Analysis of the Cartesian Tensor Transfer Method for Calculating Vibrational Spectra of Polypeptides

Accelerating Molecular Vibrational Spectra Simulations with a Physically Informed Deep Learning Model

In recent years, machine learning (ML) surrogate models have emerged as an indispensable tool to accelerate simulations of physical and chemical processes. However, there is still a lack of ML models that can accurately predict molecular vibrational spectra. Here, we present a highly efficient multitask ML surrogate model termed Vibrational Spectra Neural Network (VSpecNN), to accurately calculate infrared (IR) and Raman spectra based on dipole moments and polarizabilities obtained on-the-fly via ML-enhanced molecular dynamics simulations. The methodology is applied to pyrazine, a prototypical polyatomic chromophore. The VSpecNN-predicted energies are well within the chemical accuracy (1 kcal/mol), and the errors for VSpecNN-predicted forces are only half of those obtained from a popular high-performance ML model. Compared to the ab initio reference, the VSpecNN-predicted frequencies of IR and Raman spectra differ only by less than 5.87 cm-1, and the intensities of IR spectra and the depolarization ratios of Raman spectra are well reproduced. The VSpecNN model developed in this work highlights the importance of constructing highly accurate neural network potentials for predicting molecular vibrational spectra.

Conformational analysis of lipid membrane mimetics modified with Aβ42 peptide by Raman spectroscopy and computer simulations

Peptide-lipid interactions play an important role in maintaining the integrity and function of the cell membrane. Even slight changes in these interactions can induce the development of various diseases. Specifically, peptide misfolding and aggregation in the membrane is considered to be one of the triggers of Alzheimer's disease (AD), however its exact mechanism is still unclear. To this end, an increase of amyloid-beta (Aβ) peptide concentration in the human brain is widely accepted to gradually produce cytotoxic Aβ aggregates (plaques). These plaques initiate a sequence of pathogenic events ending up in observable symptoms of dementia. Understanding the mechanism of the Aβ interaction with cells is crucial for early detection and prevention of Alzheimer's disease. Hence, in this work, a comprehensive Raman analysis of the Aβ42 conformational dynamics in water and in liposomes and lipodiscs that mimic the membrane system is presented. The obtained results show that the secondary structure of Aβ42 in liposomes is dominated by the α-helix conformation, which remains stable over time. However, it comes as a surprise to reveal that the lipodisc environment induces the transformation of the Aβ42 secondary structure to a β-turn/random coil. Our Raman spectroscopy findings are supported with molecular dynamics (MD) and density functional theory (DFT) simulations, showing their good agreement.Communicated by Ramaswamy H. Sarma.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

Intense chiral signal from α-helical poly-L-alanine observed in low-frequency Raman optical activity

Raman optical activity (ROA) spectral features reliably indicate the structure of peptides and proteins, but the signal is often weak. However, we observed significantly enhanced low-frequency bands for α-helical poly-L-alanine (PLA) in solution. The biggest ROA signal at ∼100 cm^-1 is about 10 times stronger than higher-frequency bands described previously, which facilitates the detection. The low-frequency bands of PLA were compared to those of α-helical proteins. For PLA, density functional simulations well reproduced the experimental spectra and revealed that about 12 alanine residues within two turns of the α-helix generate the strong ROA band. Averaging based on molecular dynamics (MD) provided an even more realistic spectrum compared to the static model. The low-frequency bands could be largely related to a collective motion of the α-helical backbone, partially modulated by the solvent. Helical and intermolecular vibrational coordinates have been introduced and the helical unwinding modes were assigned to the strongest ROA signal at 101-128 cm^-1. Further analysis indicated that the helically arranged amide and methyl groups are important for the strong chiral signal of PLA, while the local chiral centers C_αH contribute in a minor way only. The strong low-frequency ROA can thus provide precious information about the motions of the peptide backbone and facilitate future protein studies.

Quantitative Comparison of Experimental and Computed IR-Spectra Extracted from Ab Initio Molecular Dynamics

Experimentally measured infrared spectra are often compared to their computed equivalents. However, the accordance is typically characterized by visual inspection, which is prone to subjective judgment. The primary challenge for a similarity-based analysis is that the artifacts introduced by each approach are very different and, therefore, may require preprocessing steps to determine and correct impeding irregularities. To allow for automated objective assessment, we propose a practical and comprehensive workflow involving scaling factors, a novel baseline correction scheme, and peak smoothing. The resulting spectra can then easily be compared quantitatively using similarity measures, for which we found the Pearson correlation coefficient to be the most suitable. The proposed procedure is then applied to compare the agreement of the experimental infrared spectra from the NIST Chemistry Web book with the calculated spectra using standard harmonic frequency analysis and spectra extracted from ab initio molecular dynamics simulations at different levels of theory. We conclude that the direct, quantitative comparison of calculated and measured IR spectra might become a novel, sophisticated approach to benchmark quantum-chemical methods. In the present benchmark, simulated spectra based on ab initio molecular dynamics show in general better agreement with the experiment than static calculations.

α-Synuclein conformations followed by vibrational optical activity. Simulation and understanding of the spectra

For α-synuclein novel structural markers were identified in vibrational optical activity spectra and supported by theoretical modeling.

Vibrational optical activity for structural characterization of natural products

This review presents the recent progress towards elucidating the structures of chiral natural products and applications using vibrational optical activity (VOA) spectroscopy.

Effects of sulfation and the environment on the structure of chondroitin sulfate studied via Raman optical activity

Raman optical activity reflects differences in the secondary structure of chondroitin caused by its sulfation.

Insight into vibrational circular dichroism of proteins by density functional modeling

Vibrational circular dichroism (VCD) spectroscopy is an excellent method to determine the secondary structure of proteins in solution. Comparison of experimental spectra with quantum-chemical simulations represents a convenient and objective way to extract information on the structure. This has been difficult for such large molecules where approximate theoretical models have to be used. In the present study we applied the Cartesian-coordinate based tensor transfer (CCT) making it possible to extend the density functional theory (DFT) and model spectral intensities of large globular proteins nearly at quantum-chemical precision. Indeed, comparison with experiment provided a better understanding of the dependence of VCD spectral shapes on the geometry, their sensitivity to fine structural details and interactions with the environment. On a model set of globular proteins the simulated spectra correlated well with experimental data and revealed which structural information can (and cannot) be obtained from this kind of spectroscopy. Although the VCD technique has been regarded as being rather insensitive to side-chain variations, we found that the spectra of human and hen lysozyme differing by a few amino acids only are quite distinct. This has been explained by long-distance coupling of the amide vibrations. Likewise, the modeling reproduced some spectral changes caused by protein deuteration even when the protein structure was conserved.

Computing Bulk Phase Raman Optical Activity Spectra from ab initio Molecular Dynamics Simulations

We present our novel methodology for computing Raman optical activity (ROA) spectra of liquid systems from ab initio molecular dynamics (AIMD) simulations. The method is built upon the recent developments to obtain magnetic dipole moments from AIMD and to integrate molecular properties by using radical Voronoi tessellation. These techniques are used to calculate optical activity tensors for large and complex periodic bulk phase systems. Only AIMD simulations are required as input, and no time-consuming perturbation theory is involved. The approach relies only on the total electron density in each time step and can readily be combined with a wide range of electronic structure methods. To the best of our knowledge, these are the first computed ROA spectra for a periodic bulk phase system. As an example, the experimental ROA spectrum of liquid (R)-propylene oxide is reproduced very well.

Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach

The present work reports the calculation of vibrational infrared (IR) and Raman spectra of large molecular systems employing molecular tailoring approach (MTA). Further, it extends the grafting procedure for the accurate evaluation of IR and Raman spectra of large molecular systems, employing a new methodology termed as Fragments-in-Fragments (FIF), within MTA. Unlike the previous MTA-based studies, the accurate estimation of the requisite molecular properties is achieved without performing any full calculations (FC). The basic idea of the grafting procedure is implemented by invoking the nearly basis-set-independent nature of the MTA-based error vis-à-vis the respective FCs. FIF has been tested out for the estimation of the above molecular properties for three isomers, viz., β-strand, 310- and α-helix of acetyl(alanine)nNH2 (n = 10, 15) polypeptides, three conformers of doubly protonated gramicidin S decapeptide and trpzip2 protein (PDB id: 1LE1), respectively, employing BP86/TZVP, M06/6-311G**, and M05-2X/6-31G** levels of theory. For most of the cases, a maximum difference of 3 cm(-1) is achieved between the grafted-MTA frequencies and the corresponding FC values. Further, a comparison of the BP86/TZVP level IR and Raman spectra of α-helical (alanine)20 and its N-deuterated derivative shows an excellent agreement with the existing experimental spectra. In view of the requirement of only MTA-based calculations and the ability of FIF to work at any level of theory, the current methodology provides a cost-effective solution for obtaining accurate spectra of large molecular systems.

Efficient calculation of anharmonic vibrational spectra of large molecules with localized modes

The analysis and interpretation of the vibrational spectra of complex (bio)molecular systems, such as polypeptides and proteins, requires support from quantum-chemical calculations. Such calculations are currently restricted to the harmonic approximation. Here, we show how one of the main bottlenecks in such calculations, the evaluation of the potential energy surface, can be overcome by using localized modes instead of the commonly employed normal modes. We apply such local vibrational self-consistent field (L-VSCF) and vibrational configuration interaction (L-VCI) calculations to a cyclic water tetramer and a helical hexa-alanine peptide. The results show that the use of localized modes is equivalent to the commonly used normal modes, but offers several advantages. First, a faster convergence with respect to the excitation level is observed in L-VCI calculations. Second, the localized modes provide a reduced representation of the couplings between modes that show a regular coupling pattern. This can be used to disregard a significant number of small two-mode potentials a priori. Several such reduced coupling approximations are explored, and we show that the number of single-point calculations required to evaluate the potential energy surface can be significantly reduced without introducing noticeable errors in the resulting vibrational spectra.

Theoretical determination of the infrared spectra of amorphous polymers

The simple procedure of calculating the infrared spectra of polymers is presented. It is based on selecting the relevant, medium-size representative fragments of a polymer, for which the vibrational frequencies are computed within the harmonic approximation, in conjunction with the multiparameter scaling techniques. Scaling is necessary to predict the reliable fundamentals, which, along with the calculated intensities and properly chosen band widths, reproduce the observed band shapes with high accuracy. Applications to the three polymers: poly(methyl methacrylate), poly(vinyl acetate), and poly(isopropenyl acetate) are presented. The simulated spectra are in good agreement with the experiment. The assignment of bands is reported. The obtained results indicate strong delocalization of the vibrational modes within polymers, which is in accord with the most recent experimental finding [Macromolecules2008, 41, 2494-2501]. Good agreement between the observed and the calculated spectra of deuterated PMMA confirms the correctness of our approach. The preliminary results obtained for the highly irregular macromolecular compound (vinyl-functionalized silica) are also shown.

Vibrational averaging of the chemical shift in crystalline α-glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.