Timothy A. Keiderling

Transfer of molecular property tensors in cartesian coordinates: A new algorithm for simulation of vibrational spectra

A direct transfer of Cartesian molecular force fields (FF) and electric property tensors is tested on model systems and compared to transfer in internal coordinates with an aim to improve simulation of vibrational spectra for larger molecules. This Cartesian transformation can be implemented easily and offers greater flexibility in practical computations. It can be also applied for transfer of anharmonic derivatives. The results for model calculations of the force field and vibrational frequencies for N‐methylacetamide show that our method removes errors associated with numerical artifacts caused by nonlinearity of the otherwise required Cartesian to internal coordinate transformation. For determination of IR absorption and vibrational circular dichroism intensities, atomic polar and axial tensors were also transferred in the Cartesian representation. For the latter, which are dependent upon the magnetic dipole operator, a distributed origin gauge is used to avoid an origin dependence. Comparison of the results of transferring ab initio FF and intensity parameters from an amide dimer fragment onto a tripeptide with those from a conventionally determined tripeptide FF document some limitations of the transfer method and its possible applications in the vibrational spectroscopy. Finally, application to determination of the FF and spectra for helical heptapeptide are presented and compared to experimental results.

Empirical modeling of the peptide amide I band IR intensity in water solution

An empirical correction to amide group vacuum force fields is proposed in order to account for the influence of the aqueous environment on the C=O stretching vibration (amide I). The dependence of the vibrational absorption spectral intensities on the geometry is studied with density functional theory methods at the BPW91/6-31G** level for N-methyl acetamide interacting with a variety of of water molecule clusters hydrogen bonded to it. These cluster results are then generalized to form an empirical correction for the force field and dipole intensity of the amide I (C=O stretch) mode. As an example of its extension, the method is applied to a larger (β-turn model) peptide molecule and its IR spectrum is simulated. The method provides realistic bandwidths for the amide I bands if the spectra are generated from the ab initio force field corrected by perturbation from an ensemble of solvent geometries obtained using molecular dynamic simulations.

Protein and peptide secondary structure and conformational determination with vibrational circular dichroism

Vibrational circular dichroism (VCD) provides alternative views of protein and peptide conformation with advantages over electronic (UV) CD (ECD) or IR spectroscopy. VCD is sensitive to short-range order, allowing it to discriminate beta-sheet and various helices as well as disordered structure. Quantitative secondary structure analyses use protein VCD bandshapes, but are best combined with ECD and IR for balance. Much recent work has focused on empirical and theoretical VCD analyses of peptides, with detailed prediction of helix, sheet and hairpin spectra and site-specific application of isotopic substitution for structure and folding.

Vibrational Circular Dichroism

Abstract Since the first discovery by Biot and Pasteur that some molecules rotate the polarization of light, this optical activity has been recognized to be a consequence of molecular structure [1]. In fact, natural optical activity is one of the most structurally sensitive techniques available to the spectroscopist and, hence, has been extensively exploited. Most spectroscopic techniques evidence sensitivity to detailed molecular geometry only via perturbation of energy levels and selection rules. However, molecular optical activity comes about as the direct result of the geometrical arrangement and interaction of the atoms in a molecule [2]. In a somewhat oversimplified manner, the observable optical activity can be viewed to have a first-order dependence on the molecular asymmetry.

Effect of sodium dodecyl sulfate on folding and thermal stability of acid-denatured cytochrome c: a spectroscopic approach.

The molten globule (MG) state can be an intermediate in the protein folding pathway; thus, its detailed description can help understanding protein folding. Sodium dodecyl sulfate (SDS), an anionic surfactant that is commonly used to mimic hydrophobic binding environments such as cell membranes, is known to denature some native state proteins, including horse cytochrome c (cyt c). In this article, refolding of acid denatured cyt c is studied under the influence of SDS to form MG‐like states at both low concentration and above the critical micelle concentration using Fourier transform Infrared (FTIR) and ultraviolet and visible absorption as well as fluorescence and circular dichroism (CD). Thermal denaturation monitored with FTIR and CD shows distinct final high temperature states starting from MG‐like states formed with different SDS/protein ratios. The results suggest that the SDS/protein ratio as well as the actual SDS (or protein) concentration affects structure and its thermal stability. Thermal denaturation monitored with CD and FTIR for cyt c at neutral pH but denatured with SDS showed that at a high SDS/protein ratio, the thermal behavior of MG‐like states formed at low and neutral pH are quite similar. Based on the results obtained, the merits of two models of the protein–surfactant structure are discussed for different SDS concentrations.

Partial optimization of molecular geometry in normal coordinates and use as a tool for simulation of vibrational spectra

A normal mode coordinate-based molecular optimization algorithm was implemented and its performance tested against other optimization techniques. In certain cases the method was found to be computationally simpler and numerically more stable than the optimization algorithms based on Cartesian or internal valence coordinates. The usual redundant/internal coordinate scheme provided fastest convergence for compact covalently bonded molecules, while the normal mode method was found to be more suitable for more weakly bonded molecular complexes. For constrained optimizations use of the normal coordinates allows one to naturally separate the lower-energy modes from those more typically studied with vibrational spectroscopy. Thus, it provides an appropriate tool for simulations of IR and Raman spectra of larger molecules and complex systems when specific conformations are desired.

Geometry and Efficacy of Cross-Strand Trp/Trp, Trp/Tyr, and Tyr/Tyr Aromatic Interaction in a β-Hairpin Peptide

The Trpzip2 peptide (WTWENGKWTWK-NH(2)), designed by Cochran and co-workers, contains two pairs of Trps having cross-strand interaction and forms a stable antiparallel beta-hairpin. In order to study the geometries and effects on the structure and stability of different aromatic interactions, selected tryptophan residues were substituted with Tyr to get three Trpzip2 mutants with different Trp/Trp, Trp/Tyr, and Tyr/Tyr interacting pairs. Their native-state structures were determined using two-dimensional (2D) NMR and shown to have the same cross-strand edge-to-face Trp/Trp interaction as that in Trpzip2 for the Trp/Trp pair. The analogous Trp/Tyr and Tyr/Tyr pairs also tended to have an edge-to-face geometry. The effects of specific Trp/Trp, Trp/Tyr, and Tyr/Tyr interactions on hairpin stability were studied by varying temperature and monitoring structure with electronic circular dichroism (CD) and infrared (IR) absorption spectra. IR and CD temperature variations were fit to a two-state model that yielded lower T(m) values for Tyr containing mutants, indicating that Trp/Tyr and Tyr/Tyr interactions have less contribution to hairpin stability than the Trp/Trp interaction. Trp/Tyr interactions can provide significant stabilization, much greater than the Trp/aliphatic interaction, but Tyr/Tyr interactions are not as significant. Cross-strand interacting residues involving Trp with an edge-to-face orientation with Trp or Tyr had the strongest impact on hairpin stability.

A Solution to the Artifact Problem in Fourier Transform Vibrational Circular Dichroism

Using a newly constructed FT-IR vibrational circular dichroism (VCD) instrument, we have found that elimination of the ellipsoidal collection mirror before the detector and its replacement by a lens leads to a significant improvement in the absorption artifact problem seen previously in FT-IR/VCD. In the mid-IR region, we have been able to measure VCD of a single enantiomer for molecules such as α-pinene, 3-methylcyclohexanone, and dimethyltartrate. More importantly, this reduction in artifact level brings the FT-IR/VCD band shape of some particularly-difficult-to-measure bands, such as carbonyl stretches, into better agreement with those found in dispersive measurements. These results imply that the dispersive results are reliable, though of lower resolution than those obtained with the use of FT-IR/VCD.

Infrared, vibrational circular dichroism, and Raman spectral simulations for β-sheet structures with various isotopic labels, interstrand, and stacking arrangements using density functional theory.

Infrared (IR), Raman, and vibrational circular dichroism (VCD) spectral variations for different β-sheet structures were studied using simulations based on density functional theory (DFT) force field and intensity computations. The DFT vibrational parameters were obtained for β-sheet fragments containing nine-amides and constrained to a variety of conformations and strand arrangements. These were subsequently transferred onto corresponding larger β-sheet models, normally consisting of five strands with ten amides each, for spectral simulations. Further extension to fibril models composed of multiple stacked β-sheets was achieved by combining the transfer of DFT parameters for each sheet with dipole coupling methods for interactions between sheets. IR spectra of the amide I show different splitting patterns for parallel and antiparallel β-sheets, and their VCD, in the absence of intersheet stacking, have distinct sign variations. Isotopic labeling by (13)C of selected residues yields spectral shifts and intensity changes uniquely sensitive to relative alignment of strands (registry) for antiparallel sheets. Stacking of multiple planar sheets maintains the qualitative spectral character of the single sheet but evidences some reduction in the exciton splitting of the amide I mode. Rotating sheets with respect to each other leads to a significant VCD enhancement, whose sign pattern and intensity is dependent on the handedness and degree of rotation. For twisted β-sheets, a significant VCD enhancement is computed even for sheets stacked with either the same or opposite alignments and the inter-sheet rotation, depending on the sense, can either further increase or weaken the enhanced VCD intensity. In twisted, stacked structures (without rotation), similar VCD amide I patterns (positive couplets) are predicted for both parallel and antiparallel sheets, but different IR intensity distributions still enable their differentiation. Our simulation results prove useful for interpreting experimental vibrational spectra in terms of β-sheet and fibril structure, as illustrated in the accompanying paper.

Vibrational Circular Dichroism of Proteins in H2O Solution

Spectroscopic studies have historically been important for estimation of the average secondary structure of proteins. Vibrational circular dichroism (VCD) is a hybrid of the more established electronic CD and infrared spectroscopies that combines the advantages of both (relatively high spectral resolution in IR region with high conformational sensitivity of CD methods). 1 For proteins the most valuable transition to study has proven to be the amide I band (assigned primarily to the C=O stretching of the amide group). Due to interference by water absorption band, all aqueous-phase VCD studies of the amide I have been done in D2O solution (termed as the amide I’). But the extent of deuteration is a poorly controlled parameter which leads to an ambiguity in interpretation of the data.