Electrostatic DFT Map for the Complete Vibrational Amide Band of NMA

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

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

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.

Refining protein amide I spectrum simulations with simple yet effective electrostatic models for local wavenumbers and dipole derivative magnitudes

Analysis of the amide I band of proteins is probably the most wide-spread application of bioanalytical infrared spectroscopy. Although highly desirable for a more detailed structural interpretation, a quantitative description of this absorption band is still difficult. This work optimized several electrostatic models with the aim to reproduce the effect of the protein environment on the intrinsic wavenumber of a local amide I oscillator. We considered the main secondary structures - α-helices, parallel and antiparallel β-sheets - with a maximum of 21 amide groups. The models were based on the electric potential and/or the electric field component along the CO bond at up to four atoms in an amide group. They were bench-marked by comparison to Hessian matrices reconstructed from density functional theory calculations at the BPW91, 6-31G** level. The performance of the electrostatic models depended on the charge set used to calculate the electric field and potential. Gromos and DSSP charge sets, used in common force fields, were not optimal for the better performing models. A good compromise between performance and the stability of model parameters was achieved by a model that considered the electric field at the positions of the oxygen, nitrogen, and hydrogen atoms of the considered amide group. The model describes also some aspects of the local conformation effect and performs similar on its own as in combination with an explicit implementation of the local conformation effect. It is better than a combination of a local hydrogen bonding model with the local conformation effect. Even though the short-range hydrogen bonding model performs worse, it captures important aspects of the local wavenumber sensitivity to the molecular surroundings. We improved also the description of the coupling between local amide I oscillators by developing an electrostatic model for the dependency of the dipole derivative magnitude on the protein environment.

Network Pharmacology Analysis and Machine-Learning Models Confirmed the Ability of YiShen HuoXue Decoction to Alleviate Renal Fibrosis by Inhibiting Pyroptosis

Purpose

YiShen HuoXue decoction (YSHXD) is a formulation that has been used clinically for the treatment of renal fibrosis (RF) for many years. We aimed to clarify therapeutic effects of YSHXD against RF and potential pharmacological mechanisms.

Materials and Methods

We used network pharmacology analysis and machine-learning to screen the core components and core targets of YSHXD against RF, followed by molecular docking and molecular dynamics simulations to confirm the reliability of the results. Finally, we validated the network pharmacology analysis experimentally in HK-2 cells and a rat model of RF established by unilateral ureteral ligation (UUO).

Results

Quercetin, kaempferol, luteolin, beta-sitosterol, wogonin, stigmasterol, isorhamnetin, baicalein, and dihydrotanshinlactone progesterone were identified as the main active components of YSHXD in the treatment of unilateral ureteral ligation-induced RF, with IL-6, IL1β, TNF, AR, and PTGS2 as core target proteins. Molecular docking and molecular dynamics simulations further confirmed the relationship between compounds and target proteins. The potential molecular mechanism of YSHXD predicted by network pharmacology analysis was confirmed in HK-2 cells and UUO rats. YSHXD downregulated NLRP3, ASC, NF-κBp65, Caspase-1, GSDMD, PTGS2, IL-1β, IL-6, IL-18, TNF-α, α-SMA and upregulated HGF, effectively alleviating the RF process.

Conclusion

YSHXD exerts important anti-inflammatory and anti-cellular inflammatory necrosis effects by inhibiting the NLRP3/caspase-1/GSDMD-mediated pyroptosis pathway, indicating that YSHXD represents a new strategy and complementary approach to RF therapy.

Machine Learning Approach Based on a Range-Corrected Deep Potential Model for Efficient Vibrational Frequency Computation

As an ensemble average result, vibrational spectrum simulation can be time-consuming with high accuracy methods. We present a machine learning approach based on the range-corrected deep potential (DPRc) model to improve the computing efficiency. The DPRc method divides the system into "probe region" and "solvent region"; "solvent-solvent" interactions are not counted in the neural network. We applied the approach to two systems: formic acid C═O stretching and MeCN C≡N stretching vibrational frequency shifts in water. All data sets were prepared using the quantum vibration perturbation approach. Effects of different region divisions, one-body correction, cut range, and training data size were tested. The model with a single-molecule "probe region" showed stable accuracy; it ran roughly 10 times faster than regular deep potential and reduced the training time by about four. The approach is efficient, easy to apply, and extendable to calculating various spectra.

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

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

Distinct electrostatic frequency tuning rates for amide I and amide I' vibrations

Amide I spectroscopy probes the backbone C=O stretch vibrations of peptides and proteins. Amide I spectra are often collected in deuterated water (D₂O) since this provides a cleaner background in the amide I frequency range; such data are often referred to as amide I' spectra since deuteration induces changes in the mode structure, including a roughly ∼10 cm^-1 redshift. For biological samples, however, deuteration is often not possible. As amide I frequency maps are increasingly applied to quantitative protein structural analysis, this raises the interesting challenge of drawing direct connections between amide I and amide I' data. We here analyze amide I and amide I' peak frequencies for a series of dipeptides and related compounds. Changes in protonation state induce large electrostatic shifts in the peak frequencies, allowing us to amass a sizable library of data points for direct amide I/amide I' comparison. While we find an excellent linear correlation between amide I and amide I' peak frequencies, the deuteration-induced shift is smaller for more red-shifted vibrations, indicating different electrostatic tuning rates in the two solvents. H₂O/D₂O shifts were negligible for proline-containing dipeptides that lack exchangeable amide hydrogens, indicating that the intrinsic properties of the solvent do not strongly influence the H/D shift. These findings indicate that the distinct tuning rates observed for the two vibrations arise from modifications to the intrinsic properties of the amide bond and provide (at least for solvated dipeptides) a simple, linear "map" for translating between amide I and amide I' frequencies.

Lanthanide-dependent coordination interactions in lanmodulin: a 2D IR and molecular dynamics simulations study

The biological importance of lanthanides, and the early lanthanides (La³⁺-Nd³⁺) in particular, has only recently been recognized, and the structural principles underlying selective binding of lanthanide ions in biology are not yet well established. Lanmodulin (LanM) is a novel protein that displays unprecedented affinity and selectivity for lanthanides over most other metal ions, with an uncommon preference for the early lanthanides. Its utilization of EF-hand motifs to bind lanthanides, rather than the Ca²⁺ typically recognized by these motifs in other proteins, has led it to be used as a model system to understand selective lanthanide recognition. Two-dimensional infrared (2D IR) spectroscopy combined with molecular dynamics simulations were used to investigate LanM's selectivity mechanisms by characterizing local binding site geometries upon coordination of early and late lanthanides as well as calcium. These studies focused on the protein's uniquely conserved proline residues in the second position of each EF-hand binding loop. We found that these prolines constrain the EF-hands for strong coordination of early lanthanides. Substitution of this proline results in a more flexible binding site to accommodate a larger range of ions but also results in less compact coordination geometries and greater disorder within the binding site. Finally, we identify the conserved glycine in the sixth position of each EF-hand as a mediator of local binding site conformation and global secondary structure. Uncovering fundamental structure-function relationships in LanM informs the development of synthetic biology technologies targeting lanthanides in industrial applications.

Segregation on the nanoscale coupled to liquid water polyamorphism in supercooled aqueous ionic-liquid solution

The most intriguing hypothesis explaining many water anomalies is a metastable liquid-liquid phase transition (LLPT) at high pressure and low temperatures, experimentally hidden by homogeneous nucleation. Recent infrared spectroscopic experiments showed that upon addition of hydrazinium trifluoroacetate to water, the supercooled ionic solution undergoes a sharp, reversible LLPT at ambient pressure, possible offspring of that in pure water. Here, we calculate the temperature-dependent signature of the OH-stretching band, reporting on the low/high density phase of water, in neat water and in the same experimentally investigated ionic solution. The comparison between the infrared signature of the pure liquid and that of the ionic solution can be achieved only computationally, providing insight into the nature of the experimentally observed phase transition and allowing us to investigate the effects of ionic compounds on the high to low density supercooled liquid water transition. We show that the experimentally observed crossover behavior in the ionic solution can be reproduced only if the phase transition between the low- and high-density liquid states of water is coupled to a mixing-unmixing transition between the water component and the ions: at low temperatures, water and ions are separated and the water component is a low density liquid. At high temperatures, water and ions get mixed and the water component is a high-density liquid. The separation at low temperatures into ion-rich and ion-poor regions allows unveiling the polyamorphic nature of liquid water, leading to a crossover behavior resembling that observed in supercooled neat water under high pressure.

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.

A computational insight into the relationship between side chain IR line shapes and local environment in fibril-like structures

Infrared spectroscopy is a widely used technique to characterize protein structures and protein mediated processes. While the amide I band provides information on proteins' secondary structure, amino acid side chains are used as infrared probes for the investigation of protein reactions and local properties. In this paper, we use a hybrid quantum mechanical/classical molecular dynamical approach based on the perturbed matrix method to compute the infrared band due to the C=O stretching mode of amide-containing side chains. We calculate, at first, the infrared band of zwitterionic glutamine in water and obtain results in very good agreement with the experimental data. Then, we compute the signal arising from glutamine side chains in a microcrystal of the yeast prion Sup35-derived peptide, GNNQQNY, with a fibrillar structure. The infrared bands obtained by selective isotopic labeling of the two glutamine residues, Q4 and Q5, of each peptide were experimentally used to investigate the local hydration in the fibrillar microcrystal. The experimental spectra of the two glutamine residues, which experience different hydration environments, feature different spectral signals that are well reproduced by the corresponding calculated spectra. In addition, the analysis of the simulated spectra clarifies the molecular origin of the experimentally observed spectroscopic differences that arise from the different local electric field experienced by the two glutamine residues, which is, in turn, determined by a different hydrogen bonding pattern.

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.

Computational IR Spectroscopy of Insulin Dimer Structure and Conformational Heterogeneity

We have investigated the structure and conformational dynamics of insulin dimer using a Markov state model (MSM) built from extensive unbiased atomistic molecular dynamics simulations and performed infrared spectral simulations of the insulin MSM to describe how structural variation within the dimer can be experimentally resolved. Our model reveals two significant conformations to the dimer: a dominant native state consistent with other experimental structures of the dimer and a twisted state with a structure that appears to reflect a ∼55° clockwise rotation of the native dimer interface. The twisted state primarily influences the contacts involving the C-terminus of insulin's B chain, shifting the registry of its intermolecular hydrogen bonds and reorganizing its side-chain packing. The MSM kinetics predict that these configurations exchange on a 14 μs time scale, largely passing through two Markov states with a solvated dimer interface. Computational amide I spectroscopy of site-specifically ¹³C¹⁸O labeled amides indicates that the native and twisted conformation can be distinguished through a series of single and dual labels involving the B24F, B25F, and B26Y residues. Additional structural heterogeneity and disorder is observed within the native and twisted states, and amide I spectroscopy can also be used to gain insight into this variation. This study will provide important interpretive tools for IR spectroscopic investigations of insulin structure and transient IR kinetics experiments studying the conformational dynamics of insulin dimer.

Infrared spectroscopy probes ion binding geometries

Infrared (IR) spectroscopy is a well-established technique for probing the structure, behavior, and surroundings of molecules in their native environments. Its characteristics-most specifically high structural sensitivity, ready applicability to aqueous samples, and broad availability-make it a valuable enzymological technique, particularly for the interrogation of ion binding sites. While IR spectroscopy of the "garden variety" (steady state at room temperature with wild-type proteins) is versatile and powerful in its own right, the combination of IR spectroscopy with specialized experimental schemes for leveraging ultrafast time resolution, protein labeling, and other enhancements further extends this utility. This book chapter provides the fundamental physical background and literature context essential for harnessing IR spectroscopy in the general context of enzymology with specific focus on interrogation of ion binding. Studies of lanthanide ions binding to calmodulin are highlighted as illustrative examples of this process. Appropriate sample preparation, data collection, and spectral interpretation are discussed from a detail-oriented and practical perspective with the goal of facilitating the reader's rapid progression from reading words in a book to collecting and analyzing their own data in the lab.

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.

Photo-initiated rupture of azobenzene micelles to enable the spectroscopic analysis of antimicrobial peptide dynamics

Antimicrobial peptides (AMPs) show promise for the treatment of bacterial infections, but many have undesired hemolytic activities. The AMP MP1 not only has broad spectrum bactericidal activity, but has been shown to have antitumor activity. The interaction between AMPs and cellular membranes gives rise to a peptide's cell-specificity and activity. However, direct analysis of the biophysical interactions between peptides and membrane is complex, in part due to the nature of membrane environments as well as structural changes in the peptide that occurs upon binding to the membrane. In order to investigate the interplay between cell selectivity, activity, and secondary structural changes involved in antimicrobial peptide activity, we sought to implement photolizable membrane mimics to assess the types of information available from infrared spectroscopic measurements that follow from photoinitiated peptide dynamics. Azo-surfactants (APEG) form micelles containing a photolizable azobenzene core, which upon irradiation can induce membrane deformation resulting in breakdown of micelles. Spectroscopic analysis of membrane deformation may provide insights into the physical behavior associated with unfolding and dissociation of antimicrobial peptides within a membrane environment. Herein, we synthesized and characterized two new azo-surfactants, APEGTMG and APEGNEt2MeI. Furthermore, we demonstrate the viability of azosurfactants as membrane mimics by examining both the membrane binding and dissociation induced secondary structural changes of the antimicrobial peptide, MP1.

Modeling amino-acid side chain infrared spectra: the case of carboxylic residues

Infrared (IR) spectroscopy is commonly utilized for the investigation of protein structures and protein-mediated processes.

Modelling vibrational relaxation in complex molecular systems

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

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala-Ala-Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala-Ala-Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.

Development of Vibrational Frequency Maps for Nucleobases

Vibrational spectroscopy provides a powerful tool to probe the structure and dynamics of nucleic acids because specific normal modes, particularly the base carbonyl stretch modes, are highly sensitive to the hydrogen bonding patterns and stacking configurations in these biomolecules. In this work, we develop vibrational frequency maps for the C═O and C═C stretches in nucleobases that allow the calculations of their site frequencies directly from molecular dynamics simulations. We assess the frequency maps by applying them to nucleobase derivatives in aqueous solutions and nucleosides in organic solvents and demonstrate that the predicted infrared spectra are in good agreement with experimental measurements. The frequency maps can be readily used to model the linear and nonlinear vibrational spectroscopy of nucleic acids and elucidate the molecular origin of the experimentally observed spectral features.

A fragmented, permutationally invariant polynomial approach for potential energy surfaces of large molecules: Application to N-methyl acetamide

We describe and apply a method to extend permutationally invariant polynomial (PIP) potential energy surface (PES) fitting to molecules with more than 10 atoms. The method creates a compact basis of PIPs as the union of PIPs obtained from fragments of the molecule. An application is reported for trans-N-methyl acetamide, where B3LYP/cc-pVDZ electronic energies and gradients are used to develop a full-dimensional potential for this prototype peptide molecule. The performance of several fragmented bases is verified against a benchmark PES using all (66) Morse variables. The method appears feasible for much larger molecules.

Multicriteria Decision Model and Thermal Pretreatment of Hotel Food Waste for Robust Output to Biogas: Case Study from City of Jaipur, India

The anaerobic batch test (45 days at 37°C) was performed to describe the effect of thermal pretreatment at moderate temperatures (60, 80, and 100°C) over durations of 10 and 20 minutes on the enhancement of biogas production using hotel food waste from city of Jaipur, India. The results showed that the total cumulative biogas production with thermal pretreatment (100°C, 10 minutes) was 41% higher than the control. Also, this alternative gets first rank using multicriteria decision making model, VIKOR. This outcome was obtained due to the enhancement of degradation of organic compounds such as protein and volatile solids that occurred in the linear trend. Modified Gompertz and Logistic models were used to study the effect of different pretreatment parameters on lag time and biogas yield. Scanning electron microscopy and Fourier transform infrared spectroscopy were also employed to investigate the effect of thermal pretreatment on the physiochemical properties of food waste.

Spectral line shapes in linear absorption and two-dimensional spectroscopy with skewed frequency distributions

The effect of Gaussian dynamics on the line shapes in linear absorption and two-dimensional correlation spectroscopy is well understood as the second-order cumulant expansion provides exact spectra. Gaussian solvent dynamics can be well analyzed using slope line analysis of two-dimensional correlation spectra as a function of the waiting time between pump and probe fields. Non-Gaussian effects are not as well understood, even though these effects are common in nature. The interpretation of the spectra, thus far, relies on complex case to case analysis. We investigate spectra resulting from two physical mechanisms for non-Gaussian dynamics, one relying on the anharmonicity of the bath and the other on non-linear couplings between bath coordinates. These results are compared with outcomes from a simpler log-normal dynamics model. We find that the skewed spectral line shapes in all cases can be analyzed in terms of the log-normal model, with a minimal number of free parameters. The effect of log-normal dynamics on the spectral line shapes is analyzed in terms of frequency correlation functions, maxline slope analysis, and anti-diagonal linewidths. A triangular line shape is a telltale signature of the skewness induced by log-normal dynamics. We find that maxline slope analysis, as for Gaussian dynamics, is a good measure of the solvent dynamics for log-normal dynamics.

Direct Anionic Effect on Water Structure and Indirect Anionic Effect on Peptide Backbone Hydration State Revealed by Thin-Layer Infrared Spectroscopy

In this work, the anionic effect on water structure and on the peptide backbone and water interaction was investigated directly in aqueous solution using thin-layer transmission infrared spectroscopy. The chaotropic anions were found to weaken the water hydrogen-bonding strength and red shift the HOH bending frequency, while the kosmotropic anions were found to strengthen the water hydrogen-bonding network and blue shift the HOH bending frequency. The kosmotropes, especially F^-, blue shift the vibrational frequencies of both amide II and amide III bands of N-methylacetamide (NMA), indicating NMA is in the "salting-in" state; while the chaotropes (Cl^-, NO₃^-, Br^-, I^-, and SCN^-) red shift the frequencies of the two normal modes, indicating NMA is in the "salting-out" state. Furthermore, the changes of the vibrational frequencies of the HOH bending, amide II and III bands were found to generally follow the Hofmeister anionic series. Our results suggest that hydrated anion influences the peptide backbone mainly through the N-H group, but a weak and indirect effect through the amide C═O group also contributes. Thus, these amide modes can be used as vibrational measures of anionic influences on peptide backbone's hydration state. Our work also suggests that deuteration of the amide unit decreases the sensitivity of the amide II and III vibrational modes in this regard.

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

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

The dynamics of peptide-water interactions in dialanine: An ultrafast amide I 2D IR and computational spectroscopy study

We present a joint experimental and computational study of the dynamic interactions of dialanine (Ala-Ala) with water, comparing the results of ultrafast 2D IR and infrared transient absorption spectroscopy of its amide I vibration with spectra modeled from molecular dynamics (MD) simulations. The experimental data are analyzed to describe vibrational frequency fluctuations, vibrational energy relaxation, and chemical exchange processes. The origin of these processes in the same underlying fluctuating forces allows a common description in terms of the fluctuations and conformational dynamics of the peptide and associated solvent. By comparing computational spectroscopy from MD simulations with multiple force fields and water models, we describe how the dynamics of water hydrogen bond fluctuations and switching processes act as a source of friction that governs the dephasing and vibrational relaxation, and provide a description of coupled water and peptide motions that give rise to spectroscopic exchange processes.

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

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

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

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

Computing infrared spectra of proteins using the exciton model

The ability to compute from first principles the infrared spectrum of a protein in solution phase representing a biological system would provide a useful connection to atomistic models of protein structure and dynamics. Indeed, such calculations are a vital complement to 2DIR experimental measurements, allowing the observed signals to be interpreted in terms of detailed structural and dynamical information. In this article, we have studied nine structurally and spectroscopically well-characterized proteins, representing a range of structural types. We have simulated the equilibrium conformational dynamics in an explicit point charge water model. Using the resulting trajectories based on MD simulations, we have computed the one and two dimensional infrared spectra in the Amide I region, using an exciton approach, in which a local mode basis of carbonyl stretches is considered. The role of solvent in shifting the Amide I band (by 30 to 50 cm-1 ) is clearly evident. Similarly, the conformational dynamics contribute to the broadening of peaks in the spectrum. The inhomogeneous broadening in both the 1D and 2D spectra reflects the significant conformational diversity observed in the simulations. Through the computed 2D cross-peak spectra, we show how different pulse schemes can provide additional information on the coupled vibrations. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Interplay between Hydrogen Bonding and Vibrational Coupling in Liquid N-Methylacetamide

Intrinsically disordered proteins play an important role in biology, and unraveling their labile structure presents a vital challenge. However, the dynamical structure of such proteins thwarts their study by standard techniques such as X-ray diffraction and NMR spectroscopy. Here, we use a neat liquid composed of N-methylacetamide molecules as a model system to elucidate dynamical and structural properties similar to those one can expect to see in intrinsically disordered proteins. To examine the structural dynamics in the neat liquid, we combine molecular dynamics, response-function-based spectral simulations, and two-dimensional polarization-resolved infrared spectroscopy in the amide I (CO stretch) region. The two-dimensional spectra reveal a delicate interplay between hydrogen bonding and intermolecular vibrational coupling effects, observed through a fast anisotropy decay. The present study constitutes a general platform for understanding the structure and dynamics of highly disordered proteins.

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.

Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

Three low-lying vibrational states of molecular systems are responsible for the signals of linear and third-order nonlinear vibrational spectroscopies. Theoretical studies based on mixed quantum/classical calculations provide a powerful way to analyze those experiments. A statistically meaningful result can be obtained from the calculations by solving the vibrational Schrödinger equation over many numbers of molecular configurations. The discrete variable representation (DVR) method is a useful technique to calculate vibrational eigenstates subject to an arbitrary anharmonic potential surface. Considering the large number of molecular configurations over which the DVR calculations are repeated, the calculations are desired to be optimized in balance between the cost and accuracy. We determine a dimension of the DVR method which appears to be optimum for the calculations of the three states of molecular vibrations with anharmonic strengths often found in realistic molecular systems. We apply the numerical technique to calculate the local OH stretching frequencies of liquid water, which are well known to be widely distributed due to the inhomogeneity in molecular configuration, and found that the frequencies of the 0-1 and 1-2 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H-Cl stretching frequency in the HCl-water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H-Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures.

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.

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

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

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.

How Sensitive is the Amide I Vibration of the Polypeptide Backbone to Electric Fields?

Site-selective isotopic labeling of amide carbonyls offers a nonperturbative means to introduce a localized infrared probe into proteins. Although this strategy has been widely used to investigate various biological questions, the dependence of the underlying amide I vibrational frequency on electric fields (or Stark tuning rate) has not been fully determined, which prevents it from being used in a quantitative manner in certain applications. Herein, through the use of experiments and molecular dynamics simulations, the Stark tuning rate of the amide I vibration of an isotopically labeled backbone carbonyl in a transmembrane α-helix is determined to be approximately 1.4 cm(-1) /(MV/cm). This result provides a quantitative basis for using this vibrational model to assess local electric fields in proteins, among other applications. For instance, by using this value, we are able to show that the backbone region of a dipeptide has a surprisingly low dielectric constant.

Modeling Vibrational Spectra of Ester Carbonyl Stretch in Water and DMSO Based on Molecular Dynamics Simulation

On the basis of molecular dynamics simulation, we model the ester carbonyl stretch FTIR signals of methyl acetate in D2O and DMSO. An ab initio map is constructed at the B3LYP/6-311++G** level to relate the carbonyl stretch frequency to the external electric field. Using this map, fluctuating Hamiltonian of the carbonyl stretch is constructed from the MD simulation trajectory. The IR spectra calculated based on this Hamiltonian are found to be in good agreement with the experiment. For methyl acetate in D2O, hydrogen bonding on alkoxy oxygen causes a blue shift of frequency, while that on carbonyl oxygen causes a red shift. Two peaks observed in FTIR signals originate from the balance of these two effects. Furthermore, in both D2O and DMSO solutions, correlations are found between the instantaneous electric field on C═O and the frequencies. Broader line width of the signal in D2O suggests a more inhomogeneous electric field distribution due to the complicated hydrogen-bonding environment.

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.