Simulation protocols for coherent femtosecond vibrational spectra of peptides

The Long and Short of Coupling and Uncoupling via 2D IR Spectroscopy

Determining dynamic structural changes along with the functional movements in biological systems has been a significant challenge for scientists for several decades. Utilizing vibrational coupling with the aid of 2D IR probe pairs has aided in uncovering structural dynamics and functional roles of chemical moieties involved in actions such as membrane peptide folding and transport, ion and water transport, and drug-protein interactions. Both native and non-native vibrational probe pairs have been developed for infrared studies, and their efficacy has been tested in various systems. With these probe pairs, 2D IR spectroscopy captures frozen snapshots of the structural events involved in biological function through vibrational coupling and correlated spectral diffusion. In this Perspective, different treatments of vibrational coupling and coupling models will be addressed, and a review of some of the specific vibrational probe pairs used to study these coupling mechanisms is presented. Overall, the intrinsic molecular dynamics detected on these ultrafast time scales will provide an atomic level view of how chosen structures traverse reaction paths. Thus, it is important to evaluate and assess the accuracy of the different vibrational coupling models and their consistency with the prediction of different molecular structures.

Artificial Intelligence-based Amide-II Infrared Spectroscopy Simulation for Monitoring Protein Hydrogen Bonding Dynamics

The structurally sensitive amide II infrared (IR) bands of proteins provide valuable information about the hydrogen bonding of protein secondary structures, which is crucial for understanding protein dynamics and associated functions. However, deciphering protein structures from experimental amide II spectra relies on time-consuming quantum chemical calculations on tens of thousands of representative configurations in solvent water. Currently, the accurate simulation of amide II spectra for whole proteins remains a challenge. Here, we present a machine learning (ML)-based protocol designed to efficiently simulate the amide II IR spectra of various proteins with an accuracy comparable to experimental results. This protocol stands out as a cost-effective and efficient alternative for studying protein dynamics, including the identification of secondary structures and monitoring the dynamics of protein hydrogen bonding under different pH conditions and during protein folding process. Our method provides a valuable tool in the field of protein research, focusing on the study of dynamic properties of proteins, especially those related to hydrogen bonding, using amide II IR spectroscopy.

Liquid-Liquid Phase Separation of the Intrinsically Disordered Domain of the Fused in Sarcoma Protein Results in Substantial Slowing of Hydration Dynamics

Formation of liquid condensates plays a critical role in biology via localization of different components or via altered hydrodynamic transport, yet the hydrogen-bonding environment within condensates, pivotal for solvation, has remained elusive. We explore the hydrogen-bond dynamics within condensates formed by the low-complexity domain of the fused in sarcoma protein. Probing the hydrogen-bond dynamics sensed by condensate proteins using two-dimensional infrared spectroscopy of the protein amide I vibrations, we find that frequency-frequency correlations of the amide I vibration decay on a picosecond time scale. Interestingly, these dynamics are markedly slower for proteins in the condensate than in a homogeneous protein solution, indicative of different hydration dynamics. All-atom molecular dynamics simulations confirm that lifetimes of hydrogen-bonds between water and the protein are longer in the condensates than in the protein in solution. Altered hydrogen-bonding dynamics may contribute to unique solvation and reaction dynamics in such condensates.

Equivalence of quantum and classical third order response for weakly anharmonic coupled oscillators

Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light-matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems.

Simulation of two-dimensional infrared Raman spectroscopy with application to proteins

Two-dimensional infrared Raman spectroscopy is a powerful technique for studying the structure and interaction in molecular and biological systems. Here, we present a new implementation of the simulation of the two-dimensional infrared Raman signals. The implementation builds on the numerical integration of the Schrödinger equation approach. It combines the prediction of dynamics from molecular dynamics with a map-based approach for obtaining Hamiltonian trajectories and response function calculations. The new implementation is tested on the amide-I region for two proteins, where one is dominated by α-helices and the other by β-sheets. We find that the predicted spectra agree well with experimental observations. We further find that the two-dimensional infrared Raman spectra at least of the studied proteins are much less sensitive to the laser polarization used compared to conventional two-dimensional infrared experiments. The present implementation and findings pave the way for future applications for the interpretation of two-dimensional infrared Raman spectra.

Cross-α/β polymorphism of PSMα3 fibrils

Phenol soluble modulins (PSMs) are an important class of peptides secreted by Staphylococcus aureus bacteria. The toxicity to human cells and unique ability of one such peptide, PSMα3, to aggregate into an α-helical amyloid-like structure may hold a key to a better understanding of the virulence of dangerous pathogens such as methicillin resistant S. aureus. In reporting a detailed two-dimensional infrared (2DIR) analysis of PSMα3, we found direct evidence of multiple aggregate architectures existing in equilibrium with one another. We also discovered a unique and characteristic 2DIR spectroscopic signature that unambiguously reports on the presence of the unusual and highly cytotoxic cross-α amyloid structure.

The formation of ordered cross-β amyloid protein aggregates is associated with a variety of human disorders. While conventional infrared methods serve as sensitive reporters of the presence of these amyloids, the recently discovered amyloid secondary structure of cross-α fibrils presents new questions and challenges. Herein, we report results using Fourier transform infrared spectroscopy and two-dimensional infrared spectroscopy to monitor the aggregation of one such cross-α–forming peptide, phenol soluble modulin alpha 3 (PSMα3). Phenol soluble modulins (PSMs) are involved in the formation and stabilization of Staphylococcus aureus biofilms, making sensitive methods of detecting and characterizing these fibrils a pressing need. Our experimental data coupled with spectroscopic simulations reveals the simultaneous presence of cross-α and cross-β polymorphs within samples of PSMα3 fibrils. We also report a new spectroscopic feature indicative of cross-α fibrils.

AI-based spectroscopic monitoring of real-time interactions between SARS-CoV-2 and human ACE2

The COVID-19 caused by SARS-CoV-2 virus has posed a tremendous threat to human health. The interactions between human angiotensin-converting enzyme 2 and the spike glycoprotein of SARS-CoV-2 hold the key to understanding the molecular mechanism to develop treatment and vaccines. However, the simulation of these interactions in fluctuating surroundings is challenging because it requires many electronic structure calculations at the quantum mechanics level for a large number of representative configurations. We report a machine learning protocol that can efficiently predict the IR spectra of SARS-CoV-2 with high efficiency and characterize fine changes in IR spectra associated with variations of protein secondary structures. Machine learning provides a cost-effective tool for monitoring of real-time interactions between the SARS-CoV-2 and human ACE2.

The novel coronavirus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), invades a human cell via human angiotensin-converting enzyme 2 (hACE2) as the entry, causing the severe coronavirus disease (COVID-19). The interactions between hACE2 and the spike glycoprotein (S protein) of SARS-CoV-2 hold the key to understanding the molecular mechanism to develop treatment and vaccines, yet the dynamic nature of these interactions in fluctuating surroundings is very challenging to probe by those structure determination techniques requiring the structures of samples to be fixed. Here we demonstrate, by a proof-of-concept simulation of infrared (IR) spectra of S protein and hACE2, that time-resolved spectroscopy may monitor the real-time structural information of the protein−protein complexes of interest, with the help of machine learning. Our machine learning protocol is able to identify fine changes in IR spectra associated with variation of the secondary structures of S protein of the coronavirus. Further, it is three to four orders of magnitude faster than conventional quantum chemistry calculations. We expect our machine learning protocol would accelerate the development of real-time spectroscopy study of protein dynamics.

Computing the frequency fluctuation dynamics of highly coupled vibrational transitions using neural networks

The description of frequency fluctuations for highly coupled vibrational transitions has been a challenging problem in physical chemistry. In particular, the complexity of their vibrational Hamiltonian does not allow us to directly derive the time evolution of vibrational frequencies for these systems. In this paper, we present a new approach to this problem by exploiting the artificial neural network to describe the vibrational frequencies without relying on the deconstruction of the vibrational Hamiltonian. To this end, we first explored the use of the methodology to predict the frequency fluctuations of the amide I mode of N-methylacetamide in water. The results show good performance compared with the previous experimental and theoretical results. In the second part, the neural network approach is used to investigate the frequency fluctuations of the highly coupled carbonyl stretch modes for the organic carbonates in the solvation shell of the lithium ion. In this case, the frequency fluctuation predicted by the neural networks shows a good agreement with the experimental results, which suggests that this model can be used to describe the dynamics of the frequency in highly coupled transitions.

Near-Ultraviolet Circular Dichroism and Two-Dimensional Spectroscopy of Polypeptides

A fully quantitative theory of the relationship between protein conformation and optical spectroscopy would facilitate deeper insights into biophysical and simulation studies of protein dynamics and folding. In contrast to intense bands in the far-ultraviolet, near-UV bands are much weaker and have been challenging to compute theoretically. We report some advances in the accuracy of calculations in the near-UV, which were realised through the consideration of the vibrational structure of the electronic transitions of aromatic side chains.

A Machine Learning Protocol for Predicting Protein Infrared Spectra

Infrared (IR) absorption provides important chemical fingerprints of biomolecules. Protein secondary structure determination from IR spectra is tedious since its theoretical interpretation requires repeated expensive quantum-mechanical calculations in a fluctuating environment. Herein we present a novel machine learning protocol that uses a few key structural descriptors to rapidly predict amide I IR spectra of various proteins and agrees well with experiment. Its transferability enabled us to distinguish protein secondary structures, probe atomic structure variations with temperature, and monitor protein folding. This approach offers a cost-effective tool to model the relationship between protein spectra and their biological/chemical properties.

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 the vibrational couplings of nucleobases

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

An efficient spectral method for numerical time-dependent perturbation theory

We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT method is extremely well-suited to simulate multiphoton pulsed laser experiments with complex pulse shapes. The n-dimensional frequency integrals of the nth order perturbative expansion are evaluated numerically using tensor products. The N-point discretized integrals are computed in O(N²) operations, a significant improvement over the O(Nⁿ) scaling of standard quadrature methods.

Coherent two-dimensional electronic and infrared crystallography

The two-dimensional electronic and infrared spectroscopy of oriented single crystals is sensitive to structure and point group symmetry. The third order response of crystals is generally different from measurements of isotropic solutions because each coherence path that contributes to the measured field scales to the ensemble average of the four-point correlation functions of the four field-dipole interactions involved in the respective Feynman paths. An analytical evaluation of 2D optical crystallography which depends on the crystal symmetry, laboratory orientation, and the orientation in the crystallographic frame is presented. Applying a symmetry operator in the basis of the allowed polarised radiation modes provides a method for evaluation of non-zero fourth rank tensor elements alternative to direct inspection methods. Uniaxial and biaxial systems are distinguished and the contributions to the rephasing and non-rephasing directions are evaluated for isolated and coupled oscillators. By exploiting coordinate analysis, the extension of non-linear electronic and infrared crystallography for coupled oscillators demonstrates the structural, directional, and symmetry dependent selection of coherences to the four-wave mixing signal.

Perspective: Quantum mechanical methods in biochemistry and biophysics

In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.

NOESY-Like 2D-IR Spectroscopy Reveals Non-Gaussian Dynamics

We have identified an unexpected signature of non-Gaussian dynamics in a conventional 2D IR measurement on a system with rapid intermolecular vibrational energy transfer. In a ternary mixture of the CO₂ reduction photocatalyst, ReCl(bpy)(CO)₃, NaSCN, and THF solvent, preferential association between the metal carbonyl catalyst and the NaSCN ion pairs facilitates intermolecular energy transfer on a few picoseconds time scale. Monitoring the cross peak between the highest frequency metal carbonyl band and the CN bands of NaSCN contact ion pairs, we find a striking time evolution of the cross-peak position on the detection axis. This frequency shift, which is due to spectral diffusion following intermolecular energy transfer, occurs with a time scale that is distinct from either the donor or acceptor spectral diffusion measured simultaneously. We argue that the energy transfer, a second-order Förster process, effectively increases the dimensionality of the 2D-IR spectroscopy and thus enables sensitivity to non-Gaussian dynamics.

Mutation-Induced Changes in the Protein Environment and Site Energies in the (M)L214G Mutant of the Rhodobacter sphaeroides Bacterial Reaction Center

This work focuses on the low-temperature (5 K) photochemical (transient) hole-burned (HB) spectra within the P870 absorption band, and their theoretical analysis, for the (M)L214G mutant of the photosynthetic Rhodobacter sphaeroides bacterial reaction center (bRC). To provide insight into system-bath interactions of the bacteriochlorophyll a (BChl a) special pair, i.e., P870, in the mutated bRC, the optical line shape function for the P870 band is calculated numerically. On the basis of the modeling studies, we demonstrate that (M)L214G mutation leads to a heterogeneous population of bRCs with modified (increased) total electron-phonon coupling strength of the special pair BChl a and larger inhomogeneous broadening. Specifically, we show that after mutation in the (M)L214G bRC a large fraction (∼50%) of the bacteriopheophytin (HA) chromophores shifts red and the 800 nm absorption band broadens, while the remaining fraction of HA cofactors retains nearly the same site energy as HA in the wild-type bRC. Modeling using these two subpopulations allowed for fits of the absorption and nonresonant (transient) HB spectra of the mutant bRC in the charge neutral, oxidized, and charge-separated states using the Frenkel exciton Hamiltonian, providing new insight into the mutant's complex electronic structure. Although the average (M)L214G mutant quantum efficiency of P(+)QA(-) state formation seems to be altered in comparison with the wild-type bRC, the average electron transfer time (measured via resonant transient HB spectra within the P870 band) was not affected. Thus, mutation in the vicinity of the electron acceptor (HA) does not tune the charge separation dynamics. Finally, quenching of the (M)L214G mutant excited states by P(+) is addressed by persistent HB spectra burned within the B band in chemically oxidized samples.

Assessing Spectral Simulation Protocols for the Amide I Band of Proteins

We present a benchmark study of spectral simulation protocols for the amide I band of proteins. The amide I band is widely used in infrared spectroscopy of proteins due to the large signal intensity, high sensitivity to hydrogen bonding, and secondary structural motifs. This band has, thus, proven valuable in many studies of protein structure-function relationships. We benchmark spectral simulation protocols using two common force fields in combination with several electrostatic mappings and coupling models. The results are validated against experimental linear absorption and two-dimensional infrared spectroscopy for three well-studied proteins. We find two-dimensional infrared spectroscopy to be much more sensitive to the simulation protocol than linear absorption and report on the best simulation protocols. The findings demonstrate that there is still room for ideas to improve the existing models for the amide I band of proteins.

Application of two-dimensional infrared spectroscopy to benchmark models for the amide I band of proteins

In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinations of molecular dynamics force fields, vibrational frequency mappings, and coupling models. We find that two-dimensional infrared spectra provide a much stronger test of the models than linear absorption does. The best modelling approach in the present study still leaves significant room for future improvement. The presented benchmarking scheme, thus, provides a way of validating future protocols for modelling the amide I band in proteins.

Histidine Orientation Modulates the Structure and Dynamics of a de Novo Metalloenzyme Active Site

The ultrafast dynamics of a de novo metalloenzyme active site is monitored using two-dimensional infrared spectroscopy. The homotrimer of parallel, coiled coil α-helices contains a His3-Cu(I) metal site where CO is bound and serves as a vibrational probe of the hydrophobic interior of the self-assembled complex. The ultrafast spectral dynamics of Cu-CO reveals unprecedented ultrafast (2 ps) nonequilibrium structural rearrangements launched by vibrational excitation of CO. This initial rapid phase is followed by much slower ∼40 ps vibrational relaxation typical of metal-CO vibrations in natural proteins. To identify the hidden coupled coordinate, small molecule analogues and the full peptide were studied by QM and QM/MM calculations, respectively. The calculations show that variation of the histidines' dihedral angles in coordinating Cu controls the coupling between the CO stretch and the Cu-C-O bending coordinates. Analysis of different optimized structures with significantly different electrostatic field magnitudes at the CO ligand site indicates that the origin of the stretch-bend coupling is not directly due to through-space electrostatics. Instead, the large, ∼3.6 D dipole moments of the histidine side chains effectively transduce the electrostatic environment to the local metal coordination orientation. The sensitivity of the first coordination sphere to the protein electrostatics and its role in altering the potential energy surface of the bound ligands suggests that long-range electrostatics can be leveraged to fine-tune function through enzyme design.

Dissecting amide-I vibration in β-peptide helices

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

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

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

Disentangling Peptide Configurations via Two-Dimensional Electronic Spectroscopy: Ab Initio Simulations Beyond the Frenkel Exciton Hamiltonian

Two-dimensional (2D) optical spectroscopy techniques based on ultrashort laser pulses have been recently extended to the optical domain in the ultraviolet (UV) spectral region. UV-active aromatic side chains can thus be used as local highly specific markers for tracking dynamics and structural rearrangements of proteins. Here we demonstrate that 2D electronic spectra of a model proteic system, a tetrapeptide with two aromatic side chains, contain enough structural information to distinguish between two different configurations with distant and vicinal side chains. For accurate simulations of the 2DUV spectra in solution, we combine a quantum mechanics/molecular mechanics approach based on wave function methods, accounting for interchromophores coupling and environmental effects, with nonlinear response theory. The proposed methodology reveals effects, such as charge transfer between vicinal aromatic residues that remain concealed in conventional exciton Hamiltonian approaches. Possible experimental setups are discussed, including multicolor experiments and signal manipulation techniques for limiting undesired background contributions and enhancing 2DUV signatures of specific electronic couplings.

Discriminating trpzip2 and trpzip4 peptides' folding landscape using the two-dimensional infrared spectroscopy: a simulation study

We analyzed, based on the theoretical spectroscopic modeling, how the differences in the folding landscapes of two β-hairpin peptides trpzip2 and trpzip4 are reflected in their thermal unfolding infrared measurements. The isotope-edited equilibrium FTIR and two dimensional infrared spectra of the two peptides were calculated, using the nonlinear exciton propagation method, at a series of temperatures. The spectra calculations were based on the configuration distributions generated using the GB(OBC) implicit solvent MD simulation and the integrated tempering sampling technique. Conformational analysis revealed the different local thermal stabilities for these two peptides, which suggested the different folding landscapes. Our study further suggested that the ellipticities of the isotope peaks in the coherent IR signals are more sensitive to these local stability differences compared with other spectral features such as the peak intensities. Our technique can thus be combined with the relevant experimental measurements to achieve a better understanding of the peptide folding behaviors.

Two-dimensional stimulated resonance Raman spectroscopy study of the Trp-cage peptide folding

We report a combined molecular dynamics (MD) and ab initio simulation study of the ultrafast broadband ultraviolet (UV) stimulated resonance Raman (SRR) spectra of the Trp-cage mini protein. Characteristic two dimensional (2D) SRR features of various folding states are identified. Structural fluctuations erode the cross peaks and the correlation between diagonal peaks is a good indicator of the α-helix formation.

Study of the γD-crystallin protein using two-dimensional infrared (2DIR) spectroscopy: experiment and simulation

Cataracts is a misfolding protein disease in which one of the major components is the γD-crystallin protein. The conformational structure of the aggregated γD-crystallin and the interactions that cause aggregation are largely unknown. A recent experimental two-dimensional infrared (2DIR) spectroscopy study determined that the C-terminal domain has a high propensity to form β-sheets whereas the N-terminal domain forms a disordered structure in the fiber state. We present a combined computational molecular dynamics and infrared spectroscopy study of the local dynamics of these domains. The computed 2DIR signals agree remarkably well with experiment. We show that the two domains, both of which have a Greek key structural fold, experience different electrostatic environments, which may be related to the fact that the C-terminal domain is more structurally stable than the N-terminal domain. We correlate the vibrational couplings to known energy dissipation mechanisms and reveal their origin.

Simulations of Two-dimensional Infrared and Stimulated Resonance Raman Spectra of Photoactive Yellow Protein

We present simulations of one and two-dimensional infrared (2DIR) and stimulated resonance Raman (SRR) spectra of the dark state (pG) and early red-shifted intermediate (pR) of photoactive yellow protein (PYP). Shifts in the amide I and Glu46 COOH stretching bands distinguish between pG and pR in the IR absorption and 2DIR spectra. The one-dimensional SRR spectra are similar to the spontaneous RR spectra. The two-dimensional SRR spectra show large changes in cross peaks involving the C=O stretch of the two species and are more sensitive to the chromophore structure than 2DIR spectra.

Modeling the thermal unfolding 2DIR spectra of a β-hairpin peptide based on the implicit solvent MD simulation

We simulated the equilibrium isotope-edited FTIR and 2DIR spectra of a β-hairpin peptide trpzip2 at a series of temperatures. The simulation was based on the configuration distributions generated using the GB(OBC) implicit solvent model and the integrated tempering sampling (ITS) technique. A soaking procedure was adapted to generate the peptide in explicit solvent configurations for the spectroscopy calculations. The nonlinear exciton propagation (NEP) method was then used to calculate the spectra. Agreeing with the experiments, the intensities and ellipticities of the isotope-shifted peaks in our simulated signals have the site-specific temperature dependences, which suggest the inhomogeneous local thermal stabilities along the peptide chain. Our simulation thus proposes a cost-effective means to understand a peptide's conformational change and related IR spectra across its thermal unfolding transition.

Molecular dynamics simulation and computational two-dimensional infrared spectroscopic study of model amyloid β-peptide oligomers

Molecular dynamics simulations were carried out to study the structure stability of model amyloid β40 (Aβ40) peptide oligomers, from monomer to hexamer, in aqueous solution at room temperature. The initial oligomer models were built by using the parallel in-register β-sheet fibril structure and then allowed to relax in the simulations. Our simulation results indicated that the stable Aβ40 monomer was a random coil, while the oligomer structures became more fibril-like with the increase of the peptide strands. Linear absorption and two-dimensional infrared spectra of the isotope-labeled oligomers were calculated and analyzed in detail, which revealed the differential secondary structural features characteristic of Aβ40 aggregation. A quantitative relation was established to make connection between the calculated spectra and experimental ensemble measurements.

Monitoring the folding of Trp-cage peptide by two-dimensional infrared (2DIR) spectroscopy

Protein folding is one of the most fundamental problems in modern molecular biology. Uncovering the detailed folding mechanism requires methods that can monitor the structures at high temporal and spatial resolution. Two-dimensional infrared (2DIR) spectroscopy is a new tool for studying protein structures and dynamics with high time resolution. Using atomistic molecular dynamics simulations, we illustrate the folding process of Trp-cage along the dominant pathway on the free energy landscape by analyzing nonchiral and chiral coherent 2DIR spectra along the pathway. Isotope labeling is used to reveal residue-specific information. We show that the high resolution structural sensitivity of 2DIR can differentiate the ensemble evolution of protein and thus provides a microscopic picture of the folding process.

Simulations of the two-dimensional electronic spectroscopy of the photosystem II reaction center

We report simulations of the two-dimensional electronic spectroscopy of the Q(y) band of the D1-D2-Cyt b559 photosystem II reaction center at 77 K. We base the simulations on an existing Hamiltonian that was derived by simultaneous fitting to a wide range of linear spectroscopic measurements and described within modified Redfield theory. The model obtains reasonable agreement with most aspects of the two-dimensional spectra, including the overall peak shapes and excited state absorption features. It does not reproduce the rapid equilibration from high energy to low energy excitonic states evident by a strong cross-peak below the diagonal. We explore modifications to the model to incorporate new structural data and improve agreement with the two-dimensional spectra. We find that strengthening the system-bath coupling and lowering the degree of disorder significantly improves agreement with the cross-peak feature, while lessening agreement with the relative diagonal/antidiagonal width of the 2D spectra. We conclude that two-dimensional electronic spectroscopy provides a sensitive test of excitonic models of the photosystem II reaction center and discuss avenues for further refinement of such models.

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.

Simulation of transient infrared spectra of a photoswitchable peptide

In transient infrared (IR) experiments, a molecular system may be photoexcited in a nonstationary conformational state, whose time evolution is monitored via IR spectroscopy with high temporal and structural resolution. As a theoretical formulation of these experiments, this work derives explicit expressions for transient one- and two-dimensional IR spectra and discusses various levels of approximation and sampling strategies. Adopting a photoswitchable octapeptide in water as a representative example, nonequilibrium molecular dynamics simulations are performed and the photoinduced conformational dynamics and associated IR spectra are discussed in detail. Interestingly, it is found that the time scales of dynamics and spectra may differ from residue to residue by up to an order of magnitude. Considering merely the cumulative spectrum of all residues, the contributions of the individual residues largely compensate each other, which may explain the surprisingly small frequency shifts and short photoproduct rise times found in experiment. Even when a localized amide I mode is probed (e.g., via isotope labeling), the vibrational frequency shift is shown to depend in a complicated way on the conformation of the entire peptide as well as on the interaction with the solvent. In this context, various issues concerning the interpretation of transient IR spectra and conformational dynamics in terms of a few exponential time scales are discussed.

Environment Polarity in Proteins Mapped Noninvasively by FTIR Spectroscopy

The polarity pattern of a macromolecule is of utmost importance to its structure and function. For example, one of the main driving forces for protein folding is the burial of hydrophobic residues. Yet polarity remains a difficult property to measure experimentally, due in part to its non-uniformity in the protein interior. Herein, we show that FTIR linewidth analysis of noninvasive 1-(13)C=(18)O labels can be used to obtain a reliable measure of the local polarity, even in a highly multi-phasic system, such as a membrane protein. We show that in the Influenza M2 H(+) channel, residues that line the pore are located in an environment that is as polar as fully solvated residues, while residues that face the lipid acyl chains are located in an apolar environment. Taken together, FTIR linewidth analysis is a powerful, yet chemically non-perturbing approach to examine one of the most important properties in proteins - polarity.

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

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

Development and validation of transferable amide I vibrational frequency maps for peptides

Infrared (IR) spectroscopy of the amide I band has been widely utilized for the analysis of peptides and proteins. Theoretical modeling of IR spectra of proteins requires an accurate and efficient description of the amide I frequencies. In this paper, amide I frequency maps for protein backbone and side chain groups are developed from experimental spectra and vibrational lifetimes of N-methylacetamide and acetamide in different solvents. The frequency maps, along with established nearest-neighbor frequency shift and coupling schemes, are then applied to a variety of peptides in aqueous solution and reproduce experimental spectra well. The frequency maps are designed to be transferable to different environments; therefore, they can be used for heterogeneous systems, such as membrane proteins.

Simulating the T-jump-triggered unfolding dynamics of trpzip2 peptide and its time-resolved IR and two-dimensional IR signals using the Markov state model approach

We proposed a computational protocol of simulating the T-jump peptide unfolding experiments and the related transient IR and two-dimensional IR (2DIR) spectra based on the Markov state model (MSM) and nonlinear exciton propagation (NEP) methods. MSMs partition the conformation space into a set of nonoverlapping metastable states, and we can calculate spectra signal for each of these states using the NEP method. Thus the overall spectroscopic observable for a given system is simply the sum of spectra of different metastable states weighted by their populations. We show that results from MSMs constructed from a large number of simulations have a much better agreement with the equilibrium experimental 2DIR spectra compared to that generated from straightforward MD simulations starting from the folded state. This indicates that a sufficient sampling of important relevant conformational states is critical for calculating the accurate spectroscopic observables. MSMs are also capable of simulating the unfolding relaxation dynamics upon the temperature jump. The agreement of the simulation using MSMs and NEP with the experiment not only provides a justification for our protocol, but also provides the physical insight of the underlying spectroscopic observables. The protocol we developed has the potential to be extended to simulate a wide range of fast triggering plus optical detection experiments for biomolecules.