Amide I vibrational circular dichroism of dipeptide: Conformation dependence and fragment analysis

Refining protein amide I spectrum simulations with simple yet effective electrostatic models for local wavenumbers and dipole derivative magnitudes

Analysis of the amide I band of proteins is probably the most wide-spread application of bioanalytical infrared spectroscopy. Although highly desirable for a more detailed structural interpretation, a quantitative description of this absorption band is still difficult. This work optimized several electrostatic models with the aim to reproduce the effect of the protein environment on the intrinsic wavenumber of a local amide I oscillator. We considered the main secondary structures - α-helices, parallel and antiparallel β-sheets - with a maximum of 21 amide groups. The models were based on the electric potential and/or the electric field component along the CO bond at up to four atoms in an amide group. They were bench-marked by comparison to Hessian matrices reconstructed from density functional theory calculations at the BPW91, 6-31G** level. The performance of the electrostatic models depended on the charge set used to calculate the electric field and potential. Gromos and DSSP charge sets, used in common force fields, were not optimal for the better performing models. A good compromise between performance and the stability of model parameters was achieved by a model that considered the electric field at the positions of the oxygen, nitrogen, and hydrogen atoms of the considered amide group. The model describes also some aspects of the local conformation effect and performs similar on its own as in combination with an explicit implementation of the local conformation effect. It is better than a combination of a local hydrogen bonding model with the local conformation effect. Even though the short-range hydrogen bonding model performs worse, it captures important aspects of the local wavenumber sensitivity to the molecular surroundings. We improved also the description of the coupling between local amide I oscillators by developing an electrostatic model for the dependency of the dipole derivative magnitude on the protein environment.

AIM: A Mapping Program for Infrared Spectroscopy of Proteins

Here, we present a new analysis program, AIM, that allows extracting the vibrational amide-I Hamiltonian using molecular dynamics trajectories for protein infrared spectroscopy modeling. The constructed Hamiltonians can be used as input for spectral calculations allowing the calculation of infrared absorption spectra, vibrational circular dichroism, and two-dimensional infrared spectra. These spectroscopies allow the study of the structure and dynamics of proteins. We will explain the essence of how AIM works and give examples of the information and spectra that can be obtained with the program using the Trypsin Inhibitor as an example. AIM is freely available from GitHub, and the package contains a demonstration allowing easy introduction to the use of the program.

Insight into the internal structure of amyloid-β oligomers by isotope-edited Fourier transform infrared spectroscopy

Isotope-edited infrared spectroscopy reveals the structural unit of amyloid-β oligomers.

Disorder and order in unfolded and disordered peptides and proteins: a view derived from tripeptide conformational analysis. II. Tripeptides with short side chains populating asx and β-type like turn conformations

In the preceding paper, we found that ensembles of tripeptides with long or bulky chains can include up to 20% of various turns. Here, we determine the structural and thermodynamic characteristics of GxG peptides with short polar and/or ionizable central residues (D, N, C), whose conformational distributions exhibit higher than average percentage (>20%) of turn conformations. To probe the side-chain conformations of these peptides, we determined the (3)J(H(α),H(β)) coupling constants and derived the population of three rotamers with χ1 -angles of -60°, 180° and 60°, which were correlated with residue propensities by DFT-calculations. For protonated GDG, the rotamer distribution provides additional evidence for asx-turns. A comparison of vibrational spectra and NMR coupling constants of protonated GDG, ionized GDG, and the protonated aspartic acid dipeptide revealed that side chain protonation increases the pPII content at the expense of turn populations. The charged terminal groups, however, have negligible influence on the conformational properties of the central residue. Like protonated GDG, cationic GCG samples asx-turns to a significant extent. The temperature dependence of the UVCD spectra and (3)J(H(N)H(α)) constants suggest that the turn populations of GDG and GNG are practically temperature-independent, indicating enthalpic and entropic stabilization. The temperature-independent J-coupling and UVCD spectra of GNG require a three-state model. Our results indicate that short side chains with hydrogen bonding capability in GxG segments of proteins may serve as hinge regions for establishing compact structures of unfolded proteins and peptides.

Development and validation of transferable amide I vibrational frequency maps for peptides

Infrared (IR) spectroscopy of the amide I band has been widely utilized for the analysis of peptides and proteins. Theoretical modeling of IR spectra of proteins requires an accurate and efficient description of the amide I frequencies. In this paper, amide I frequency maps for protein backbone and side chain groups are developed from experimental spectra and vibrational lifetimes of N-methylacetamide and acetamide in different solvents. The frequency maps, along with established nearest-neighbor frequency shift and coupling schemes, are then applied to a variety of peptides in aqueous solution and reproduce experimental spectra well. The frequency maps are designed to be transferable to different environments; therefore, they can be used for heterogeneous systems, such as membrane proteins.

Infrared optical activity: electric field approaches in time domain

Vibrational circular dichroism (VCD) spectroscopy provides detailed information about the absolute configurations of chiral molecules including biomolecules and synthetic drugs. This method is the infrared (IR) analogue of the more popular electronic CD spectroscopy that uses the ultraviolet and visible ranges of the electromagnetic spectrum. Because conventional electronic CD spectroscopy measures the difference in signal intensity, problems such as weak signal and low time-resolution can limit its utility. To overcome the difficulties associated with that approach, we have recently developed femtosecond IR optical activity (IOA) spectrometry, which directly measures the IOA free-induction-decay (FID), the impulsive chiroptical IR response that occurs over time. In this Account, we review the time-domain electric field measurement and calculation methods used to simultaneously characterize VCD and related vibrational optical rotatory dispersion (VORD) spectra. Although conventional methods measure the electric field intensity, this vibrational technique is based on a direct phase-and-amplitude measurement of the electric field of the chiroptical signal over time. This method uses a cross-polarization analyzer to carry out heterodyned spectral interferometry. The cross-polarization scheme enables us to selectively remove the achiral background signal, which is the dominant noise component present in differential intensity measurement techniques. Because we can detect the IOA FID signal in a phase-amplitude-sensitive manner, we can directly characterize the time-dependent electric dipole/magnetic dipole response function and the complex chiral susceptibility that contain information about the angular oscillations of charged particles. These parameters yield information about the VCD and VORD spectra. In parallel with such experimental developments, we have also calculated the IOA FID signal and the resulting VCD spectrum. These simulations use a quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) method and calculate the electric dipole/magnetic dipole cross-correlation function in the time domain. Although many quantum chemistry calculation approaches can only consider a limited number of geometry-optimized conformations of chiral molecules in a gas phase, this computational method includes the solute-solvent interactions and the inhomogeneous distributions of solute conformers in condensed phases. A subsequent Fourier transformation of the chiral response function produced a theoretical VCD spectrum in the entire mid-IR frequency range. Directly comparing theory and experiment, we demonstrate quantitative agreement between frequency-tunable femtosecond IOA measurements and QM/MM MD simulations of (1S)-β-pinene in CCl(4) solution. We anticipate that these direct IOA measurement and calculation methods will be applied to the studies of equilibrium chiroptical properties and structure determinations. These methods provide tools to investigate ultrafast structural dynamics of chiral systems with unprecedented time resolution.

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.

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.

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.

Vibrational solvatochromism and electrochromism: coarse-grained models and their relationships

A theoretical description of vibrational solvatochromism and electrochromism is presented by using a coarse-grained model based on a distributed charge and multipole interaction theory. Solvatochromic frequency shift has been described by considering the interaction between distributed charges of a solute and electrostatic potential due to distributed charges of solvent molecules. Another approach was based on the expansion of the solvatochromic frequency shift in terms of solvent electric field and its gradient at distributed sites on solute. The relationship between these two approaches is elucidated and their validities are discussed. It is also shown that the distributed charge and multipole model for solvatochromism developed here can be used to describe vibrational Stark effects on frequency and transition dipole moment. The relationship between the vibrational Stark tuning rate and the parameters obtained from recent vibrational solvatochromism studies is clarified and used to determine the vibrational Stark tuning rates of a few stretching modes, which are then directly compared with experimentally measured values. We anticipate that the present theoretical model can be used to study a variety of vibrational solvatochromic and electrochromic phenomena and to extract critical information on local electrostatic environment around a small IR probe in solution or protein from linear and nonlinear IR spectroscopic studies.

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.

Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: comparisons with IR and vibrational circular dichroism spectra

We have implemented the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulations of alanine dipeptide in water along with the polarizable and nonpolarizable classical MD simulations with different models of water. For the QM/MM MD simulation, the alanine dipeptide is treated with the AM1 or PM3 approximations and the fluctuating solute dipole moment is calculated by the Mulliken population analysis. For the classical MD simulations, the solute is treated with the polarizable or nonpolarizable AMBER and polarizable CHARMM force fields and water is treated with the TIP3P, TIP4P, or TIP5P model. It is found that the relative populations of right-handed alpha-helix and extended beta and P(II) conformations in the simulation trajectory strongly depend on the simulation method. For the QM/MM MD simulations, the PM3/MM shows that the P(II) conformation is dominant, whereas the AM1/MM predicts that the dominant conformation is alpha(R). Polarizable CHARMM force field gives almost exclusively P(II) conformation and other force fields predict that both alpha-helical and extended (beta and P(II)) conformations are populated with varying extents. Solvation environment around the dipeptide is investigated by examining the radial distribution functions and numbers and lifetimes of hydrogen bonds. Comparing the simulated IR and vibrational circular dichroism spectra with experimental results, we concluded that the dipeptide adopts the P(II) conformation and PM3/MM, AMBER03 with TIP4P water, and AMBER polarizable force fields are acceptable for structure determination of the dipeptide considered in this paper.

Conformation and dynamics of the three-helix bundle UBA domain of p62 from experiment and simulation

The ubiquitin associated domain of p62 is a small three-helix bundle of approximately 50 residues that mediates the recognition of polyubiquitin chains and ubiquitylated substrates. The solution structure of a 52 residue construct containing this domain has been characterized using heteronuclear nuclear magnetic resonance (NMR) methods. The resulting ensemble of NMR-derived structures was used in molecular dynamics (MD) simulations to investigate the equilibrium conformation and dynamics of this domain. NOE and (15)N relaxation data have been used to validate the structural ensemble produced by the MD simulations and show a good correlation for residues in regions of secondary structure. A similar approach was taken using an ensemble of structures from the MD simulations to calculate electronic circular dichroism (CD) and IR spectra from first principles with an encouraging correlation with the experimental CD and IR data.

Dipeptide Structure Determination by Vibrational Circular Dichroism Combined with Quantum Chemistry Calculations

The solution structure and the local solvation environments of alanine dipeptide (AD, 1 a) and its isotopomer (AD*, 1 b, 13C on the acetyl end C==O) are studied by using infrared (IR) spectroscopy and vibrational circular dichroism (VCD). From the amide I IR spectra of AD* in various protic solvents, it is found that each of the two carbonyl groups is fully H-bonded to two water molecules. However, the number of alcohol molecules H-bonded to each C==O varies from one to two, and the local solvation environments are asymmetric around the two peptides of AD* in alcohol solutions. The amide I VCD spectra of AD and AD* in D2O are also measured, and a series of density functional theory (DFT, B3LYP/6-311++G**) calculations are performed to obtain the amide I normal-mode rotational strengths of AD and the intrinsic rotational strengths of its two peptide fragments. By combining the VCD-measurement and DFT-calculation results and employing a coupled oscillator theory, we show that the aqueous-solution structure of the dipeptide can be determined. We believe that the present method will be of use in building up a library of dipeptide solution structures in water.

DNA oligonucleotide-cis-platin binding: Ab initio interpretation of the vibrational spectra

The cis-platin binding to the d(CCTGGTCC)*d(GGACCAGG) model DNA octamer was monitored with infrared absorption (IR) and vibrational circular dichroism (VCD) spectroscopies. The spectra were modeled with the aid of density functional computations and a Cartesian coordinate-based transfer of molecular property tensors from smaller DNA fragments. Because of the fragmentation, the tensors could be calculated with a higher precision. Environmental effects, such as the presence of the solvent or the cis-platin ligand, could be included in the modeling. The solvent was modeled by an explicit inclusion of hydrogen-bound water molecules, positions of which were estimated from a molecular dynamics simulation, or by the polarized continuum COSMO model. The B3LYP and BPW91 functionals used for the calculations of the spectral parameters were combined with the relativistic LANL2DZ platinum pseudo-potentials. The simulations reproduced the main IR and VCD DNA spectral features and explained most of the changes observed experimentally upon metal binding. The results confirmed that the influence of the ligand on DNA vibrational properties is quite complex; it originates in the geometry deformation and normal mode coupling pattern changes of the platinated octamer, as well as in local perturbations of the electronic structure and force field of the GC base pairs to which the platinum is bound. Many of the local effects could be accounted for by a point charge used in place of the metal in the GC complex.

Vibrational dynamics of DNA. I. Vibrational basis modes and couplings

Carrying out density functional theory calculations of four DNA bases, base derivatives, Watson-Crick (WC) base pairs, and multiple-layer base pair stacks, we studied vibrational dynamics of delocalized modes with frequency ranging from 1400 to 1800 cm(-1). These modes have been found to be highly sensitive to structure fluctuation and base pair conformation of DNA. By identifying eight fundamental basis modes, it is shown that the normal modes of base pairs and multilayer base pair stacks can be described by linear combinations of these vibrational basis modes. By using the Hessian matrix reconstruction method, vibrational coupling constants between the basis modes are determined for WC base pairs and multilayer systems and are found to be most strongly affected by the hydrogen bonding interaction between bases. It is also found that the propeller twist and buckle motions do not strongly affect vibrational couplings and basis mode frequencies. Numerically simulated IR spectra of guanine-cytosine and adenine-thymine bases pairs as well as of multilayer base pair stacks are presented and described in terms of coupled basis modes. It turns out that, due to the small interlayer base-base vibrational interactions, the IR absorption spectrum of multilayer base pair system does not strongly depend on the number of base pairs.

Vibrational dynamics of DNA. II. Deuterium exchange effects and simulated IR absorption spectra

In Paper I, we studied vibrational properties of normal bases, base derivatives, Watson-Crick base pairs, and multiple layer base pair stacks in the frequency range of 1400-1800 cm(-1). However, typical IR absorption spectra of single- and double-stranded DNA have been measured in D(2)O solution. Consequently, the more relevant bases and base pairs are those with deuterium atoms in replacement with labile amino hydrogen atoms. Thus, we have carried out density functional theory vibrational analyses of properly deuterated bases, base pairs, and stacked base pair systems. In the frequency range of interest, both aromatic ring deformation modes and carbonyl stretching modes appear to be strongly IR active. Basis mode frequencies and vibrational coupling constants are newly determined and used to numerically simulate IR absorption spectra. It turns out that the hydration effects on vibrational spectra are important. The numerically simulated vibrational spectra are directly compared with experiments. Also, the (18)O-isotope exchange effect on the poly(dG):poly(dC) spectrum is quantitatively described. The present calculation results will be used to further simulate two-dimensional IR photon echo spectra of DNA oligomers in the companion Paper III.

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.

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.

The alanine-rich XAO peptide adopts a heterogeneous population, including turn-like and polyproline II conformations

The solution structure of the hepta-alanine polypeptide Ac-X(2)A(7)O(2)-NH(2) (XAO) has been a matter of controversy in the current literature. On one side of the argument is a claim that the peptide adopts a mostly polyproline II (PPII) structure, with a <20% population of beta conformations at room temperature [Shi Z, Olson CA, Rose GA, Baldwin RL, Kallenbach NR (2002) Proc Natl Acad Sci USA 99:9190-9195], whereas the other side of the argument insists that the peptide exists as an ensemble of conformations, including multiple beta-turn structures [Makowska J, Rodziewicz-Motowidlo S, Baginska K, Vila JA, Liwo A, Chmurzynski L, Scheraga HA (2006) Proc Natl Acad Sci USA 103:1744-1749]. We have used an excitonic coupling model to simulate the amide I band of the FTIR, vibrational circular dichroism, and isotropic and anisotropic Raman spectra of XAO, where, for each residue, the backbone dihedral angle varphi was constrained by using the reported (3)J(CalphaHNH) values and a modified Karplus relation. The best reproduction of the experimental data could only be achieved by assuming an ensemble of conformations, which contains various beta-turn conformations ( approximately 26%), in addition to beta-strand ( approximately 23%) and PPII ( approximately 50%) conformations. PPII is the dominant conformation in segments not involved in turn formations. Most of the residues were found to sample the bridge region connecting the PPII and right-handed helix troughs in the Ramachandran plot, which is part of the very heterogeneous ensemble of conformations generally termed type IV beta-turn.

Vibrational dynamics of DNA: IV. Vibrational spectroscopic characteristics of A-, B-, and Z-form DNA’s

Linear and nonlinear IR spectroscopic studies of nucleic acids can provide crucial information on solution conformations of DNA double helix and its complex with other molecules. Carrying out density functional theory calculations of A-, B-, and Z-form DNA's, the authors obtained vibrational spectroscopic properties as well as coupling constants between different basis modes. The vibrational couplings that determine the extent of exciton delocalization are strongly dependent on DNA conformation mainly because the interlayer distance between two neighboring base pairs changes with respect to the DNA conformation. The Z-DNA has comparatively small interlayer vibrational coupling constants so that its vibrational spectrum depends little on the number of base pairs, whereas the A-DNA shows a notable dependency on the size. Furthermore, it is shown that a few distinctively different line shape changes in both IR and two-dimensional IR spectra as the DNA conformation changes from B to A or from B to Z can be used as marker bands and characteristic features distinguishing different DNA conformations.

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.

Site-Specific Hydrogen-Bonding Interaction between N-Acetylproline Amide and Protic Solvent Molecules: Comparisons of IR and VCD Measurements with MD Simulations

The effects of solute-solvent interactions on solution structures of small peptides have been paid a great deal of attention. To study the effect of hydrogen-bonding interactions on peptide solution structures, we measured the amide I IR and VCD spectra of N-acetylproline amide (AP) in various protic solvents, i.e., D2O, MeOD, EtOD, and PrOD, and directly compared them with theoretically simulated ones. The numbers of protic solvent molecules hydrogen-bonded to the two peptide bonds in the AP were quantitatively determined by carrying out the molecular dynamics (MD) simulations and then compared with the spectral analyses of the experimentally measured amide I bands. The two peptides in the AP have different propensities of forming H-bonds with protic solvent molecules, and the H-bond population distribution is found to be strongly site-specific and solvent-dependent. However, it is found that adoption of the polyproline II (PII) conformation by AP in protic solvents does not strongly depend on the hydrogen bond network-forming ability of protic solvents nor on the solvent polarity. We present a brief discussion on the validity as well as limitation of the currently available force field parameters used for the present MD simulation study.

Simulation of Infrared Spectra for β-Hairpin Peptides Stabilized by an Aib-Gly Turn Sequence: Correlation between Conformational Fluctuation and Vibrational Coupling

Vibrational spectra of a 12-residue beta-hairpin peptide, RYVEVBGKKILQ (HBG), stabilized by an Aib-Gly turn sequence (B = Aib) were investigated theoretically using a combination of molecular dynamics (MD) and density functional theory (DFT) calculations. Selected conformations of HBG were extracted from a classical MD trajectory and used for spectral simulations. DFT calculations, based on the Cartesian coordinate spectral property transfer protocol, were carried out for peptide structures in which all residues are replaced with Ala, except for the Aib and Gly residues, but the backbone (phi, psi, omega) structure of the original configuration is retained. The simulations provide a basis for interpretation of the HBG amide I infrared spectra in terms of structural variables such as detailed secondary structure and thermal conformational fluctuation as well as vibrational coupling as indicated by spectra of 13C isotope-labeled variants. The characteristic amide I band shape of such small beta-hairpin peptides appears to arise from the structure of the short antiparallel beta-sheet strands. The role of structural parameter fluctuation in vibrational coupling is evaluated by comparison of DFT-derived amide coupling constants for selected configurations and from transition dipole coupling calculations of coupling parameters between (13)C isotopically labeled residues for a MD-derived ensemble of configurations. Calculated results were compared with the experimentally obtained spectra for several (13)C isotope-labeled peptides of this sequence.

Geometry and Solvent Dependence of the Electronic Spectra of the Amide Group and Consequences for Peptide Circular Dichroism

The influence of geometry variations and solvent environment of N-methylacetamide on its energies and absorption intensities was systematically analyzed with the aid of the time-dependent density functional theory (TD DFT). Selective and often complicated reactions of individual electronic levels on the perturbations were found important for the resultant spectral profile. For example, the n-pi band position varied by tens of nanometers due to the C=O bond length oscillations, while it was rather unaffected by surrounding water. On the contrary, pi-pi type transition energies and intensities were broadly dispersed by the aqueous environment but exhibited a modest coordinate dependence. A simple electrostatic model used previously for absorption in the IR region (J. Chem. Phys. 2005, 122, 144501) explained these changes only partially. Additionally, electronic transfer between the solute and the solvent had to be considered for faithful modeling of the ultraviolet light absorption. The inclusion of the environment and dynamics in the modeling then provided more accurate positions, intensities, and realistic inhomogeneous widths of spectral lines. These factors were found important for absorption and circular dichroism spectra of larger peptides and proteins. This was demonstrated with a combined DFT/coupled oscillator model providing principal features observed in electronic circular dichroism spectra of standard peptide conformations.

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.

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

Fragment analyses of vibrational circular dichroic response of dipeptides were carried out recently [Choi and Cho, J. Chem. Phys. 120, 4383 (2004)]. In the present paper, by using a minimal size unit peptide containing two chiral carbons covalently bonded to the peptide group, a generalized fragmentation approximation method is discussed and applied to the calculations of infrared-absorption and vibrational circular dichroism (VCD) intensities of amide I vibrations in various secondary structure polypeptides. Unlike the dipole strength determining IR-absorption intensity, the rotational strength is largely determined by the cross terms that are given by the inner product between the transition electric dipole and the transition magnetic dipole of two different peptides. This explains why the signs and magnitudes of VCD peaks are far more sensitive to the relative orientation and distance between different peptide bonds in a given protein. In order to test the validity of fragmentation approximation, three different segments in a globular protein ubiquitin, i.e., right-handed alpha-helix, beta-sheet, and beta-turn regions, were chosen for density-functional theory (DFT) calculations of amide I vibrational properties and the numerically simulated IR-absorption and VCD spectra by using the fragmentation method are directly compared with DFT results. It is believed that the fragmentation approximation method will be of use in numerically simulating vibrational spectra of proteins in solutions.

Empirical solvent correction for multiple amide group vibrational modes

Previously proposed solvent correction to the amide I peptide vibration was extended so that it can be applied to a general solvated chromophore. The combined molecular and quantum mechanics (MMQM) method is based on a linear dependence of harmonic force field and intensity tensor components of the solute on solvent electrostatic field. For N-methylacetamide, realistic solvent frequency and intensity changes as well as inhomogeneous band widths were obtained for amide A, I, II , and III modes. A rather anomalous basis set size dependence was observed for the amide A and I vibrations, when bigger basis lead to narrowing of spectral bands and lesser molecular sensibility to the environment. For a model alpha-helical peptide, a W-shape of the vibrational circular dichroism signal observed in deuterated solvent for the amide I band was reproduced correctly, unlike with previous vacuum models.

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.