Transition Dipole Coupling Model Research Articles

Transition dipole coupling modeling of optical activity enhancements in macromolecular protein systems.

The transition dipole coupling model allows to vary systematically many parameters, such as chromophore geometries and transition dipoles. We used it to explore conditions favorable to chirality enhancement observed in many experiments on protein amyloidal precipitates. Stacking of β-sheet planes has been identified as a particularly powerful mechanism of the enhancement.

Aggregates from perylene bisimide oligopeptides as a test case for giant vibrational circular dichroism.

Vibrational circular dichroism (VCD) spectroscopy has become an excellent tool to study biological nanostructures and biomimetic materials in their functional environment and is thus complementary to otherwise employed diffraction, imaging, and spectroscopy methods. However, it is still difficult to relate the observed exceptionally large VCD signals to specific structural elements. Here, we systematically studied the VCD signatures of structurally well-defined and thoroughly characterized nanofibrils from oligopeptide-substituted perylene bisimides that comprise single parallel β-sheets. These nanofibrils show a giant VCD signal in the absence of β-sheet stacking and a negative VCD couplet despite their right-handed helicity. The giant VCD signal was very sensitive to subtle changes in the molecular structure as well as (13)C-labeling, which caused a strong disruption of the exciton system as confirmed by two-dimensional infrared spectroscopy. Simulations based on the commonly applied transition dipole coupling model qualitatively reproduced the IR spectra but failed to account for the observed giant VCD or the strong isotope effect. Because our model system and isotope labeling imposes stringent structural constraints of the observed spectroscopic features, our results challenge current assumptions regarding the structural parameters determining VCD sign and intensity. The investigated system may, hence, serve as a benchmark for more sophisticated models with better predictive power for the investigation of protein aggregates in biomedical context or novel oligopeptide-based nanomaterials.

Determining In Situ Protein Conformation and Orientation from the Amide-I Sum-Frequency Generation Spectrum: Theory and Experiment

Vibrational sum-frequency generation (VSFG) spectra of the amide-I band of proteins can give detailed insight into biomolecular processes near membranes. However, interpreting these spectra in terms of the conformation and orientation of a protein can be difficult, especially in the case of complex proteins. Here we present a formalism to calculate the amide-I infrared (IR), Raman, and VSFG spectra based on the protein conformation and orientation distribution. Based on the protein conformation, we set up the amide-I exciton Hamiltonian for the backbone amide modes that generate the linear and nonlinear spectroscopic responses. In this Hamiltonian, we distinguish between nearest-neighbor and non-nearest-neighbor vibrational couplings. To determine nearest-neighbor couplings we use an ab initio 6-31G+(d) B3LYP-calculated map of the coupling as a function of the dihedral angles. The other couplings are estimated using the transition-dipole coupling model. The local-mode frequencies of hydrogen-bonded peptide bonds and of peptide bonds to proline residues are red-shifted. To obtain realistic hydrogen-bond shifts we perform a molecular dynamics simulation in which the protein is solvated by water. As a first application, we measure and calculate the amide-I IR, Raman, and VSFG spectra of cholera toxin B subunit docked to a model cell membrane. To deduce the orientation of the protein with respect to the membrane from the VSFG spectra, we compare the experimental and calculated spectral shapes of single-polarization results, rather than comparing the relative amplitudes of VSFG spectra recorded for different polarization conditions for infrared, visible, and sum-frequency light. We find that the intrinsic uncertainty in the interfacial refractive index--essential to determine the overall amplitude of the VSFG spectra--prohibits a meaningful comparison of the intensities of the different polarization combinations. In contrast, the spectral shape of most of the VSFG spectra is independent of the details of the interfacial refractive index and provides a reliable way of determining molecular interfacial orientation. Specifically, we find that the symmetry axis of the cholera toxin B subunit is oriented at an angle of 6° ± 17° relative to the surface normal of the lipid monolayer, in agreement with 5-fold binding between the toxin's five subunits and the receptor lipids in the membrane.

Excitonic splitting and vibronic coupling in 1,2-diphenoxyethane: Conformation-specific effects in the weak coupling limit

Vibrationally and rotationally resolved electronic spectra of 1,2-diphenoxyethane (C6H5-O-CH2-CH2-O-C6H5, DPOE) are reported for the isolated molecule under jet-cooled conditions. The spectra demonstrate that the two excited surfaces are within a few cm(-1) of one another over significant regions of the torsional potential energy surfaces that modulate the position and orientation of the two aromatic rings with respect to one another. Two-color resonant two-photon ionization (2C-R2PI) and laser-induced fluorescence excitation spectra were recorded in the near-ultraviolet in the region of the close-lying S0-S1 and S0-S2 states (36,400-36,750 cm(-1)). In previous work, double resonance spectroscopy in the ultraviolet and alkyl CH stretch regions of the infrared was used to identify and assign transitions to two conformational isomers differing primarily in the central C-C dihedral angle, a tgt conformation with C2 symmetry and a ttt conformation with C2h symmetry [E. G. Buchanan, E. L. Sibert, and T. S. Zwier, J. Phys. Chem. A 117, 2800 (2013)]. Comparison of 2C-R2PI spectra recorded in the m∕z 214 (all (12)C) and m∕z 215 (one (13)C) mass channels demonstrate the close proximity of the S1 and S2 excited states for both conformations, with an upper bound of 4 cm(-1) between them. High resolution spectra of the origin band of the tgt conformer reveal it to consist of two transitions at 36,422.91 and 36,423.93 cm(-1), with transition dipole moments perpendicular to one another. These are assigned to the S0-S1 and S0-S2 origin transitions with excited states of A and B symmetry, respectively, and an excitonic splitting of only 1.02 cm(-1). The excited state rotational constants and transition dipole coupling model directions prove that the electronic excitation is delocalized over the two rings. The ttt conformer has only one dipole-allowed electronic transition (Ag→Bu) giving rise to a pure b-type band at 36,508.77 cm(-1). Here, the asymmetry induced by a single (13)C atom in one of the rings is sufficient to localize the electronic excitation in one or the other ring. Dispersed fluorescence (DFL) spectra are used to provide assignments for all vibronic structure in the first 200 cm(-1)of both conformers. In the tgt conformer, both "a" and "b" symmetry fundamentals are observed, consistent with extensive vibronic coupling between the two dipole-allowed, nearly degenerate excited states. In the ttt conformer, the lowest frequency vibronic transition located 46 cm(-1) above the Bu origin is assigned to a bu fundamental (labeled R[overline]) built off the dipole-forbidden Ag state origin. The DFL spectrum of the Ag(R[overline](1)) level contains strong transitions to v(")(R[overline]) = 0, 1, and 2, seemingly at odds with vibronic coupling models. Studies of the DFL spectrum of this band as a function of distance from the nozzle reveal that much of the intensity in v(") = 1 arises from collisions of DPOE while in the excited state Ag(vb' = 1) level with He, producing Bu(R[overline] = 1) levels with large collision cross section. The remaining intensity in the fundamental at large x∕D is ascribed to emission from the (13)C isotopomer, for which this emission is dipole-allowed.

Theoretical Study of Raman Spectra of Methanol in Aqueous Solutions: Non-Coincident Effect of the CO Stretch

Raman spectra of the CO stretch for liquid methanol and its aqueous solutions were simulated using the combined electronic structure and molecular dynamics simulation method. The instantaneous vibrational frequencies were obtained from an empirical mapping to the electrostatic potentials, while vibrational couplings between different molecules were calculated using the transition dipole coupling model. It is found that noncoincident effects (NCEs) at high concentrations are dominated by the intermolecular couplings of CO stretch and decrease monotonically as the methanol concentration decreases. This behavior is explained as the effect of reduced methanol-methanol hydrogen bonding with the addition of water. A non-monotonic change of the NCEs defined by the peak position of the CO stretch as a function of methanol mole fraction is found, which is ascribed to band asymmetry caused by reorientational dynamics.

Excitonic effects in two-dimensional vibrational spectra of liquid formamide

The linear and two-dimensional infrared (2DIR) responses of the amide I vibrational mode in liquid formamide are investigated experimentally and theoretically using molecular dynamics simulations. The recent method based on the numerical integration of the Schrödinger equation is employed to calculate the 2DIR spectra. Special attention is devoted to the interplay of the structural dynamics and the excitonic nature of the amide I modes in determining the optical response of the studied system. In particular, combining experimental data, simulated spectra and analysis of the simulated atomic trajectory in terms of a transition dipole coupling model, we provide a convincing explanation of the peculiar features of the 2DIR spectra, which show a substantial increase of the antidiagonal bandwidth with increasing frequency. We point out that, at variance with liquid water, the 2DIR spectral profile of formamide is determined more by the excitonic nature of the vibrational states than by the fast structural dynamics responsible for the frequency fluctuations.

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.

Circular dichroism enhancement in large DNA aggregates simulated by a generalized oscillator model

An increased circular dichroism (CD) signal of large molecular aggregates formed upon DNA condensation was observed a long time ago, and is often referred to as psi-CD. The effort to understand this phenomenon is further motivated by the latest DNA packing studies and advances in macromolecular chemistry. In the present work, the transition dipole coupling model describing interactions of molecules with light has been extended to handle systems of arbitrary size. The analytical formulae obtained retain the simplicity and computational speed of the standard approach. The origin of the psi-effect was investigated on several model systems. The results suggest that the CD enhancement is primarily caused by delocalized phonon-like excitations in nucleic acid strands. The size of the system exhibiting the effect thus does not need to be comparable with or greater than the wavelength of the absorbed light. Small structural irregularities still allow for the enhancement while a larger disorder breaks it. The modeling is consistent with previous experimental electronic and vibrational CD studies, and makes it possible to correlate the enhancement with the geometry of the nucleic acid systems.

The origin of vibrational mode couplings in various secondary structural motifs of polypeptides.

Electrostatic (through-space) and covalent (through-bond) contributions to couplings involving the C[double bond]O and C[bond]N vibrational stretching modes of the amide group in the alpha-helix and the parallel and antiparallel beta-sheet structures of alanine polypeptides are analyzed. Coupling constants computed at the density functional theory level are compared with the transition dipole coupling model and the complete electrostatic interaction between transition densities. We find that the transition densities of C[double bond]O modes are localized, and the electrostatic mechanism then holds. In contrast, the C[bond]N mode transition densities are delocalized, and covalent contributions to the coupling are significant.

Location of Structural Transitions in an Isotopically Labeled Lung Surfactant SP-B Peptide by IRRAS

Pulmonary surfactant, a lipid/protein complex that lines the air/water interface in the mammalian lung, functions to reduce the work of breathing. Surfactant protein B (SP-B) is a small, hydrophobic protein that is an essential component of this mixture. Structure-function relationships of SP-B are currently under investigation as the protein and its peptide analogs are being incorporated into surfactant replacement therapies. Knowledge of the structure of SP-B and its related peptides in bulk and monolayer phases will facilitate the design of later generation therapeutic agents. Prior infrared reflection-absorption spectroscopic studies reported notable, reversible surface pressure-induced antiparallel β-sheet formation in a synthetic peptide derived from human SP-B, residues 9–36 (SP-B 9–36). In the current work, infrared reflection-absorption spectroscopy is applied in conjunction with isotopic labeling to detect the site and pressure dependence of the conformational change. SP-B 9–36, synthesized with 13C=O-labeled Ala residues in positions 26, 28, 30, and 32, shifted the β-sheet marker band to ∼1600 cm −1 and thus immediately identified this structural element within the labeled region. Surface pressure-induced alterations in the relative intensities of Amide I band constituents are interpreted using a semiempirical transition dipole coupling model. In addition, electron micrographs reveal the formation of tubular myelin structures from in vitro preparations using SP-B 9–36 in place of porcine SP-B indicating that the peptide has the potential to mimic this property of the native protein.

Inter-peptide interaction and delocalization of amide I vibrational excitons in myoglobin and flavodoxin

The amide I vibrational normal-mode analyses of two globular proteins, myoglobin and flavodoxin, were carried out and the spatial delocalization and phase correlation of each normal mode was studied. The Hessian matrix in the restricted space constructed by the N peptides was obtained by using both ab initio quantum chemistry calculation results and empirical transition dipole coupling model. For both of the two proteins, the amide I normal modes are fairly delocalized and on average about 15% of the polypeptides in myoglobin and flavodoxin are participated in the formation of each amide I normal mode. The analysis of vibrational phase correlation of myoglobin reveals that the high-frequency amide I normal modes are mostly (symmetric) A-mode like, whereas the low-frequency ones are (antisymmetric) E-mode like. For flavodoxin, among the three distinct bands at 1653, 1636, and 1628 cm−1, the high-frequency modes are found to be fairly localized in the four α helices, the low-frequency modes around 1628 cm−1 are strictly localized in the five β sheets, and the midfrequency modes around 1636 cm−1 are delocalized in both the α helices and β sheets. Effects of the diagonal disorder on the amide I band of both proteins were studied. We found that the sharp peak at 1628 cm−1 in the resolution enhanced amide I infrared spectrum of flavodoxin is a direct signature that the through-space interactions between two different β sheets exist.

Amide I vibrational modes in glycine dipeptide analog: Ab initio calculation studies

Coupling between two local amide I vibrational motions of peptides has been quantitatively estimated by assuming that the two peptides interact with each other via dipole–dipole interaction, the so-called transition dipole coupling (TDC) model. The TDC theory has been applied to describing amide I IR and Raman band envelopes and further used to interpret the two-dimensional IR pump–probe and photon echo spectra of polypeptides recently. In order to quantitatively test the validity of the TDC model or in general dipole–dipole interaction model for a dipeptide, we carry out systematic investigations, by using both the ab initio calculation methods and extended TDC theory, on the potential energy surface, vibrational frequencies of symmetric and antisymmetric amide I vibrational normal modes, transition dipole and transition polarizability, IR and Raman intensities of the two modes, IR-Raman noncoincidence phenomena in the full Ramachandran space for a model dipeptide, glycine dipeptide analog. It is found that the spectroscopic properties of dipeptide can be quantitatively well described by the TDC model, but the quantities related to the potential energy surface such as absolute magnitudes of vibrational frequencies and frequency splitting between the two normal modes cannot be accounted for by using the TDC model. A further investigation of dimeric system with two formamide molecules is presented and the applicability of the TDC model to through space vibrational interaction as a function of intermolecular distance between the two peptides is examined.

V−V Energy Transfer from Highly Vibrationally Excited Molecules through Transition Dipole Coupling: A Quantitative Test on Energy Transfer from SO2 (v ≫ 0) to SF6(31)

Time-resolved Fourier transform IR emission spectroscopy has been used to monitor the population distribution of both the energy giving molecules and the energy receiving molecules during collisional quenching of highly vibrationally excited SO2 by bath-gas SF6. The change in population of the SF6 v3 = 1 level measured as a function of time is compared with that calculated based on the transition dipole coupling model with the transition dipole of highly excited SO2 extracted from its IR emission spectra. The excellent agreement indicates that long-range interaction through transition dipole coupling is responsible for the vibration to vibration energy transfer from the highly excited molecules.

Collisional energy transfer of highly vibrationally excited NO2: The role of intramolecular vibronic coupling and the transition dipole coupling mechanism

The collisional relaxation of highly vibrationally excited NO2 has been studied for a variety of collision partners (He, Ar, CO, N2, O2, N2O, NO2, CO2, SF6, and toluene) by time-resolved Fourier transform infrared emission spectroscopy. The average energy 〈E〉 of the vibrationally excited NO2 molecules during collisional quenching was obtained from the IR spectra by modeling the ν3 and ν1+ν3 bands, using the known harmonic frequencies and anharmonicity constants. The average amount of energy lost per collision 〈ΔE〉 was determined from the 〈E〉 versus time data. The results show that there is a dramatic increase in the amount of energy transferred for all bath gases at NO2 energies above 10 000–12 000 cm−1, which is near the origin of the NO2 Ã2B2/B̃2B1 states. This threshold in the energy-transfer rate occurs because of strong vibronic coupling between the X̃2A1 and Ã2B2/B̃2B1 electronic states. The increase in vibration-to-vibration (V-V) energy transfer can be understood within the context of the transition dipole coupling model. Vibronic coupling in NO2 produces extensive broadband emission in the IR and near-IR, which enhances the V-V energy-transfer rate by relaxing the resonance conditions in dipole coupling. The V-V energy-transfer probability was calculated using the dipole coupling model, where the transition dipole moment of excited NO2 was directly extracted from the IR emission spectra. These calculations successfully reproduced the observed threshold in the V-V energy transfer probability. The transition dipole coupling model was also used to estimate the relative contribution of V-V versus vibration-to-translation, rotation (V-T,R) energy transfer for NO2 deactivation. The calculations showed that V-T,R energy transfer is the major relaxation channel for triatomic or smaller collision partners. For larger species like SF6, however, V-V energy transfer is the dominant channel. Vibronic coupling may cause an increase in the V-T,R energy-transfer rate by allowing electronic potential related terms, possibly the electronic transition dipole moment, to contribute to the matrix elements responsible for V-T,R energy transfer.

Observation of large vibration-to-vibration energy transfer collisions (ΔE≳3500 cm−1) in quenching of highly excited NO2 by CO2 and N2O

Time-resolved Fourier transform infrared emission spectra, recorded after 475 nm excitation of NO2 in a CO2 or N2O bath, show IR emission from collisionally populated vibrational levels of the bath gas. The frequency of the observed bands proves that the emission arises from either the (1,00,1), (0,2l,1), and/or (0,00,2) levels of CO2 or N2O. From the pressure dependence of the emission intensity it was determined that these levels are populated by single collisions with excited NO2. Under typical conditions (1:10 ratio of NO2 to bath gas and 1–2 Torr total pressure) a steady state concentration is reached in our experiments where 0.016±0.006 multiply excited CO2 molecules, or 0.03±0.01 multiply excited N2O molecules were generated per laser excited NO2. A transition dipole coupling model is applied to explain these results, where the resonance conditions for vibration-to-vibration energy transfer are relaxed by extensive vibronic and vibrational couplings in highly excited NO2. In this model the energy-dependent transition dipole of excited NO2 is derived from the time-resolved IR emission spectra. The probability of Δv=1 energy transfer collisions for excited NO2 with CO2 or N2O can be accurately calculated. However, the number of multiply excited species produced (Δv≳1) is grossly underestimated. Analysis of the time-resolved data shows that the probability for Δv≳1 V–V energy transfer is ca. two orders of magnitude larger than the probability predicted by the dipole coupling model, and that NO2 molecules with energies as low as 5000 cm−1 have a non-negligible probability for exciting the overtone levels of CO2 and N2O. Finally, it was found that the dipole coupling model also underestimates the probability for the ΔE≳10 000 cm−1 supercollisions deduced in previous experiments (see Refs. ).