Amide I vibrational circular dichroism of polypeptides: Generalized fragmentation approximation method

Forbidden Secondary Structures Found in Gel-Forming Fibrils of Glycylphenylalanylglycine

The zwitterionic l-tripeptide glycylphenylalanylglycine self-assembles into very long crystalline fibrils in an aqueous solution, which causes the formation of an exceptionally strong gel phase (G' ∼ 5 × 10⁶ Pa). The Rietveld refinement analysis of its powder X-ray diffraction (PXRD) pattern reveals a unit cell with four peptides forming a P2₁2₁2₁ space group and adopting an inverse polyproline II conformation, that is, a right-handed helical structure that occupies the "forbidden" region of the Ramachandran plot. This unusual structure is stabilized by a plethora of intermolecular interactions facilitated by the large number of different functional groups of the unblocked tripeptide. Comparisons of simulated and experimental Fourier transform infrared and vibrational circular dichroism (VCD) amide I' profiles corroborate the PXRD structure. Our experimental setup reduces the sample to a quasi-two-dimensional network of fibrils. We exploited the influence of this reduced dimensionality on the amide I VCD to identify the main fibril axis. We demonstrate that PXRD, vibrational spectroscopy, and amide I simulations provide a powerful toolset for secondary structure and fibril axis determination.

Exploring machine learning methods for absolute configuration determination with vibrational circular dichroism

The added value of supervised Machine Learning (ML) methods to determine the Absolute Configuration (AC) of compounds from their Vibrational Circular Dichroism (VCD) spectra was explored. Among all ML methods considered, Random Forest (RF) and Feedforward Neural Network (FNN) yield the best performance for identification of the AC. At its best, FNN allows near-perfect AC determination, with accuracy of prediction up to 0.995, while RF combines good predictive accuracy (up to 0.940) with the ability to identify the spectral areas important for the identification of the AC. No loss in performance of either model is observed as long as the spectral sampling interval used does not exceed the spectral bandwidth. Increasing the sampling interval proves to be the best method to lower the dimensionality of the input data, thereby decreasing the computational cost associated with the training of the models.

Membrane-dependent amyloid aggregation of human BAX α9 (173-192)

Mitochondrial outer membrane permeabilization, which is a critical step in apoptosis, is initiated upon transmembrane insertion of the C-terminal α-helix (α9) of the proapoptotic Bcl-2 family protein BAX. The isolated α9 fragment (residues 173-192) is also competent to disrupt model membranes, and the structures of its membrane-associated oligomers are of interest in understanding the potential roles of this sequence in apoptosis. Here, we used ultrafast two-dimensional infrared (2D IR) spectroscopy, thioflavin T binding, and transmission electron microscopy to show that the synthetic BAX α9 peptide (α9p) forms amyloid aggregates in aqueous environments and on the surfaces of anionic small unilamellar vesicles. Its inherent amyloidogenicity was predicted by sequence analysis, and 2D IR spectra reveal that vesicles modulate the β-sheet structures of insoluble aggregates, motivating further examination of the formation or suppression of BAX amyloids in apoptosis.

Analysis of Vibrational Circular Dichroism Spectra of Peptides: A Generalized Coupled Oscillator Approach of a Small Peptide Model Using VCDtools

Vibrational circular dichroism (VCD) is one of the major spectroscopic tools to study peptides. Nevertheless, a full understanding of what determines the signs and intensities of VCD bands of these compounds in the amide I and amide II spectral regions is still far from complete. In the present work, we study the origin of these VCD signals using the general coupled oscillator (GCO) analysis, a novel approach that has recently been developed. We apply this approach to the ForValNHMe model peptide in both α-helix and β-sheet configurations. We show that the intense VCD signals observed in the amide I and amide II spectral regions essentially have the same underlying mechanism, namely, the through-space coupling of electric dipoles. The crucial role played by intramolecular hydrogen bonds in determining VCD intensities is also illustrated. Moreover, we find that the contributions to the rotational strengths, considered to be insignificant in standard VCD models, may have sizable magnitudes and can thus not always be neglected. In addition, the VCD robustness of the amide I and II modes has been investigated by monitoring the variation of the rotational strength and its contributing terms during linear transit scans and by performing calculations with different computational parameters. From these studies-and in particular, the decomposition of the rotational strength made possible by the GCO analysis-it becomes clear that one should be cautious when employing measures of robustness as proposed previously.

Revisiting an old concept: the coupled oscillator model for VCD. Part 1: the generalised coupled oscillator mechanism and its intrinsic connection to the strength of VCD signals

This work reports the development of a generalised coupled oscillator expression for VCD that is exact within the harmonic approximation and is applicable to all types of normal modes, regardless whether the considered molecule is symmetric or asymmetric.

Simulation of the amide I absorption of stacked β-sheets

Aggregated β-sheet structures are associated with amyloid and prion diseases. Techniques capable of revealing detailed structural and dynamical information on β-sheet structure are thus of great biomedical and biophysical interest. In this work, the infrared (IR) amide I spectral characteristics of stacked β-sheets were modeled using the transition dipole coupling model. For a test set of β-sheet stacks, the simulated amide I spectrum was analyzed with respect to the following parameters; intersheet distance, relative rotation of the sheets with respect to each other and the effect of number of sheets stacked. The amide I maximum shifts about 5 cm(-1) to higher wavenumbers when the intersheet distance between two identical β-sheets decreases from 20 to 5 Å. Rotation around the normal of one of the sheets relative to the other results in maximum intersheet coupling near 0° and 180°. Upon of rotation from 0° to 90° at an intersheet distance of 9 Å, the amide I maximum shifts about 3 cm(-1). Tilting of one of the sheets by 30° from the normal results in a shift of the amide I maximum by less than 1 cm(-1). When stacking several β-sheets along the normal, the amide I maximum shifts to higher wavenumbers with increasing stack size. The amide I maximum shifts about 6 cm(-1) when stacking four sheets with an intersheet distance of 9 Å. The study provides an aid in the interpretation of the IR amide I region for experiments involving β-sheets and creates awareness of the many effects that determine the spectrum of β-sheet structures.

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.

Computational vibrational spectroscopy of peptides and proteins in one and two dimensions

Vibrational spectroscopy provides direct information on molecular environment and motions but, its interpretation is often hampered by band broadening. Over the past decade, two-dimensional (2D) vibrational spectroscopy has emerged as a promising technique to overcome a number of difficulties associated with linear spectroscopy and provided significantly detailed information on the structure and dynamics of complex molecules in condensed phases. This Account reviews recently developed computational methods used to simulate 1D and 2D vibrational spectra. The central quantity to calculate in computational spectroscopy is the spectroscopic response function, which is the product of many contributing factors such as vibrational transition energies, transition moments, and their modulations by fluctuating local environment around a solute. Accurate calculations of such linear and nonlinear responses thus require a concerted effort employing a wide range of methods including electronic structure calculation (ESC) and molecular dynamics (MD) simulation. The electronic structure calculation can provide fundamental quantities such as normal-mode frequencies and transition multipole strengths. However, since the treatable system size is limited with this method, classical MD simulation has also been used to account for the dynamics of the solvent environment. To achieve chemical accuracy, these two results are combined to generate time series of fluctuating transition frequencies and transition moments with the distributed multipole analysis, and this particular approach has been known as the hybrid ESC/MD method. For coupled multichromophore systems, vibrational properties of each chromophore such as a peptide are individually calculated by electronic structure methods and the Hessian matrix reconstruction scheme was used to obtain local mode frequencies and couplings of constituting anharmonic oscillators. The spectra thus obtained, especially for biomolecules including polypeptides and proteins, have proven to be reliable and in good agreement with experimental spectra. An alternative to the hybrid method has also been developed, where the classical limit of the vibrational response function was considered. Its main attraction is the capability to obtain the spectra directly from a set of MD trajectories. A novel development along this direction has been achieved by using quantum mechanical/molecular mechanical (QM/MM) force fields for the accurate description of vibrational anharmonicity and chromophore polarization effects. The latter aspects are critical in the 2D case because classical force fields employing harmonic intramolecular potential cannot produce reliable 2D signal. We anticipate that the computational methods presented here will continue to evolve along with experimental advancements and will be of use to further elucidate ultrafast dynamics of chemical and biological systems.

Comparison of vibrational circular dichroism instruments: development of a new dispersive VCD

A dispersive vibrational circular dichroism (VCD) instrument has been designed and optimized for the measurement of mid-infrared (MIR) bands such as the amide I and amide II vibrational modes of peptides and proteins. The major design considerations were to construct a compact VCD instrument for biological molecules, to increase signal-to-noise (S/N) ratio, to simultaneously collect and digitize the sample transmission and polarization modulation signals, and to digitally ratio them to yield a VCD spectrum. These were realized by assembling new components using design factors adapted from previous VCD instruments. A collection of spectra for peptides and proteins having different dominant secondary structures (alpha-helix, beta-sheet, and random coil) measured for identical samples under the same conditions showed that the new instrument had substantially improved S/N as compared with our previous dispersive VCD instrument. These instruments both provide protein VCD for the amide I that are comparable to or somewhat better than those measurable with commercial Fourier transform (FT) VCD instruments if just the amide I band in the spectra is obtained at modest resolution (8 cm(-1)) with the same total data collection time on each type of instrument.

Amide I Raman optical activity of polypeptides: fragment approximation

Vibrational optical activity (VOA) is an important property used to determine the absolute configuration of a chiral molecule in condensed phases. In particular, vibrational circular dichroism and Raman optical activity (ROA) are two representative VOA measurement techniques that have been extensively used to study structures and dynamics of biomolecules. Recently, the amide I vibrational circular dichroism of polypeptides was theoretically described by using fragment approximation methods, which are based on the assumption that amide I VOA can be described as a linear combination of those of constituent fragment peptide units. Here, we develop a fragment approximation theory applicable to numerical simulations of Raman and Raman optical activity spectra for the amide I vibrations in polypeptides. For an alanine dipeptide and pentapeptide analogs, we carried out density functional theory calculations of polarizability, magnetic dipole-, and electric quadrupole-ROA tensors. Numerically simulated spectra using the fragment approximation are directly compared to density functional theory results. Furthermore, the simulated ROA spectra of alanine-based right-handed alpha-helix and polyproline II polypeptides are directly compared to the previously reported experimental results. The agreements were found to be excellent, which suggests that the fragment approximation method developed for the numerical simulation of ROA spectrum of polypeptide in solution is valid and useful.

Vibrational-exciton couplings for the amide I, II, III, and A modes of peptides

The couplings between all amide fundamentals and their overtones and combination vibrational states are calculated. Combined with the level energies reported previously (Hayashi, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. A 2005, 109, 9747), we obtain a complete effective vibrational Hamiltonian for the entire amide system. Couplings between neighboring peptide units are obtained using the anharmonic vibrational Hamiltonian of glycine dipeptide (GLDP) at the BPW91/6-31G(d,p) level. Electrostatic couplings between non-neighboring units are calculated by the fourth rank transition multipole coupling (TMC) expansion, including 1/R3 (dipole-dipole), 1/R4 (quadrupole-dipole), and 1/R5 (quadrupole-quadrupole and octapole-dipole) interactions. Exciton delocalization length and its variation with frequency in the various amide bands are calculated. The simulated infrared amide I and II absorptions and CD spectra of 24 residue alpha-helical motifs (SPE3) are in good agreement with experiment.

Quadrupole contribution to the third-order optical activity spectroscopy

Time-resolved nonlinear optical activity measurement spectroscopy can be a useful tool for studying biomolecular and chemical reaction dynamics of chiral molecules. Only recently, the two-dimensional (2D) circularly polarized photon echo (CP-PE) spectroscopy of polypeptides and a photosynthetic light-harvesting complex were discussed, where the beam configuration was specifically controlled in such a way to eliminate the quadrupole contribution to the CP-PE signal. In this paper, we generalize the CP-PE spectroscopy by including the transition quadrupole contributions from peptide amide I vibrational transition and chlorophyll electronic transition. By using a density functional theory calculation method, the corresponding amide I vibrational and chlorophyll Q(y) electronic transition quadrupole tensor elements are determined. Amplitude of nonlinear optical transition pathway involving a quadrupole transition is found to be comparable to those of magnetic dipole terms for two different cases considered, i.e., dipeptides and photosynthetic antenna complex. However, due to the rotational averaging factors, the overall quadrupole contribution is an order of magnitude smaller than the magnetic dipole contribution. This suggests that the conventional 2D photon echo method and experimental scheme can be directly used to measure the 2D CP-PE signal from proteins and molecular complexes and that the 2D CP-PE signal is mainly dictated by the magnetic dipole contribution.

Phosphorylation effect on the GSSS peptide conformation in water: Infrared, vibrational circular dichroism, and circular dichroism experiments and comparisons with molecular dynamics simulations

The phosphorylation effect on the small peptide conformation in water has not been clearly understood yet, despite the widely acknowledged notion that control of protein activity by phosphorylation works mainly by inducing conformational change. To elucidate the detailed mechanism, we performed infrared (IR) absorption and vibrational and electronic circular dichroism studies of both unphosphorylated and phosphorylated tetrapeptides, GSSS 1 and GSSpS 2. The solution structure of the tetrapeptide is found to be little dependent on the presence of the neutral or negatively charged phosphoryl group, and to be a mixture of extended structures including polyproline II (PII) and beta-sheet conformations. The additional band at 1598 cm(-1) in the amide I IR spectrum of the phosphorylated peptide GSSpS at neutral pD appears to be clear spectroscopic evidence for direct intramolecular hydrogen-bonding interaction between the side chain dianionic phosphoryl group and the backbone amide proton. On the basis of amide I IR band analyses, the authors found that the probability of finding the phosphoryl group strongly H bonded to the backbone proton in GSSpS is about 43% at pD 7.0 and 37 degrees C. Such a H-bonding interaction in GSSpS has the biological standard enthalpy and entropy of -15.1 kJ/mol and -51.2 J/K mol, respectively. Comparisons between the experimentally measured IR and VCD spectra and the numerically simulated ones suggested that the currently available force field parameters need to be properly modified. The results in this paper may shed light on an unknown mechanism of controlling the peptide conformation by phosphorylation.

Two-Dimensional Circularly Polarized IR Photon Echo Spectroscopy of Polypeptides: Four-Wave-Mixing Optical Activity Measurement

A coherent two-dimensional (2D) optical spectroscopy utilizing circularly polarized (CP) beams, which was shown to be useful in studying molecular chirality in condensed phases, was theoretically proposed recently [Cho et al. J. Chem. Phys. 2003, 119, 7003]. A photon echo (PE) version of 2D optical activity spectroscopy is discussed in this paper. Considering various dipeptide and polypeptide systems, where the amide I local modes constitute the set of basis modes used to describe exciton and biexciton states as linear combinations of those basis modes, we present numerically simulated 2D circularly polarized IR PE spectra. It is shown that this novel spectroscopic method can provide additional information on the angles between the transition magnetic dipole and the transition electric dipole of two different vibrationally excited states, which are highly sensitive to the 3D structure and chirality of a given polypeptide. Also, a hierarchical relation of IR absorption, vibrational circular dichroism, 2D IR PE, and 2D CP-IR PE is discussed to show advantages of 2D optical activity spectroscopy in general.

Computational spectroscopy of ubiquitin: Comparison between theory and experiments

Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution.

Thermal Denaturation of Polyalanine Peptide in Water by Molecular Dynamics Simulations and Theoretical Prediction of Infrared Spectra: Helix−Coil Transition Kinetics

Perspectives in the helix-coil transition kinetics of secondary structures are examined by temperature-jump molecular dynamics (T-jump MD) simulations and theoretically calculated infrared (IR) spectra. Homopolymeric polyalanine, Ac-(A)(21)-NHMe (A21), is unfolded in water by T-jumps from 273 to 300 K approximately 450 K using AMBER ff99 and ff03 force fields. MD simulation results provide in silico evidence that 3(10)-helix and type I beta-turn motifs are highly probable in both ff99 and ff03 results. Temperature-dependent difference IR spectra of A21 do not possess an isosbestic point in both results, and isotope-labeled difference IR spectra in ff03 results predict characteristic profiles observed in experiments. Unfolding rates obtained from simulated time-resoled IR spectra are in good agreement with those estimated by helical contents, but they are still an order of magnitude smaller than experimental values. We demonstrate that the conventional criteria such as single-exponential fit of transient amide I absorbance, sigmoidal fit of temperature-dependent amide I absorbance, and Arrhenius plot of relaxation rates cannot guarantee the validity of assuming a two-state mechanism. We suggest a way of determining T(m) by the temperature dependence of center frequency and full width at half-maximum of amide I band. Overall, both ff99 and ff03 force fields give consistent results in reproducing key aspects concerned experimentally, but are not predominantly satisfactory in quantitative aspects.

Explicit factorization of external coordinates in constrained statistical mechanics models

If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass-metric tensors. In this work, the authors explicitly write the determinant of the mass-metric tensor G and of the reduced mass-metric tensor g, for any molecule, general internal coordinates and arbitrary constraints, as a product of two functions; one depending only on the external coordinates that describe the overall translation and rotation of the system, and the other only on the internal coordinates. This work extends previous results in the literature, proving with full generality that one may integrate out the external coordinates and perform Monte Carlo simulations in the internal conformational space of macromolecules.

Vibrational spectroscopic characteristics of secondary structure polypeptides in liquid water: Constrained MD simulation studies

Using the constrained MD simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, we established a computational scheme for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and 2D IR photon echo spectra of peptides in solution. Six different secondary structure peptides, i.e., alpha-helix, 3(10)-helix, pi-helix, antiparallel and parallel beta-sheets, and polyproline II (P(II)), are considered, and the vibrational characteristic features in their linear and nonlinear spectra in the amide I band region are discussed. Isotope-labeling effects on IR and VCD spectra are notable only for alpha- and pi-helical peptides due to the strong vibrational couplings between two nearest neighboring amide I local oscillators. The amplitudes of difference 2D IR spectra are shown to be strongly dependent on both the extent of mode delocalization and the relative orientation of local mode transition dipoles determined by secondary structure.

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

Infrared absorption and vibrational circular dichroism (IR and VCD) spectra of model fragments of TrpZip-style beta-hairpin structures are simulated using density functional theory (DFT) methods to estimate the influence of fragment size, end effects, conformational irregularities, peptide side chains, and solvent. Different fragmentation schemes, computing the strands and turn segments separately, were tested by varying the sizes of each and their respective overlaps. For suitably overlapping fragments, atomic property tensors were found to be reliably transferable, as tested by their ability to generate simulated spectra in good agreement with results from ab initio DFT computations for the entire peptide. This fragment approach significantly reduces computational times and opens up a wider range of systems that can be studied with a DFT-based approach as compared to previous methods based on uniform repeating sequences. However, vacuum calculations do not adequately represent the frequency dispersion of solvated molecules, and thus, some alternate strategies for solvation correction are explored for improving the simulation accuracy. Unlike for regular periodic secondary structure, the solvent significantly impacts the spectral shapes of hairpins, due to the different degrees of hydration of individual amide groups, which can be exposed to or shielded from water due to external vs internal hydrogen bonding. This is amplified by the shielding of selected amides from the solvent due to bulky side chains. The peptide plus solvent was structurally modeled with molecular dynamics methods, and then an electrostatic field-based parametrization correction was added to the force field and intensity tensors to compensate for the solvent dipolar field. The effect of the shielding and subsequent reordering of modes has a larger impact on VCD than IR band shapes.