information in describing the configuration of the water system. We here show that the predicted vibrational frequency shifts by trained neural networks successfully describe the solvent-solute interaction-induced fluctuations of OH stretch frequencies.

An effective potential for Frenkel excitons

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is introduced that is valid in a wide range of intermolecular distances. The proposed approach is based on the effective elimination of electron repulsion integrals from the excitonic Hamiltonian matrix elements via the density-fitting approach and distributed multipole approximation. The excitonic Hamiltonian represented in a basis including charge transfer (CT) states is re-cast in terms of the effective one-electron potential functions (EOPs) and adapted into the effective fragment parameter (EFP) framework. Calculations for model systems indicate that the speedup of at least three orders of magnitude, as compared to the state-of-the-art methods, can be achieved while maintaining the accuracy of the EET couplings even at short intermolecular distances.

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.

Differential evolution algorithm approach for describing vibrational solvatochromism

We model the solvation-induced vibrational frequency shifts of the amide I and amide II modes of N-methylacetamide in water and the nitrile stretch mode of acetonitrile in water by expressing the frequency shift as a polynomial function expanded by the inverse power of interatomic distances. The coefficients of the polynomial are optimized to minimize the deviation between the predicted frequency shifts and those calculated with quantum chemistry methods. Here, we show that a differential evolution algorithm combined with singular value decomposition is useful to find the optimum set of coefficients of polynomial terms. The differential evolution optimization shows that only a few terms in the polynomial are dominant in the contribution to the vibrational frequency shifts. We anticipate that the present work paves the way for further developing different genetic algorithms and machine learning schemes for their applications to vibrational spectroscopic studies.

Mapping the amide-I vibrations of model dipeptides with secondary structure sensitivity and amino acid residue specificity, and its application to amyloid β-peptide in aqueous solution

Vibrational spectroscopy has been known as particularly well-suited for deciphering the polypeptide's structure. To decode structural information encoded in IR spectra, we developed amide-I frequency maps on the basis of model dipeptides to correlate the amide-I frequency of interest to the combination of the calculated secondary structure dependent amide-I frequency by using DFT method and the electrostatic potentials that projected onto the amide unit from the micro-environment within molecular mechanics force field. The constructed maps were applied to model dipeptides and amyloid β-peptide fragment (Aβ_25-35). The dipeptide specified map (DS map) and the hybrid map (HYB map) predicted amide-I bands of Aβ_25-35 in solution satisfactorily reproduce experimental observation, and indicate the preference of forming β-sheet and random coil structure for Aβ_25-35 in D₂O just as the results of cluster analysis suggested. These maps with secondary structural sensitivity and amino acid residue specificity open up a way for the interpretation of amide-I vibrations and show their potentials in the understanding of molecular structure of polypeptides in solution.

Cyanylated Cysteine Reports Site-Specific Changes at Protein-Protein-Binding Interfaces Without Perturbation

To investigate the cyanylated cysteine vibrational probe group’s ability to report on binding-induced changes along a protein–protein interface, the probe group was incorporated at several sites in a peptide of the calmodulin (CaM)-binding domain of skeletal muscle myosin light chain kinase. Isothermal titration calorimetry was used to determine the binding thermodynamics between calmodulin and each peptide. For all probe positions, the binding affinity was nearly identical to that of the unlabeled peptide. The CN stretching infrared band was collected for each peptide free in solution and bound to calmodulin. Binding-induced shifts in the IR spectral frequencies were correlated with estimated solvent accessibility based on molecular dynamics simulations. This work generally suggests (1) that site-specific incorporation of this vibrational probe group does not cause major perturbations to its local structural environment and (2) that this small probe group might be used quite broadly to map dynamic protein-binding interfaces. However, site-specific perturbations due to artificial labeling groups can be somewhat unpredictable and should be evaluated on a site-by-site basis through complementary measurements. A fully quantitative, simulation-based interpretation of the rich probe IR spectra is still needed but appears to be possible given recent advances in simulation techniques.

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.

Conformational Ensembles of Calmodulin Revealed by Nonperturbing Site-Specific Vibrational Probe Groups

Seven native residues on the regulatory protein calmodulin, including three key methionine residues, were replaced (one by one) by the vibrational probe amino acid cyanylated cysteine, which has a unique CN stretching vibration that reports on its local environment. Almost no perturbation was caused by this probe at any of the seven sites, as reported by CD spectra of calcium-bound and apo calmodulin and binding thermodynamics for the formation of a complex between calmodulin and a canonical target peptide from skeletal muscle myosin light chain kinase measured by isothermal titration. The surprising lack of perturbation suggests that this probe group could be applied directly in many protein–protein binding interfaces. The infrared absorption bands for the probe groups reported many dramatic changes in the probes’ local environments as CaM went from apo- to calcium-saturated to target peptide-bound conditions, including large frequency shifts and a variety of line shapes from narrow (interpreted as a rigid and invariant local environment) to symmetric to broad and asymmetric (likely from multiple coexisting and dynamically exchanging structures). The fast intrinsic time scale of infrared spectroscopy means that the line shapes report directly on site-specific details of calmodulin’s variable structural distribution. Though quantitative interpretation of the probe line shapes depends on a direct connection between simulated ensembles and experimental data that does not yet exist, formation of such a connection to data such as that reported here would provide a new way to evaluate conformational ensembles from data that directly contains the structural distribution. The calmodulin probe sites developed here will also be useful in evaluating the binding mode of calmodulin with many uncharacterized regulatory targets.

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.

Conformational Heterogeneity and the Affinity of Substrate Molecular Recognition by Cytochrome P450cam

The broad and variable substrate specificity of cytochrome P450 enzymes makes them a model system for studying the determinants of protein molecular recognition. The archetypal cytochrome P450cam (P450cam) is a relatively specific P450, a feature once attributed to the high rigidity of its active site. However, increasingly studies have provided evidence of the importance of conformational changes to P450cam activity. Here we used infrared (IR) spectroscopy to investigate the molecular recognition of P450cam. Toward this goal, and to assess the influence of a hydrogen bond (H-bond) between active site residue Y96 and substrates, two variants in which Y96 is replaced by a cyanophenyl (Y96CNF) or phenyl (Y96F) group were characterized in complexes with the substrates camphor, isoborneol, and camphane. These combinations allow for a comparison of complexes in which the moieties on both the protein and substrate can serve as a H-bond donor, acceptor, or neither. The IR spectra of heme-bound CO and the site-specifically incorporated CN of Y96CNF were analyzed to characterize the number and nature of environments in each protein, both in the free and bound states. Although the IR spectra do not support the idea that protein-substrate H-bonding is central to P450cam recognition, the data altogether suggest that the differing conformational heterogeneity in the active site of the P450cam variants and changes in heterogeneity upon binding of different substrates likely contribute to their variable affinities via a conformational selection mechanism. This study further extends our understanding of the molecular recognition of archetypal P450cam and demonstrates the application of IR spectroscopy combined with selective protein modification to delineate protein-ligand interactions.

Vibrational Probes: From Small Molecule Solvatochromism Theory and Experiments to Applications in Complex Systems

The vibrational frequency of a chosen normal mode is one of the most accurately measurable spectroscopic properties of molecules in condensed phases. Accordingly, infrared absorption and Raman scattering spectroscopy have provided valuable information on both distributions and ensemble-average values of molecular vibrational frequencies, and these frequencies are now routinely used to investigate structure, conformation, and even absolute configuration of chemical and biological molecules of interest. Recent advancements in coherent time-domain nonlinear vibrational spectroscopy have allowed the study of heterogeneous distributions of local structures and thermally driven ultrafast fluctuations of vibrational frequencies. To fully utilize IR probe functional groups for quantitative bioassays, a variety of biological and chemical techniques have been developed to site-specifically introduce vibrational probe groups into proteins and nucleic acids. These IR-probe-labeled biomolecules and chemically reactive systems are subject to linear and nonlinear vibrational spectroscopic investigations and provide information on the local electric field, conformational changes, site-site protein contacts, and/or function-defining features of biomolecules. A rapidly expanding library of data from such experiments requires an interpretive method with atom-level chemical accuracy. However, despite prolonged efforts to develop an all-encompassing theory for describing vibrational solvatochromism and electrochromism as well as dynamic fluctuations of instantaneous vibrational frequencies, purely empirical and highly approximate theoretical models have often been used to interpret experimental results. They are, in many cases, based on the simple assumption that the vibrational frequency of an IR reporter is solely dictated by electric potential or field distribution around the vibrational chromophore. Such simplified description of vibrational solvatochromism generally referred to as vibrational Stark effect theory has been considered to be quite appealing and, even in some cases, e.g., carbonyl stretch modes in amide, ester, ketone, and carbonate compounds or proteins, it works quantitatively well, which makes it highly useful in determining the strength of local electric field around the IR chromophore. However, noting that the vibrational frequency shift results from changes of solute-solvent intermolecular interaction potential along its normal coordinate, Pauli exclusion repulsion, polarization, charge transfer, and dispersion interactions, in addition to the electrostatic interaction between distributed charges of both vibrational chromophore and solvent molecules, are to be properly included in the theoretical description of vibrational solvatochromism. Since the electrostatic and nonelectrostatic intermolecular interaction components have distinctively different distance and orientation dependences, they affect the solvatochromic vibrational properties in a completely different manner. Over the past few years, we have developed a systematic approach to simulating vibrational solvatochromic data based on the effective fragment potential approach, one of the most accurate and rigorous theories on intermolecular interactions. We have further elucidated the interplay of local electric field with the general vibrational solvatochromism of small IR probes in either solvents or complicated biological systems, with emphasis on contributions from non-Coulombic intermolecular interactions to vibrational frequency shifts and fluctuations. With its rigorous foundation and close relation to quantitative interpretation of experimental data, this and related theoretical approaches and experiments will be of use in studying and quantifying the structure and dynamics of biomolecules with unprecedented time and spatial resolution when combined with time-resolved vibrational spectroscopy and chemically sensitive vibrational imaging techniques.

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.

Vibrational Stark Effects of Carbonyl Probes Applied to Reinterpret IR and Raman Data for Enzyme Inhibitors in Terms of Electric Fields at the Active Site

IR and Raman frequency shifts have been reported for numerous probes of enzyme transition states, leading to diverse interpretations. In the case of the model enzyme ketosteroid isomerase (KSI), we have argued that IR spectral shifts for a carbonyl probe at the active site can provide a connection between the active site electric field and the activation free energy (Fried et al. Science 2014, 346, 1510-1514). Here we generalize this approach to a much broader set of carbonyl probes (e.g., oxoesters, thioesters, and amides), first establishing the sensitivity of each probe to an electric field using vibrational Stark spectroscopy, vibrational solvatochromism, and MD simulations, and then applying these results to reinterpret data already in the literature for enzymes such as 4-chlorobenzoyl-CoA dehalogenase and serine proteases. These results demonstrate that the vibrational Stark effect provides a general framework for estimating the electrostatic contribution to the catalytic rate and may provide a metric for the design or modification of enzymes. Opportunities and limitations of the approach are also described.

Conformational Heterogeneity in the Michaelis Complex of Lactate Dehydrogenase: An Analysis of Vibrational Spectroscopy Using Markov and Hidden Markov Models

Lactate dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate. Recent isotope-edited IR spectroscopy suggests that conformational heterogeneity exists within the Michaelis complex of LDH, and this heterogeneity affects the propensity toward the on-enzyme chemical step for each Michaelis substate. By combining molecular dynamics simulations with Markov and hidden Markov models, we obtained a detailed kinetic network of the substates of the Michaelis complex of LDH. The ensemble-average electric fields exerted onto the vibrational probe were calculated to provide a direct comparison with the vibrational spectroscopy. Structural features of the Michaelis substates were also analyzed on atomistic scales. Our work not only clearly demonstrates the conformational heterogeneity in the Michaelis complex of LDH and its coupling to the reactivities of the substates, but it also suggests a methodology to simultaneously resolve kinetics and structures on atomistic scales, which can be directly compared with the vibrational spectroscopy.

Site-Specific Characterization of Cytochrome P450cam Conformations by Infrared Spectroscopy

Conformational changes are central to protein function but challenging to characterize with both high spatial and temporal precision. The inherently fast time scale and small chromophores of infrared (IR) spectroscopy are well-suited for characterization of potentially rapidly fluctuating environments, and when frequency-resolved probes are incorporated to overcome spectral congestion, enable characterization of specific sites in proteins. We selectively incorporated p-cyanophenylalanine (CNF) as a vibrational probe at five distinct locations in the enzyme cytochrome P450cam and used IR spectroscopy to characterize the environments in substrate and/or ligand complexes reflecting those in the catalytic cycle. Molecular dynamics (MD) simulations were performed to provide a structural basis for spectral interpretation. Together the experimental and simulation data suggest that the CN frequencies are sensitive to both long-range influences, resulting from the particular location of a residue within the enzyme, as well as short-range influences from hydrogen bonding and packing interactions. The IR spectra demonstrate that the environments and effects of substrate and/or ligand binding are different at each position probed and also provide evidence that a single site can experience multiple environments. This study illustrates how IR spectroscopy, when combined with the spectral decongestion and spatial selectivity afforded by CNF incorporation, provides detailed information about protein structural changes that underlie function.

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.

Vibrational solvatochromism of nitrile infrared probes: beyond the vibrational Stark dipole approach

Systematic probing of local environments around biopolymers is important for understanding their functions.