Improved Theoretical π−π* Absorption and Circular Dichroic Spectra of Helical Polypeptides Using New Polarizabilities of Atoms and NC‘O Chromophores

Optical absorption of single-layer hexagonal boron nitride in the ultraviolet

In this paper we theoretically describe the absorption of hexagonal boron nitride (hBN) single layer. We develop the necessary formalism and present an efficient method for solving the Wannier equation for excitons. We give predictions for the absorption of hBN on quartz and on graphite. We compare our predictions with recently published results (Elias et al 2019 Nat. Commun. 10 2639) for a monolayer of hBN on graphite. The spontaneous radiative lifetime of excitons in hBN is also computed. We argue that the optical properties of hBN in the ultraviolet are very useful for the study of peptides and other biomolecules.

Introducing DInaMo: A Package for Calculating Protein Circular Dichroism Using Classical Electromagnetic Theory

The dipole interaction model is a classical electromagnetic theory for calculating circular dichroism (CD) resulting from the π-π* transitions of amides. The theoretical model, pioneered by J. Applequist, is assembled into a package, DInaMo, written in Fortran allowing for treatment of proteins. DInaMo reads Protein Data Bank formatted files of structures generated by molecular mechanics or reconstructed secondary structures. Crystal structures cannot be used directly with DInaMo; they either need to be rebuilt with idealized bond angles and lengths, or they need to be energy minimized to adjust bond lengths and bond angles because it is common for crystal structure geometries to have slightly short bond lengths, and DInaMo is sensitive to this. DInaMo reduces all the amide chromophores to points with anisotropic polarizability and all nonchromophoric aliphatic atoms including hydrogens to points with isotropic polarizability; all other atoms are ignored. By determining the interactions among the chromophoric and nonchromophoric parts of the molecule using empirically derived polarizabilities, the rotational and dipole strengths are determined leading to the calculation of CD. Furthermore, ignoring hydrogens bound to methyl groups is initially explored and proves to be a good approximation. Theoretical calculations on 24 proteins agree with experiment showing bands with similar morphology and maxima.

Vibronic structure in the far-UV electronic circular dichroism spectra of proteins

The Franck–Condon effect is considered and the vibrational structure of the π_nbπ* transition of the peptide backbone is incorporated into matrix method calculations of the electronic circular dichroism (CD) spectra of proteins in the far-ultraviolet. We employ the state-averaged CASPT2 method to calculate the ground and π_nbπ* excited state geometries and frequencies of N-methylacetamide (NMA), which represents the peptide chromophore. The results of these calculations are used to incorporate vibronic levels of the excited states into the matrix method calculation. The CD spectra of a set of 49 proteins, comprising a range of structural types, are calculated to assess the influence of the vibrational structure. The calculated spectra of α-helical proteins are better resolved using the vibronic parameters and correlation between the experimental and the calculated intensity of less regular β structure proteins improves over most wavelengths in the far-UV. No obvious improvement is observed in the calculated spectra of regular β-sheet proteins. Our high-level ab initio calculations of the vibronic structure of the π_nbπ* transition in NMA have provided some further insight into the physical origins of the nature of protein CD spectra in the far-UV.

Conformational averaging in structural biology: issues, challenges and computational solutions

Most experimental methods in structural biology provide time- and ensemble-averaged signals and, consequently, molecular structures based on such signals often exhibit only idealized, average features. Second, most experimental signals are only indirectly related to real, molecular geometries, and solving a structure typically involves a complicated procedure, which may not always result in a unique solution. To what extent do such conformationally-averaged, non-linear experimental signals and structural models derived from them accurately represent the underlying microscopic reality? Are there some structural motifs that are actually artificially more likely to be "seen" in an experiment simply due to the averaging artifact? Finally, what are the practical consequences of ignoring the averaging effects when it comes to functional and mechanistic implications that we try to glean from experimentally-based structural models? In this review, we critically address the work that has been aimed at studying such questions. We summarize the details of experimental methods typically used in structural biology (most notably nuclear magnetic resonance, X-ray crystallography and different types of spectroscopy), discuss their individual susceptibility to conformational (motional) averaging, and review several theoretical approaches, most importantly molecular dynamics simulations that are increasingly being used to aid experimentalists in interpreting structural biology experiments.

Two Dimensional Electronic Correlation Spectroscopy of the npi* and pipi* Protein Backbone Transitions: A Simulation Study

The two dimensional (2D) photon echo spectrum of the amide ultraviolet (UV) bands of proteins are simulated. Two effective exciton Hamiltonian parameter sets developed by Woody and Hirst, which predict similar CD spectra, may be distinguished by their very different 2DUV spectra. These differences are enhanced in specific configurations of pulse polarizations which provide chirality-induced signals.

Circular and linear dichroism of proteins

Circular dichroism (CD) is an important technique in the structural characterisation of proteins, and especially for secondary structure determination. The CD of proteins can be calculated from first principles using the so-called matrix method, with an accuracy which is almost quantitative for helical proteins. Thus, for proteins of unknown structure, CD calculations and experimental data can be used in conjunction to aid structure analysis. Linear dichroism (LD) can be calculated using analogous methodology and has been used to establish the relative orientations of subunits in proteins and protein orientation in an environment such as a membrane. However, simple analysis of LD data is not possible, due to overlapping transitions. So coupling the calculations and experiment is an important strategy. In this paper, the use of LD for the determination of protein orientation and how these data can be interpreted with the aid of calculations, are discussed. We review methods for the calculation of CD spectra, focusing on semiempirical and ab initio parameter sets used in the matrix method. Lastly, a new web interface for online CD and LD calculation is presented.

Theoretical UV Circular Dichroism of Cyclo(l-Proline-l-Proline)

MP2, DFT, and molecular mechanics (AMBER, CVFF, and CFF91) geometry optimizations were performed on the cyclic dipeptide cyclo(L-Pro-L-Pro) starting from crystal structure data. Three stable conformations were identified as energy minima by all methods, but assignment of relative energy varied between the methods. The pi-pi transition feature of the UV circular dichroic (CD) spectrum was predicted for each minimized structure using the classical physics method of the dipole interaction model. The model was sensitive to the different conformations. The UV-CD predictions were compared individually and as a Boltzmann-weighted composite with published experimental CD spectra [Bowman, R. L.; Kellerman, M.; Johnson, W. C., Jr. Biopolymers 1983, 22, 1045]. For all structures, the original parameters of Applequist [Applequist, J. J. Chem. Phys. 1979, 71, 4324] with a bandwidth of 3000 cm(-1) most accurately replicated experiment, except for the CFF91 structures, which matched experiment best with a bandwidth of 4000 cm(-1). The inclusion of solvent by a continuum model did not significantly alter the minimized geometries obtained by molecular or quantum mechanics, but it did have an effect on the relative predicted energies of CFF91 and B3LYP conformations. The overall effect of solvent inclusion was negligible when Boltzmann-weighted spectra were considered. Gas-phase CFF91 structures were also reasonably good for prediction of CD spectra, and when water was included via a continuum model for energy calculations, the weighting scheme resembled that of the higher-level weightings. The CD calculated using the MP2/6-311G structures and energies for weighting were most descriptive of the 180 nm negative band in the experimental CD, but red-shifted the location of the 205 nm band. DFT structures were comparably, though not identically, as descriptive of the first pi-pi band, and did a better job with placement of the second (positive) pi-pi band. DFT calculations were less sensitive to basis set effect than the MP2 calculations, with 6-31G results in close agreement with 6-311G. The results suggest that it is possible to use geometries obtained from a variety of different methods (molecular mechanical or quantum mechanical) with the classical physics dipole interaction model to qualitatively reproduce the UV CD of model amides.

First-principles calculations of protein circular dichroism in the far-ultraviolet and beyond

Understanding the relationship between the amino acid sequence of a protein and its unique, compact three-dimensional structure is one of the grand challenges in molecular biophysics. One exciting approach to the protein-folding problem is fast time-resolved spectroscopy in the ultra-violet (UV). Time-resolved electronic circular dichroism (CD) spectroscopy offers resolution on a nanosecond (or faster) timescale, but does not provide the spatial resolution of techniques like X-ray crystallography or NMR. There is a need to underpin fast timescale spectroscopic studies of protein folding with a stronger theoretical foundation. We review some recent studies in this regard and briefly highlight how modern quantum chemical models of aromatic groups have improved the accuracy of calculations of protein CD spectra near-UV. On the other side of the far-UV, we describe calculations indicating that charge-transfer transitions are likely to be responsible for bands observed in the vacuum UV in protein CD.

Theoretical UV Circular Dichroism of Aliphatic Cyclic Dipeptides

Four cyclic dipeptides (piperazine-2,5-diones), cyclo(L-Pro-Gly), cyclo(L-Pro-L-Leu), cyclo(L-Ala-L-Ala), and cyclo(L-Pro-L-Ala), were modeled from crystal structure data. Conformations resulting from energy minimization using molecular mechanics were compared with traditional ab initio and density functional theory geometric optimizations for each dipeptide. In all computational cases, the gas phase was assumed. The pi-pi transition feature of the UV circular dichroic (CD) spectra was predicted for each peptide structure via the classical dipole interaction model. The dipole interaction model predicted CD spectra that qualitatively agreed with experiment when MP2 or DFT geometries were used. By coupling MP2 or DFT geometric optimizations with the classical physics method of the dipole interaction model, significantly better CD spectra were calculated than those using geometries obtained by molecular mechanics. Thus, one can couple quantum mechanical geometries with a classical physics model for calculation of circular dichroism.

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.

Heme-heme interactions in tetramers and dimers of hemoglobin subunits: DeVoe theory calculations

Detectable exciton couplets arising from heme-heme interactions in the hemoglobin (Hb) tetramers of HbO(2) and deoxyHb were predicted by DeVoe theory. This prediction was supported by the observation of an exciton couplet in the CD difference spectrum between the Hb tetramer and the alphabeta dimer of HbCO. In this paper, DeVoe theory is used to calculate the heme-heme interactions in the CO complex of the Hb tetramer (alpha(2)beta(2)) and dimer (alphabeta), the systems studied by Goldbeck et al. The couplet strength of the resulting theoretical CD difference spectrum agrees well with experiment, thus confirming that heme-heme interactions contribute significantly to the CD of HbCO. Given that the heme-heme distances in HbCO are 25 A and more, it is highly likely that heme-heme interactions also contribute significantly to the CD of other multi-heme proteins, e.g., cytochrome c(3), cytochrome oxidase, cytochrome bc(1), etc., where the hemes are in closer proximity.

Structural determinations by circular dichroism spectra analysis using coupled oscillator methods: An update of the applications of the DeVoe polarizability model

The exciton (coupled oscillator) model for optical activity is a very useful and powerful method which allows to analyze a circular dichroism (CD) spectrum in a nonempirical way, arriving at a safe assignment of the absolute configuration of organic and inorganic compounds. Usually in this model only the exciton coupling of two electrically allowed transitions (oscillators) is taken into account. This approach has the important advantage of an easy application but, sometimes, it may lead to wrong results. Thus, in this review article a more general treatment, which allows considering the simultaneous coupling of several oscillators, i.e., the DeVoe model, is presented and critically analyzed, discussing in detail the latest applications reported in the literature. In the authors opinion, since the DeVoe model joins generality and reliability requiring an almost negligible computational effort, it represents the method of choice for stereochemical assignments, even by nonspecialists.

Dipole interaction model predicted pi-pi* circular dichroism of cyclo(L-Pro)3 using structures created by semi-empirical, ab initio, and molecular mechanics methods

Cyclo(l-Pro)3 (CP3) is a synthetic peptide created to model cis and torsionally strained peptide bonds that also exhibits a strong distinctive UV circular dichroic (CD) spectrum. Circular dichroic spectra were computed for the amide pi-pi* transition using the dipole interaction model for various conformations of the peptide. Conformations of CP3 were created initially from crystal data, and followed by energy minimizations via molecular mechanics using the cvff force field; the effects of additional geometric optimizations by semi-empirical and ab initio quantum mechanics were investigated. The CD spectra for each conformation were calculated using a variety of different parameters, and each result was compared with the published experimental spectrum [Deber, C.M., Scatturin, A., Vaidya, V.M. & Blout, E.R. (1970) Small cyclic proline peptides: UV absorption and CD. In: Peptides: Chemistry and Biochemistry, Proceedings of the First American Peptide Symposium (Weinstein, B., ed.), Marcel Dekker, New York pp. 163-173]. Herein, two distinct conformations, a C3 symmetric and an asymmetric form, gave CD predictions that separately did not resemble the experimental spectrum. Energy differences were predicted at various theoretical levels, including MP2 and density functional theory. When the predicted CD spectra for each conformation were multiplied by Boltzmann weighting factors created using heats of formation determined by the AM1 optimizations, the weighted composite CD spectrum created did resemble experiment for the pi-pi* transition indicating that both conformations may exist simultaneously in solution.

Helix bundles and coiled coils in alpha-spectrin and tropomyosin: a theoretical CD study

The dipole interaction model is used to investigate the effects of interactions between helices and supertwisting of helices by determining whether the predicted UV absorption and CD spectra for the three-helix bundle and coiled coil are significantly different from spectra for the single straight alpha-helix. Crystallographic data by Yan et al. for alpha-spectrin are used to construct a three-helix bundle of poly(L-alanine) modeling the protein. Backbone torsion angles represented by Fourier series are used to generate supertwisted helices and coiled coil models of poly(L-alanine) that have pitch, radius, and residue repeat similar to experimental crystallographic data on tropomyosin. Calculated CD spectra are compared with available experimental data. Theoretical spectra for the three-helix bundle and the supertwisted structures are quite similar to predictions for the straight alpha-helix of the same length with similar torsion angles, suggesting that CD is primarily dependent on the average backbone conformation and would not be a sensitive tool for distinguishing between single straight helices and closely packed or twisted alpha-helices.