Vibrational Spectral Simulation for Peptides of Mixed Secondary Structure: Method Comparisons with the Trpzip Model Hairpin

An Improved Diabatization Scheme for Computing the Electronic Circular Dichroism of Proteins

We advance the quality of first-principles calculations of protein electronic circular dichroism (CD) through an amelioration of a key deficiency of a previous procedure that involved diabatization of electronic states on the amide chromophore (to obtain interamide couplings) in a β-strand conformation of a diamide. This yields substantially improved calculated far-ultraviolet (far-UV) electronic circular dichroism (CD) spectra for β-sheet conformations. The interamide couplings from the diabatization procedure for 13 secondary structural elements (13 diamide structures) are applied to compute the CD spectra for seven example proteins: myoglobin (α helix), jacalin (β strand), concanavalin A (β type I), elastase (β type II), papain (α + β), 310-helix bundle (310-helix) and snow flea antifreeze protein (polyproline). In all cases, except concanavalin A and papain, the CD spectra computed using the interamide couplings from the diabatization procedure yield improved agreement with experiment with respect to previous first-principles calculations.

Determining the nanostructure and main axis of gly-his-gly fibrils using the amide I' bands in FTIR, VCD, and Raman spectra

The zwitterionic tripeptide glycyl-histidine-glycine (GHG) has been shown to self-assemble into visible crystalline fibrils that form a gel-supporting network with a very high storage modulus. Here we elaborate on the theory and experimental setup behind our novel approach employed to determining the main fibril axis for these gel-forming fibrils by simulating the amide I band profile for infrared absorption (IR), vibrational circular dichroism (VCD), and visible Raman scattering. We also highlight that combining these three vibrational spectroscopies can help in validating structures that are solved using powder x-ray diffraction analysis (PXRD). The PXRD analysis yielded a GHG fibril unit cell with P21 symmetry containing two peptide monomers and two water molecules. The monomers adopt a conformation reminiscent of the distorted polyproline II conformation obtained for tri-lysine in aqueous solution. Stabilization occurs primarily through peptide-peptide intermolecular hydrogen bond interactions, while the role of water in peptide hydration is minimal. The comparison of simulated and experimental amide I' band profiles suggests that the xz plane of the crystal unit cell is being predominantly probed in the experimental IR and VCD spectra, with the x axis of the unit cell pointing in the direction of the main fibril axis. The monomer peptide in the unit cell interacts with six adjacent peptides forming hydrophobic channels by edge-to-face and parallel-displaced ππstacking in the y direction. These cores are further stabilized by a plethora of intermolecular interactions in the x and z directions. Our result suggests that the hydrophobic xz-surfaces would be a good target for the adsorption of hydrophobic drugs.

Electromagnetic bioeffects: a multiscale molecular simulation perspective

Electromagnetic bioeffects remain an enigma from both the experimental and theoretical perspectives despite the ubiquitous presence of related technologies in contemporary life. Multiscale computational modelling can provide valuable insights into biochemical systems and predict how they will be perturbed by external stimuli. At a microscopic level, it can be used to determine what (sub)molecular scale reactions various stimuli might induce; at a macroscopic level, it can be used to examine how these changes affect dynamic behaviour of essential molecules within the crowded biomolecular milieu in living tissues. In this review, we summarise and evaluate recent computational studies that examined the impact of externally applied electric and electromagnetic fields on biologically relevant molecular systems. First, we briefly outline the various methodological approaches that have been employed to study static and oscillating field effects across different time and length scales. The practical value of such modelling is then illustrated through representative case-studies that showcase the diverse effects of electric and electromagnetic field on the main physiological solvent - water, and the essential biomolecules - DNA, proteins, lipids, as well as some novel biomedically relevant nanomaterials. The implications and relevance of the theoretical multiscale modelling to practical applications in therapeutic medicine are also discussed. Finally, we summarise ongoing challenges and potential opportunities for theoretical modelling to advance the current understanding of electromagnetic bioeffects for their modulation and/or beneficial exploitation in biomedicine and industry.

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.

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.

Heterogeneity in the Folding of Villin Headpiece Subdomain HP36

Small single domain proteins that fold on the microsecond time scale have been the subject of intense interest as models for probing the complexity of folding energy landscapes. The villin headpiece subdomain (HP36) has been extensively studied because of its simple three helix structure, ultrafast folding lifetime of a few microseconds, and stable native fold. We have previously shown that folding as measured by a single ¹³C═¹⁸O isotopic label on residue A57 in helix 2 occurs at a different rate than that measured by global probes of folding, indicating noncooperative complexity in the folding of HP36. In order to determine whether this complexity reflects intermediates or parallel pathways over a small activation barrier, ¹³C═¹⁸O labels were individually incorporated at six different positions in HP36, including into all 3 helices. The equilibrium thermal unfolding transitions and the folding/unfolding dynamics were monitored using the unique IR signature of the ¹³C═¹⁸O label by temperature dependent FTIR and temperature jump IR spectroscopy, respectively. Equilibrium experiments reveal that the ¹³C═¹⁸O labels at different positions in HP36 show drastic differences in the midpoint of their transitions ( T_m), ranging from 45 to 67 °C. Heterogeneity is also observed in the relaxation kinetics; there are differences in the microsecond phase when different labeled positions are probed. At a final temperature of 45 °C, the relaxation rate for ¹³C═¹⁸O A57 is 2.4e + 05 s^-1 whereas for ¹³C═¹⁸O L69 HP36 the relaxation rate is 5.1e + 05 s^-1, two times faster. The observation of site-dependent midpoints for the equilibrium unfolding transitions and differences in the relaxation rates of the labeled positions enables us to probe the progressive accumulation of the folded structure, providing insight into the microscopic details of the folding mechanism.

Advances of Vibrational Circular Dichroism (VCD) in bioanalytical chemistry. A review

Vibrational Circular Dichroism (VCD) is a unique and relatively new spectroscopic technique that is capable of determining an absolute configuration of chiral molecules. VCD can be also used to determine structure of large macromolecules. This review highlights the most recent advances of VCD in bioanalytical chemistry. It shows that VCD is capable of unraveling supramolecular organization of peptides, proteins, saccharides, glycerophospholipids, polypeptide microcrystals, as well as amyloid fibrils and DNA. This review also demonstrates how VCD can be utilized to explore molecule-molecule interactions that determine mechanisms of chiral separations in chromatography. It aims to attract attention of scientists from all different research areas demonstrating the strength and capability of this very powerful spectroscopic technique.

Not All β-Sheets Are the Same: Amyloid Infrared Spectra, Transition Dipole Strengths, and Couplings Investigated by 2D IR Spectroscopy

We report the transition dipole strengths and frequencies of the amyloid β-sheet amide I mode for the aggregated proteins amyloid-β_1-40, calcitonin, α-synuclein, and glucagon. According to standard vibrational coupling models for proteins, the frequencies of canonical β-sheets are set by their size and structural and environmental disorder, which determines the delocalization length of the vibrational excitons. The larger the delocalization the lower the frequency of the main infrared-allowed transition, A_⊥. The models also predict an accompanying increase in transition dipole strength. For the proteins measured here, we find no correlation between transition dipole strengths and amyloid β-sheet transition frequency. To understand this observation, we have extracted from the protein data bank crystal structures of amyloid peptides from which we calculate the amide I vibrational couplings, and we use these in a model β-sheet Hamiltonian to simulate amyloid vibrational spectra. We find that the variations in amyloid β-sheet structures (e.g., dihedral angles, interstrand distances, and orientations) create significant differences in the average values for interstrand and nearest neighbor couplings, and that those variations encompass the variation in measured A_⊥ frequencies. We also find that off-diagonal disorder about the average values explains the range of transition dipole strengths observed experimentally. Thus, we conclude that the lack of correlation between transition dipole-strength and frequency is caused by variations in amyloid β-sheet structure. Taken together, these results indicate that the amide I frequency is very sensitive to amyloid β-sheet structure, the β-sheets of these 4 proteins are not identical, and the assumption that frequency of amyloids scales with β-sheet size cannot be adopted without an accompanying measurement of transition dipole strengths.

Use of vibrational spectroscopy to study 2-[4-(N-dodecanoylamino)phenyl]-5-(4-nitrophenyl)-1,3,4-oxadiazole: a combined theoretical and experimental approach

Quantum chemical calculations of geometric structure and vibrational wavenumbers of 2-[4-(N-dodecanoylamino)phenyl]-5-(4-nitrophenyl)-1,3,4-oxadiazole (AF51) were carried out by using density functional theory (DFT/B3LYP/6-311G(d,p) method. The fundamental vibrational modes were characterized depending on their potential energy distribution (PED). In order to predict the reactive sites for electrophilic and nucleophilic attacks of the title molecule, electrostatic potential surface has been plotted. The UV absorption spectrum was examined in chloroform solvent and compared with the calculated one in gas phase as well as in solvent environment using TD-DFT/ PCM approach. The (1)H NMR spectra was recorded. Comparison between the experimental and the theoretical results is satisfactory. The thermodynamic properties of the title compound at different temperatures have been calculated. A relationship between molecular structural features, non-linear responses and hyperpolarizability of AF51 has been established using vibrational spectra with emphasis on the role of intramolecular charge transfer mechanism in such organic NLO materials.

Deducing conformational variability of intrinsically disordered proteins from infrared spectroscopy with Bayesian statistics

As it remains practically impossible to generate ergodic ensembles for large intrinsically disordered proteins (IDP) with molecular dynamics (MD) simulations, it becomes critical to compare spectroscopic characteristics of the theoretically generated ensembles to corresponding measurements. We develop a Bayesian framework to infer the ensemble properties of an IDP using a combination of conformations generated by MD simulations and its measured infrared spectrum. We performed 100 different MD simulations totaling more than 10 µs to characterize the conformational ensemble of αsynuclein, a prototypical IDP, in water. These conformations are clustered based on solvent accessibility and helical content. We compute the amide-I band for these clusters and predict the thermodynamic weights of each cluster given the measured amide-I band. Bayesian analysis produces a reproducible and non-redundant set of thermodynamic weights for each cluster, which can then be used to calculate the ensemble properties. In a rigorous validation, these weights reproduce measured chemical shifts.

CH Stretching Region: Computational Modeling of Vibrational Optical Activity

Most organic compounds provide vibrational spectra within the CH stretching region, yet the signal is difficult to interpret because of multiple difficulties in experiment and modeling. To better understand various factors involved, the ability of several harmonic and anharmonic computational approaches to describe these vibrations was explored for α-pinene, fenchone, and camphor as test compounds. Raman, Raman optical activity (ROA), infrared absorption (IR), and vibrational circular dichroism (VCD) spectra were measured and compared to quantum chemical computations. Surprisingly, the harmonic vibrational approach reasonably well reproduced the measured spectral patterns, including the vibrational optical activity (VOA). The CH stretching, however, appeared to be more sensitive to the basis set and solvent variations than lower-frequency vibrations. For a higher accuracy in frequencies and spectral shapes, anharmonic corrections were necessary. Accurate harmonic and anharmonic force fields were obtained with the mPW2PLYP double-hybrid functional. A limited vibrational configuration interaction (LVCI) where the CH stretching motion was decoupled from other vibrations provided the best simulated spectra. A balanced harmonic oscillator basis set had to be used, containing also states indirectly interacting with fundamental vibrations. A simpler second-order perturbational approach (PT2) appeared less useful. The modeling provided unprecedented agreement with experimental vibrational frequencies; spectral shapes were reproduced less faithfully. The possibility of ab initio interpretation of the CH spectral region for relatively large molecules further broadens the application span of vibrational spectroscopy.

QM and QM/MM simulations of proteins

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

Three types of induced tryptophan optical activity compared in model dipeptides: theory and experiment

The tryptophan (Trp) aromatic residue in chiral matrices often exhibits a large optical activity and thus provides valuable structural information. However, it can also obscure spectral contributions from other peptide parts. To better understand the induced chirality, electronic circular dichroism (ECD), vibrational circular dichroism (VCD), and Raman optical activity (ROA) spectra of Trp-containing cyclic dipeptides c-(Trp-X) (where X = Gly, Ala, Trp, Leu, nLeu, and Pro) are analyzed on the basis of experimental spectra and density functional theory (DFT) computations. The results provide valuable insight into the molecular conformational and spectroscopic behavior of Trp. Whereas the ECD is dominated by Trp π-π* transitions, VCD is dominated by the amide modes, well separated from minor Trp contributions. The ROA signal is the most complex. However, an ROA marker band at 1554 cm(-1) indicates the local χ(2) angle value in this residue, in accordance with previous theoretical predictions. The spectra and computations also indicate that the peptide ring is nonplanar, with a shallow potential so that the nonplanarity is primarily induced by the side chains. Dispersion-corrected DFT calculations provide better results than plain DFT, but comparison with experiment suggests that they overestimate the stability of the folded conformers. Molecular dynamics simulations and NMR results also confirm a limited accuracy of the dispersion-DFT model in nonaqueous solvents. Combination of chiral spectroscopies with theoretical analysis thus significantly enhances the information that can be obtained from the induced chirality of the Trp aromatic residue.

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.

Structure analysis of unfolded peptides I: vibrational circular dichroism spectroscopy

Vibrational circular dichroism (VCD) spectroscopy is an invaluable spectroscopic techniques utilized to exploit the optical strength of vibrational transitions for structure analysis. In this chapter, we describe the protocol for measuring and self-consistently analyzing VCD and the corresponding FT-IR spectra of short peptides. This process involves the decomposition of the IR spectrum as well as simulations of the amide I band profiles in both spectra based on structural models of the peptides investigated. This type of spectral analysis should be complemented with similar investigations of Raman spectra, which are described in the subsequent chapter. The structural analysis of short, unfolded peptides described in this chapter can easily be extended for the analysis of longer unfolded peptides or even proteins. This is particularly important in view of the demonstrated biological relevance of intrinsically disordered peptides and proteins (IDPs).

Tryptophan residues: scarce in proteins but strong stabilizers of β-hairpin peptides

Tryptophan plays important roles in protein stability and recognition despite its scarcity in proteins. Except as fluorescent groups, they have been used rarely in peptide design. Nevertheless, Trp residues were crucial for the stability of some designed minimal proteins. In 2000, Trp-Trp pairs were shown to contribute more than any other hydrophobic interaction to the stability of β-hairpin peptides. Since then, Trp-Trp pairs have emerged as a paradigm for the design of stable β-hairpins, such as the Trpzip peptides. Here, we analyze the nature of the stabilizing capacity of Trp-Trp pairs by reviewing the β-hairpin peptides containing Trp-Trp pairs described up to now, the spectroscopic features and geometry of the Trp-Trp pairs, and their use as binding sites in β-hairpin peptides. To complete the overview, we briefly go through the other relevant β-hairpin stabilizing Trp-non-Trp interactions and illustrate the use of Trp in the design of short peptides adopting α-helical and mixed α/β motifs. This review is of interest in the field of rational design of proteins, peptides, peptidomimetics, and biomaterials.

Amide vibrations and their conformational dependences in β-peptide

The characteristics of the amide-A and amide-I modes in a β-homoalanine dipeptide (β-HADP) have been examined as a function of backbone dihedral angles. The harmonic frequencies were obtained using the density functional theory. The anharmonic frequencies and diagonal anharmonicities were obtained by using the Morse potential. Local-mode frequencies and intermode couplings were obtained using the computed normal-mode frequencies and eigenvectors. It was found that the vibrational frequencies for the two types of amide modes are both conformational-dependent. The inter-amide-A and inter-amide-I couplings in the β-peptides were predicted to be generally weaker than those in the α-peptides. Structural bases of the amide-A and amide-I local modes in the β-peptides are discussed.

VCD spectroscopic properties of the beta-hairpin forming miniprotein CLN025 in various solvents

Electronic and vibrational circular dichroism are often used to determine the secondary structure of proteins, because each secondary structure has a unique spectrum. Little is known about the vibrational circular dichroic spectroscopic features of the beta-hairpin. In this study, the VCD spectral features of a decapeptide, YYDPETGTWY (CLN025), which forms a stable beta-hairpin that is stabilized by intramolecular weakly polar interactions and hydrogen bonds were determined. Molecular dynamics simulations and ECD spectropolarimetry were used to confirm that CLN025 adopts a beta-hairpin in water, TFE, MeOH, and DMSO and to examine differences in the secondary structure, hydrogen bonds, and weakly polar interactions. CLN025 was synthesized by microwave-assisted solid phase peptide synthesis with N(alpha)-Fmoc protected amino acids. The VCD spectra displayed a (-,+,-) pattern with bands at 1640 to 1656 cm(-1), 1667 to 1687 cm(-1), and 1679 to 1686 cm(-1) formed by the overlap of a lower frequency negative couplet and a higher frequency positive couplet. A maximum IR absorbance was observed at 1647 to 1663 cm(-1) with component bands at 1630 cm(-1), 1646 cm(-1), 1658 cm(-1), and 1675 to 1680 cm(-1) that are indicative of the beta-sheet, random meander, either random meander or loop and turn, respectively. These results are similar to the results of others, who examined the VCD spectra of beta-hairpins formed by (D)Pro-Xxx turns and indicated that observed pattern is typical of beta-hairpins.

Structure of the alanine hydration shell as probed by NMR chemical shifts and indirect spin-spin coupling

The structure of the alanine hydration shell was modeled by Carr-Parinello molecular dynamics (CPMD) to explain subtle differences in NMR chemical shifts and indirect spin-spin coupling constants of the neutral (zwitterionic), cationic, and anionic forms of this amino acid. In comparison with classical molecular dynamics (MD), the quantum mechanical CPMD approach revealed a more structured solvent and significant differences in the radial and angular distributions of the water molecules around the solute. In particular, the solvent was predicted to be organized around the uncharged COOH and NH(2) residues to a similar degree as that for the charged ones. This was not the case with MD. For snapshot CPMD configurations, the NMR parameters were computed by density functional theory (DFT) and averaged. Obtained values were significantly closer to experimental parameters known for (15)N and (13)C isotopically labeled alanine than those calculated by the conventional implicit dielectric solvent model. The NMR results also quantitatively reflect a superiority of the CPMD over the MD explicit solvent treatment. A further improvement of the computed spin-spin coupling constants could be achieved by taking into account vibrational averaging beyond the harmonic approximation. Differently positioned water molecules in the clusters cause an unexpectedly large scattering of the NMR parameters. About 10-15 dynamics snapshots were required for a satisfactory convergence of the shifts and couplings. The NMR chemical shift was found to be much more sensitive to the molecular hydration than the coupling. The results thus indicate a large potential of the NMR spectroscopy and quantum simulations to probe not only the structure of molecules but also their interactions with the environment.