Vibrational frequency shifts and relaxation rates for a selected vibrational mode in cytochrome C

Simultaneous bond-selective deuterium-based isotopic labeling sensing with disposable ultra-miniature CARS fiber probe

Deuterium-based isotopic labeling is an important technique for tracking cellular metabolism with the Raman signals analysis of low-wavenumber (LW) C-D bonds and high-wavenumber (HW) C-H bonds. We propose and demonstrate a disposable ultra-miniature fiber probe to detect LW and HW coherent anti-Stokes Raman scattering (CARS) spectra for deuterated compounds simultaneously and bond-selectively sensing. The 10.78 µm diameter disposable fiber probe, comprised of focusing taper as fiber probe head and time-domain walk-off eliminating fiber section with designed length, realizes wide-frequency-interval dual Stokes pulse delivering and focusing. The fiber probe enables quantitative concentration determination with resolution down to 11 mM. The chemical vibration modes of LW region C-D bonds and HW region C-H bonds of the mixture samples of organic compounds and their deuterated counterparts in a simulated cell are simultaneously excited and characterized. The CARS disposable fiber probe introduces a promising handle for in vivo biochemical detection based on isotopic labeling sensing.

Origin of thiocyanate spectral shifts in water and organic solvents

Vibrational spectroscopy is a useful technique for probing chemical environments. The development of models that can reproduce the spectra of nitriles and azides is valuable because these probes are uniquely suited for investigating complex systems. Empirical vibrational spectroscopic maps are commonly employed to obtain the instantaneous vibrational frequencies during molecular dynamics simulations but often fail to adequately describe the behavior of these probes, especially in its transferability to a diverse range of environments. In this paper, we demonstrate several reasons for the difficulty in constructing a general-purpose vibrational map for methyl thiocyanate (MeSCN), a model for cyanylated biological probes. In particular, we found that electrostatics alone are not a sufficient metric to categorize the environments of different solvents, and the dominant features in intermolecular interactions in the energy landscape vary from solvent to solvent. Consequently, common vibrational mapping schemes do not cover all essential interaction terms adequately, especially in the treatment of van der Waals interactions. Quantum vibrational perturbation (QVP) theory, along with a combined quantum mechanical and molecular mechanical potential for solute-solvent interactions, is an alternative and efficient modeling technique, which is compared in this paper, to yield spectroscopic results in good agreement with experimental FTIR. QVP has been used to analyze the computational data, revealing the shortcomings of the vibrational maps for MeSCN in different solvents. The results indicate that insights from QVP analysis can be used to enhance the transferability of vibrational maps in future studies.

Protein vibrations and their localization behaviour. A numerical scaling analysis

Using a classical force field, we investigate the localization properties of protein normal modes. For a set of eighteen proteins that cover five classes of increasing size, we compute the participation ratio as a measure of the spatial extent of protein vibrations. In this scaling analysis, we find extended low-frequency far-infrared and Terahertz modes, in contrast to localized high-frequency near-infrared vibrations. These regimes are separated by a broad crossover around a wave number of 260 cm^-1. Biophysical and biochemical implications are discussed, and the vibrational localization properties are compared to those of amorphous solids.

Spreading of Cell Aggregates on Zwitterion-Modified Chitosan Films

The sulfobetaine (SB) moiety, which comprises a quaternary ammonium group linked to a negatively charged sulfonate ester, is known to impart nonfouling properties to interfaces coated with polysulfobetaines or grafted with SB-polymeric brushes. Increasingly, evidence emerges that the SB group is, overall, a better antifouling group than the phosphorylcholine (PC) moiety extensively used in the past. We report here the synthesis of a series of SB-modified chitosans (CH-SB) carrying between 20 and 40 mol % SB per monosaccharide unit. Chitosan (CH) itself is a naturally derived copolymer of glucosamine and N-acetyl-glucosamine linked with a β-1,4 bond. Analysis by quartz crystal microbalance with dissipation (QCM-D) indicates that CH-SB films (thickness ∼ 20 nm) resist adsorption of bovine serum albumin (BSA) with increasing efficiency as the SB content of the polymer augments (surface coverage ∼ 15 μg cm^-2 for films of CH with 40 mol % SB). The cell adhesivity of CH-SB films coated on glass was assessed by determining the spreading dynamics of CT26 cell aggregates. When placed on chitosan films, known to be cell-adhesive, the CT26 cell aggregates spread by forming a cell monolayer around them. The spreading of CT26 cell aggregates on zwitterion-modified chitosans films is thwarted remarkably. In the cases of CH-SB30 and CH-SB40 films, only a few isolated cells escape from the aggregates. The extent of aggregate spreading, quantified based on the theory of liquid wetting, provides a simple in vitro assay of the nonfouling properties of substrates toward specific cell lines. This assay can be adopted to test and compare the fouling characteristics of substrates very different from the chemical viewpoint.

Temperature-dependent conformational dynamics of cytochrome c: Implications in apoptosis

Heat, electric shock, and burn injuries induce apoptosis by releasing cytochrome c (cyt-c) from mitochondria and by subsequently activating the death protease, caspases-3. During apoptosis, cyt-c undergoes changes in the secondary structure that have been suggested to increase its peroxidase activity. Information about these structural changes will provide better understanding of the apoptotic mechanism. Hence, temperature-dependent conformational dynamics of cyt-c has been investigated through molecular dynamics (MD) simulations to explain the structural changes and to correlate them with its apoptotic behavior. We observe that, at lower temperatures (223, 248, and 300K), the secondary structure of cyt-c, remains stable, while at higher temperatures (323, 373, 423, and 473K), the secondary structural regions change significantly. Further, our MD results indicate that these structural changes are mainly localized on α-helices, turns, β-sheets, and important loops that were involved in the stabilization of the heme conformation. This conformational transition between specific regions of secondary structure of cyt-c directly affects the electron tunneling properties of the proteins as observed experimentally. We quantify and compare these changes and explain that the temperature plays a vital role in assuring the structural stability of cyt-c and thus its functions. Our findings from this MD study reproduce experimental results at high temperatures and provide evidence for the alteration of the heme through the disruption of the H-bonding interactions between specific regions of cyt-c, thereby enhancing its peroxidase activity which plays a crucial role in the apoptotic process.

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H-Cl stretching frequency in the HCl-water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H-Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures.

Computation of the memory functions in the generalized Langevin models for collective dynamics of macromolecules

We present a numerical method to approximate the memory functions in the generalized Langevin models for the collective dynamics of macromolecules. We first derive the exact expressions of the memory functions, obtained from projection to subspaces that correspond to the selection of coarse-grain variables. In particular, the memory functions are expressed in the forms of matrix functions, which will then be approximated by Krylov-subspace methods. It will also be demonstrated that the random noise can be approximated under the same framework, and the second fluctuation-dissipation theorem is automatically satisfied. The accuracy of the method is examined through several numerical examples.

Hybrid quantum/classical simulations of the vibrational relaxation of the amide I mode of N-methylacetamide in D2O solution

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

On the role of nonbonded interactions in vibrational energy relaxation of cyanide in water

The vibrationally excited cyanide ion (CN(-)) in H2O or D2O relaxes back to the ground state within several tens of picoseconds. Pump-probe infrared spectroscopy has determined relaxation times of T1 = 28 ± 7 and 71 ± 3 ps in H2O and D2O, respectively. Atomistic simulations of this process using nonequilibrium molecular dynamics simulations allow determination of whether it is possible at all to describe such a process, what level of accuracy in the force fields is required, and whether the information can be used to understand the molecular mechanisms underlying vibrational relaxation. It is found that, by using the best electrostatic models investigated, absolute relaxation times can be described rather more qualitatively (T1(H2O) = 19 ps and T1(D2O) = 34 ps) whereas the relative change in going from water to deuterated water is more quantitatively captured (factor of 2 vs 2.5 from experiment). However, moderate adjustment of the van der Waals ranges by less than 20% (for NVT) and 7.5% (for NVE), respectively, leads to almost quantitative agreement with experiment. Analysis of the energy redistribution establishes that the major pathway for CN(-) relaxation in H2O or D2O proceeds through coupling to the water-bending plus libration mode.

Instantaneous normal modes and the protein glass transition

In the instantaneous normal mode method, normal mode analysis is performed at instantaneous configurations of a condensed-phase system, leading to modes with negative eigenvalues. These negative modes provide a means of characterizing local anharmonicities of the potential energy surface. Here, we apply instantaneous normal mode to analyze temperature-dependent diffusive dynamics in molecular dynamics simulations of a small protein (a scorpion toxin). Those characteristics of the negative modes are determined that correlate with the dynamical (or glass) transition behavior of the protein, as manifested as an increase in the gradient with T of the average atomic mean-square displacement at approximately 220 K. The number of negative eigenvalues shows no transition with temperature. Further, although filtering the negative modes to retain only those with eigenvectors corresponding to double-well potentials does reveal a transition in the hydration water, again, no transition in the protein is seen. However, additional filtering of the protein double-well modes, so as to retain only those that, on energy minimization, escape to different regions of configurational space, finally leads to clear protein dynamical transition behavior. Partial minimization of instantaneous configurations is also found to remove nondiffusive imaginary modes. In summary, examination of the form of negative instantaneous normal modes is shown to furnish a physical picture of local diffusive dynamics accompanying the protein glass transition.

Resilience of the iron environment in heme proteins

Conformational flexibility is essential to the functional behavior of proteins. We use an effective force constant introduced by Zaccai, the resilience, to quantify this flexibility. Site-selective experimental and computational methods allow us to determine the resilience of heme protein active sites. The vibrational density of states of the heme Fe determined using nuclear resonance vibrational spectroscopy provides a direct experimental measure of the resilience of the Fe environment, which we compare quantitatively with values derived from the temperature dependence of atomic mean-squared displacements in molecular dynamics simulations. Vibrational normal modes in the THz frequency range dominate the resilience. Both experimental and computational methods find a higher resilience for cytochrome c than for myoglobin, which we attribute to the increased number of covalent links to the peptide in the former protein. For myoglobin, the resilience of the iron environment is larger than the average resilience previously determined for hydrogen sites using neutron scattering. Experimental results suggest a slightly reduced resilience for cytochrome c upon oxidation, although the change is smaller than reported in previous Mössbauer investigations on a bacterial cytochrome c, and is not reproduced by the simulations. Oxidation state also has no significant influence on the compressibility calculated for cyt c, although a slightly larger compressibility is predicted for myoglobin.

Dynamics of essential collective motions in proteins: theory

A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.

Vibrational Energy Relaxation of Isotopically Labeled Amide I Modes in Cytochrome c: Theoretical Investigation of Vibrational Energy Relaxation Rates and Pathways

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes. Key differences of VER among different amide I modes are demonstrated, leading to a detailed picture of the spatial anisotropy of the VER. The results support the experimental observation that amide I modes in proteins relax with subpicosecond time scales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.

Vibrational dynamics of N–H, C–D, and CO modes in formamide

By means of heterodyned two-dimensional IR photon echo experiments on liquid formamide and isotopomers the vibrational frequency dynamics of the N-H stretch mode, the C-D mode, and the C=O mode were obtained. In each case the vibrational frequency correlation function is fitted to three exponentials representing ultrafast (few femtoseconds), intermediate (hundreds of femtoseconds), and slow (many picoseconds) correlation times. In the case of N-H there is a significant underdamped contribution to the correlation decay that was not seen in previous experiments and is attributed to hydrogen-bond librational modes. This underdamped motion is not seen in the C-D or C=O correlation functions. The motions probed by the C-D bond are generally faster than those seen by N-H and C=O, indicating that the environment of C-D interchanges more rapidly, consistent with a weaker C-D...O=C bond. The correlation decays of N-H and C=O are similar, consistent with both being involved in strong H bonding.

Vibrational dephasing and hydrodynamic effects on vibrational relaxation rates in acetophenone: Raman bandshape analysis

The isotropic component of Raman band for C=O stretching mode of acetophenone in solution was analyzed by estimating the correlation coefficient with reference to Lorentzian lineshape. In the intermediate region of solute/solvent concentration there is a sharp decrease in the correlation coefficient and there appears to be a transition from non-Lorentzian to Lorentzian lineshape. The vibrational relaxation rates have been estimated from the isotropic component of Raman band in different solvents. The rate is shown to be dependent on several macroscopic as well as microscopic properties of the solute-solvent system and intermolecular interactions. The hydrodynamic and dispersion forces appear to play a major role in determining the vibrational relaxation rate and the broadening of the bands.

Vibrational energy relaxation in proteins

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied by using two theoretical approaches. One approach is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach, which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in similar estimates of the VER time (subpicoseconds) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with previous experimental data. A perspective on directions for the detailed study of time scales and mechanisms of VER in proteins is presented.

MoViES: molecular vibrations evaluation server for analysis of fluctuational dynamics of proteins and nucleic acids

Analysis of vibrational motions and thermal fluctuational dynamics is a widely used approach for studying structural, dynamic and functional properties of proteins and nucleic acids. Development of a freely accessible web server for computation of vibrational and thermal fluctuational dynamics of biomolecules is thus useful for facilitating the relevant studies. We have developed a computer program for computing vibrational normal modes and thermal fluctuational properties of proteins and nucleic acids and applied it in several studies. In our program, vibrational normal modes are computed by using modified AMBER molecular mechanics force fields, and thermal fluctuational properties are computed by means of a self-consistent harmonic approximation method. A web version of our program, MoViES (Molecular Vibrations Evaluation Server), was set up to facilitate the use of our program to study vibrational dynamics of proteins and nucleic acids. This software was tested on selected proteins, which show that the computed normal modes and thermal fluctuational bond disruption probabilities are consistent with experimental findings and other normal mode computations. MoViES can be accessed at http://ang.cz3.nus.edu.sg/cgi-bin/prog/norm.pl.