Fast protein dynamics probed with infrared vibrational echo experiments

Genetically encoded non-canonical amino acids reveal asynchronous dark reversion of chromophore, backbone and side-chains in EL222

Photoreceptors containing the light-oxygen-voltage (LOV) domain elicit biological responses upon excitation of their flavin mononucleotide (FMN) chromophore by blue light. The mechanism and kinetics of dark-state recovery are not well understood. Here we incorporated the non-canonical amino acid p-cyanophenylalanine (CNF) by genetic code expansion technology at forty-five positions of the bacterial transcription factor EL222. Screening of light-induced changes in infrared (IR) absorption frequency, electric field and hydration of the nitrile groups identified residues CNF31 and CNF35 as reporters of monomer/oligomer and caged/decaged equilibria, respectively. Time-resolved multi-probe UV/Visible and IR spectroscopy experiments of the lit-to-dark transition revealed four dynamical events. Predominantly, rearrangements around the A'α helix interface (CNF31 and CNF35) precede FMN-cysteinyl adduct scission, folding of α-helices (amide bands), and relaxation of residue CNF151. This study illustrates the importance of characterizing all parts of a protein and suggests a key role for the N-terminal A'α extension of the LOV domain in controlling EL222 photocycle length. This article is protected by copyright. All rights reserved.

Molecular Simulation-Guided Spectroscopy of Imidazolium-Based Ionic Liquids and Effects of Methylation on Ion-Cage and -Pair Dynamics

Classical molecular dynamics simulations were performed to assess an atomistic interpretation of the ion-probe structural interactions in two typical ionic liquids (ILs), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [BMIm][NTf₂] and 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide [BDimIm][NTf₂] through computational ultrafast spectroscopy. The nitrile stretching vibrations of the thiocyanate anion, [SCN]^-, serve as the local mode of the ultrafast system dynamics within the imidazolium-based ionic liquid environment. The wavelet transform of classical trajectories determines the time-varying fluctuating frequencies and the stretch spectral signatures of SCN^- in the normalized distribution. However, computational modeling of the two-dimensional (2D) spectra from the wavelet-derived vibrational frequencies yields time evolution of the local molecular structure along with the varied time-dependent dynamics of the spectral diffusion process. We calculated the frequency-frequency correlation functions (FFCFs), time correlations associated with the ion-pair and -cage dynamics, and mean square displacements as a function of time, depicting diffusive dynamics. The calculated results based on the pair correlation functions and the distribution of atomic density suggest that the hydrogen and methylated carbon at the two-position of the imidazolium ring of [BMIm] and [BDimIm] cations, respectively, strongly interact with the probe through the N of the thiocyanate anion rather than the S atom. The center-of-mass center-of-mass (COM-COM) cation-probe radial distribution functions (RDFs) in conjunction with the site-specific structural analysis further reveal well-structured interactions of the thiocyanate ion and [BMIm]⁺ cation rather than the [BDimIm] cation. In contrast, the anion-probe COM-COM RDFs depict weak interactive associations within the vibrational probe [SCN]^- and [NTf₂]^- ions. Methylation at the two-position of the imidazolium ring predicts slower structural reorganization and breaking and reformation dynamics of the ion pairs and cages within the ionic liquid framework.

Low-Frequency Vibrational Motions of Polystyrene in Carbon Tetrachloride: Comparison with Model Monomer and Dependence on Concentration and Molecular Weight

In this study, the low-frequency vibrational dynamics of polystyrene (PS) in CCl₄ was investigated by femtosecond Raman-induced Kerr effect spectroscopy. Ethylbenzene (EBz) was also investigated as a model monomer of the polymer to elucidate the unique dynamical features of PS in solution. The broadened low-frequency spectrum of the PS/CCl₄ in the frequency region below 150 cm^-1 is significantly different from that of the EBz/CCl₄. Difference spectra between the PS or EBz solutions and neat CCl₄, normalized to an internal vibrational mode of CCl₄, clearly show a much lower spectral intensity for the PS/CCl₄ than the EBz/CCl₄ in the low-frequency region below ca. 20 cm^-1. This indicates that translational motions are suppressed in the PS/CCl₄ compared to the EBz/CCl₄. Moreover, the high-frequency motion at ca. 70 cm^-1, mainly due to phenyl ring librations, occurs at higher frequency in PS (78 cm^-1) than EBz (65 cm^-1). In addition, the results of concentration-dependent experiments show that the first moment (M₁) of the low-frequency difference spectra of both PS/CCl₄ and EBz/CCl₄ is almost independent of the concentration. The molecular weight dependence of the low-frequency spectrum in the PS/CCl₄ shows that the M₁ value of the low-frequency spectral band of PS shifts to higher frequencies when the molecular weight of PS increases up to M_w = ∼1000, which corresponds approximately to the decamer, and then remains constant upon further increasing the molecular weight.

Vibrational energy redistribution during donor–acceptor electronic energy transfer: criteria to identify subsets of active normal modes

Photoinduced electronic energy transfer in conjugated donor–acceptor systems is naturally accompanied by intramolecular vibrational energy redistributions accepting an excess of electronic energy.

Role of hydration water in the onset of protein structural dynamics

Proteins are the molecular workhorses in a living organism. Their 3D structures are animated by a multitude of equilibrium fluctuations and specific out-of-equilibrium motions that are required for proteins to be biologically active. When studied as a function of temperature, functionally relevant dynamics are observed at and above the so-called protein dynamical transition (~240 K) in hydrated, but not in dry proteins. In this review we present and discuss the main experimental and computational results that provided evidence for the dynamical transition, with a focus on the role of hydration water dynamics in sustaining functional protein dynamics. The coupling and mutual influence of hydration water dynamics and protein dynamics are discussed and the hypotheses illustrated that have been put forward to explain the physical origin of their onsets.

Echo dephasing and heat capacity from constrained and unconstrained dynamics of triiodothyronine nuclear receptor protein

The objective of this study is to observe the echo feature curves, vibrational dephasing, and heat capacity of a protein-hormone system taking thyroid hormone receptor-beta (THR-β) as an example. Constrained and unconstrained molecular dynamics simulations are performed by implementing the theory of velocity reassignments to probe the phase coherent state in terms of echo pulses. The constrained vibrations are incorporated by adjusting rigid bonds to all hydrogen atoms with an integrator parameter of 2 fs/step in order to reduce the degrees of freedom whereas 1 fs/step is used in the free vibrations of the atomic cluster. The nature of temperature auto-correlation functions changes so that echo feature curves also show a distinct nature in the cases of constrained and unconstrained vibrations. There is a large variation in kinetic temperature and internal potential energy in the echo time zone. The temperature rate of change of internal potential energy is the main contributor to the heat capacity of the native state protein-hormone system. The heat capacity of proteins estimated from this technique is in good agreement with the values from experiments. This study shows that triiodothyronine (T3) hormone makes some differences in heat capacity upon binding to the THR-β ligand binding domain (LBD). The physical properties of unliganded THR-β and T3-bound THR-β LBD in the cases of constrained and unconstrained dynamics are observed distinctly under the effect of anharmonicity on the phase coherent state of normal modes and the dephasing time lies in a range of 0.6-0.8 ps when the systems are perturbed suddenly.

Revealing true coupling strengths in two-dimensional spectroscopy with sparsity-based signal recovery

Two-dimensional (2D) spectroscopy is used to study the interactions between energy levels in both the field of optics and nuclear magnetic resonance (NMR). Conventionally, the strength of interaction between two levels is inferred from the value of their common off-diagonal peak in the 2D spectrum, which is termed the cross peak. However, stronger diagonal peaks often have long tails that extend into the locations of the cross peaks and alter their values. Here, we introduce a method for retrieving the true interaction strengths by using sparse signal recovery techniques and apply our method in 2D Raman spectroscopy experiments.

Solvation dynamics of an ionic probe in choline chloride-based deep eutectic solvents

Study of the solvation dynamics of an ionic probe in different choline-based deep eutectic solvents shows that the process is controlled by the motions of the choline ions within the pseudo lattice formed by the solvent.

Hydrogen bond flexibility correlates with Stokes shift in mPlum variants

Fluorescent proteins have revolutionized molecular biology research and provide a means of tracking subcellular processes with extraordinary spatial and temporal precision. Species with emission beyond 650 nm offer the potential for deeper tissue penetration and lengthened imaging times; however, the origin of their extended Stokes shift is not fully understood. We employed spectrally resolved transient grating spectroscopy and molecular dynamics simulations to investigate the relationship between the flexibility of the chromophore environment and Stokes shift in mPlum. We examined excited state solvation dynamics in a panel of strategic point mutants of residues E16 and I65 proposed to participate in a hydrogen-bonding interaction thought responsible for its red-shifted emission. We observed two characteristic relaxation constants of a few picoseconds and tens of picoseconds that were assigned to survival times of direct and water-mediated hydrogen bonds at the 16-65 position. Moreover, variants of the largest Stokes shift (mPlum, I65V) exhibited significant decay on both time scales, indicating the bathochromic shift correlates with a facile switching between a direct and water-mediated hydrogen bond. This dynamic model underscores the role of environmental flexibility in the mechanism of excited state solvation and provides a template for engineering next-generation red fluorescent proteins.

Two-dimensional Raman-terahertz spectroscopy of water

Two-dimensional Raman-terahertz (THz) spectroscopy is presented as a multidimensional spectroscopy directly in the far-IR regime. The method is used to explore the dynamics of the collective intermolecular modes of liquid water at ambient temperatures that emerge from the hydrogen-bond networks water forming. Two-dimensional Raman-THz spectroscopy interrogates these modes twice and as such can elucidate couplings and inhomogeneities of the various degrees of freedoms. An echo in the 2D Raman-THz response is indeed identified, indicating that a heterogeneous distribution of hydrogen-bond networks exists, albeit only on a very short 100-fs timescale. This timescale appears to be too short to be compatible with more extended, persistent structures assumed within a two-state model of water.

Conformational analysis of Gly-Ala-NHMe in D(2)O and DMSO solutions: a two-dimensional infrared spectroscopy study

A relevant number of experiments on short peptides has been performed in recent years. One of the major problems rises from the simultaneous presence of slightly different conformers at equilibrium in solution. In the present paper, the conformational characteristics of the Gly-l-Ala-Methyl amide dipeptide in D2O and DMSO solutions are investigated by nonlinear IR spectroscopy. The pump-probe scheme with ultrashort mid-infrared pulses, in the Amide I region, is used to determine the mutual orientation of the two C═O bonds and the dynamics due to solute-solvent interactions. The coupling between Amide I modes is evaluated from both linear and 2D spectra. The interconversion between the different conformations occurs on time scales longer than the vibrational lifetime, and the spectral diffusion observed in 2D spectra is attributed to the solvent dynamics. Quantum mechanical calculations and molecular dynamics simulations are performed to identify the most stable geometries. By comparing the experimental and the theoretical data, we establish the prevalence of β-like polar conformers in both water and DMSO solvents.

Computational infrared and two-dimensional infrared photon echo spectroscopy of both wild-type and double mutant myoglobin-CO proteins

The CO stretching mode of both wild-type and double mutant ( T67R / S92D ) MbCO (carbonmonoxymyoglobin) proteins is an ideal infrared (IR) probe for studying the local electrostatic environment inside the myoglobin heme pocket. Recently, to elucidate the conformational switching dynamics between two distinguishable states, extensive IR absorption, IR pump-probe, and two-dimensional (2D) IR spectroscopic studies for various mutant MbCO's have been performed by the Fayer group. They showed that the 2D IR spectroscopy of the double mutant, which has a peroxidase enzyme activity, reveals a rapid chemical exchange between two distinct states, whereas that of the wild-type does not. Despite the fact that a few simulation studies on these systems were already performed and reported, such complicated experimental results have not been fully reproduced nor described in terms of conformational state-to-state transition processes. Here, we first develop a distributed vibrational solvatochromic charge model for describing the CO stretch frequency shift reflecting local electric potential changes. Then, by carrying out molecular dynamic simulations of the two MbCO's and examining their CO frequency trajectories, it becomes possible to identify a proper reaction coordinate consisting of His64 imidazole ring rotation and its distance to the CO ligand. From the 2D surfaces of the resulting potential of mean forces, the spectroscopically distinguished A1 and A3 states of the wild-type as well as two more substates of the double mutant are identified and their vibrational frequencies and distributions are separately examined. Our simulated IR absorption and 2D IR spectra of the two MbCO's are directly compared with the previous experimental results reported by the Fayer group. The chemical exchange rate constants extracted from the two-state kinetic analyses of the simulated 2D IR spectra are in excellent agreement with the experimental values. On the basis of the quantitative agreement between the simulated spectra and experimental ones, we further examine the conformational differences in the heme pockets of the two proteins and show that the double mutation, T67R / S92D , suppresses the A1 population, restricts the imidazole ring rotation, and increases hydrogen-bond strength between the imidazole Nε-H and the oxygen atom of the CO ligand. It is believed that such delicate change of distal His64 imidazole ring dynamics induced by the double mutation may be responsible for its enhanced peroxidase catalytic activity as compared to the wild-type myoglobin.

Molecular dynamics simulation and computational two-dimensional infrared spectroscopic study of model amyloid β-peptide oligomers

Molecular dynamics simulations were carried out to study the structure stability of model amyloid β40 (Aβ40) peptide oligomers, from monomer to hexamer, in aqueous solution at room temperature. The initial oligomer models were built by using the parallel in-register β-sheet fibril structure and then allowed to relax in the simulations. Our simulation results indicated that the stable Aβ40 monomer was a random coil, while the oligomer structures became more fibril-like with the increase of the peptide strands. Linear absorption and two-dimensional infrared spectra of the isotope-labeled oligomers were calculated and analyzed in detail, which revealed the differential secondary structural features characteristic of Aβ40 aggregation. A quantitative relation was established to make connection between the calculated spectra and experimental ensemble measurements.

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.

Computational strategy for tuning spectral properties of red fluorescent proteins

Computational methods of quantum chemistry are used to characterize structures and vertical excitation energies of the S(0)-S(1) optical transitions in the chromophore binding pockets of the red fluorescent proteins DsRed and of its artificial mutant mCherry. As previously shown, optimizing the equilibrium geometry configurations with B3LYP density functional theory, followed by ZINDO calculations of the electronic excitations, yields positions of the optical bands in good agreement with experimental data. These large scale quantum calculations elucidate the role of the hydrogen bonded network as well as point mutations in the absorption spectra of the DsRed and mCherry proteins. The effect of an external electric field applied to the fluorescent protein chromophores is examined and shows that such fields may result in large shifts in spectral bands. These strategies can be applied for rational design of the fluorescent proteins by site-directed mutagenesis.

Dynamics of a myoglobin mutant enzyme: 2D IR vibrational echo experiments and simulations

Myoglobin (Mb) double mutant T67R/S92D displays peroxidase enzymatic activity in contrast to the wild type protein. The CO adduct of T67R/S92D shows two CO absorption bands corresponding to the A(1) and A(3) substates. The equilibrium protein dynamics for the two distinct substates of the Mb double mutant are investigated by using two-dimensional infrared (2D IR) vibrational echo spectroscopy and molecular dynamics (MD) simulations. The time-dependent changes in the 2D IR vibrational echo line shapes for both of the substates are analyzed using the center line slope (CLS) method to obtain the frequency-frequency correlation function (FFCF). The results for the double mutant are compared to those from the wild type Mb. The experimentally determined FFCF is compared to the FFCF obtained from molecular dynamics simulations, thereby testing the capacity of a force field to determine the amplitudes and time scales of protein structural fluctuations on fast time scales. The results provide insights into the nature of the energy landscape around the free energy minimum of the folded protein structure.

Characterizing the dynamics of functionally relevant complexes of formate dehydrogenase

The potential for femtosecond to picosecond time-scale motions to influence the rate of the intrinsic chemical step in enzyme-catalyzed reactions is a source of significant controversy. Among the central challenges in resolving this controversy is the difficulty of experimentally characterizing thermally activated motions at this time scale in functionally relevant enzyme complexes. We report a series of measurements to address this problem using two-dimensional infrared spectroscopy to characterize the time scales of active-site motions in complexes of formate dehydrogenase with the transition-state-analog inhibitor azide (N(3)(-)). We observe that the frequency-frequency time correlation functions (FFCF) for the ternary complexes with NAD(+) and NADH decay completely with slow time constants of 3.2 ps and 4.6 ps, respectively. This result suggests that in the vicinity of the transition state, the active-site enzyme structure samples a narrow and relatively rigid conformational distribution indicating that the transition-state structure is well organized for the reaction. In contrast, for the binary complex, we observe a significant static contribution to the FFCF similar to what is seen in other enzymes, indicating the presence of the slow motions that occur on time scales longer than our measurement window.

Folding dynamics of a small protein at room temperature via simulated coherent two-dimensional infrared spectroscopy

Understanding protein folding is of fundamental and practical importance in chemistry and biology. Despite the great success that has been made in tackling this problem, a detailed knowledge of how the elementary processes such as hydrogen-bond formation occur during protein folding has remained largely elusive. Using the combined power of molecular dynamics simulation with electrostatic polarization and coherent two-dimensional infrared spectroscopy, we are able to delineate the order of the hydrogen-bond formation event of a 17-residue peptide during its folding from an extended state to the native α-helix state. The folding is carried out by a single trajectory room-temperature molecular dynamics simulation that includes the polarization effect of hydrogen bonding, which is critical to the successful folding of the peptide. The onset and evolution of the isotope-labeled amide I vibration diagonal and cross peaks on the simulated 2DIR spectra allow us to build a structure-spectrum connection, and thus provide a microscopic picture of the helix folding process.

Ultrafast proteinquake dynamics in cytochrome c

We report here our systematic studies of the heme dynamics and induced protein conformational relaxations in two redox states of ferric and ferrous cytochrome c upon femtosecond excitation. With a wide range of probing wavelengths from the visible to the UV and a site-directed mutation we unambiguously determined that the protein dynamics in the two states are drastically different. For the ferrous state the heme transforms from 6-fold to 5-fold coordination with ultrafast ligand dissociation in less than 100 fs, followed by vibrational cooling within several picoseconds, but then recombining back to its original 6-fold coordination in 7 ps. Such impulsive bond breaking and late rebinding generate proteinquakes and strongly perturb the local heme site and shake global protein conformation, which were found to completely recover in 13 and 42 ps, respectively. For the ferric state the heme however maintains its 6-fold coordination. The dynamics mainly occur at the local site, including ultrafast internal conversion in hundreds of femtoseconds, vibrational cooling on the similar picosecond time scale, and complete ground-state recovery in 10 ps, and no global conformation relaxation was observed.

Novel mechanism for temperature-independent transitions in flexible molecules: role of thermodynamic fluctuations

A novel physical mechanism is proposed to explain the temperature-independent transition reactions in molecular systems. The mechanism becomes effective in the case of conformation transitions between quasi-isoenergetic molecular states. It is shown that at room temperatures, stochastic broadening of molecular energy levels predominates the energy of low-frequency vibrations accompanying the transition. This leads to a cancellation of temperature dependence in the stochastically averaged rate constants. As an example, a physical interpretation of temperature-independent onset of P2X{3} receptor desensitization in neuronal membranes is provided.

Dynamical transition in a small helical peptide and its implication for vibrational energy transport

The two-dimensional infrared spectrum of an octameric helical peptide in chloroform was measured as a function of temperature. Isotope labeling of the carbonyl group of one of the amino acids was used to obtain information for an isolated vibration. The antidiagonal width of the 2D-IR signal, which is a measure of the homogeneous dephasing time T(2), is constant from 220 to 260 K (within experimental error), and increases steeply above. The homogeneous dephasing time of the carbonyl vibration is attributed to the flexibility of the system and/or its immediate surrounding. The system undergoes a dynamical transition at about 270 K, with similarities to the protein dynamical transition. Furthermore, the temperature dependence of the antidiagonal width strongly resembles that of the efficiency of vibrational energy transport along the helix, which has been studied in a recent paper (J. Phys. Chem. B 2008, 112, 15487). The connection between the two processes, structural flexibility and energy transport mechanism, is discussed.

Suppression of perturbed free-induction decay and noise in experimental ultrafast pump-probe data

We apply a Fourier filtering technique for the global removal of coherent contributions, like perturbed free-induction decay, and noise, to experimental pump-probe spectra. A further filtering scheme gains access to spectra otherwise only recordable by scanning the probe's center frequency with adjustable spectral resolution. These methods cleanse pump-probe data and allow improved visualization and simpler analysis of the contained dynamics. We demonstrate these filters using visible pump/mid-infrared probe spectroscopy of ligand dissociation in carboxyhemoglobin.

Integrated and dispersed photon echo studies of nitrile stretching vibration of 4-cyanophenol in methanol

By means of integrated and dispersed IR photon echo measurement methods, the vibrational dynamics of C-N stretch modes in 4-cyanophenol and 4-cyanophenoxide in methanol is investigated. The vibrational frequency-frequency correlation function (FFCF) is retrieved from the integrated photon echo signals by assuming that the FFCF is described by two exponential functions with about 400 fs and a few picosecond components. The excited state lifetimes of the C-N stretch modes of neutral and anionic 4-cyanophenols are 1.45 and 0.91 ps, respectively, and the overtone anharmonic frequency shifts are 25 and 28 cm(-1). At short waiting times, a notable underdamped oscillation, which is attributed to a low-frequency intramolecular vibration coupled to the CN stretch, in the integrated and dispersed vibrational echo as well as transient grating signals was observed. The spectral bandwidths of IR absorption and dispersed vibrational echo spectra of the 4-cyanophenoxide are significantly larger than those of its neutral form, indicating that the strong interaction between phenoxide and methanol causes large frequency fluctuation and rapid population relaxation. The resonance effects in a paradisubstituted aromatic compound would be of interest in understanding the conjugation effects and their influences on chemical reactivity of various aromatic compounds in organic solvents.

Exploring the molecular origins of protein dynamics in the active site of human carbonic anhydrase II

We present three-pulse vibrational echo measurements of azide ion bound to the active site Zn of human carbonic anhydrase II (HCA II) and of two separate active-site mutants Thr199 --> Ala (T199A) and Leu198 --> Phe (L198F). Because structural motions of the protein active site influence the frequency of bound ligands, the differences in the time scales of the frequency-frequency correlation functions (FFCFs) obtained from global fits to each set of data allow us to make inferences about the time scales of the active site dynamics of HCA II. Surprisingly, the deletion of a potential electrostatic interaction in results in very little change in the FFCF, but the insertion of the bulky phenylalanine ring in causes much faster dynamics. We conclude that the fast, sub-picosecond time scale in the correlation function is attributable to hydrogen bond dynamics, and the slow, apparently static contribution is due to the conformational flexibility of Zn-bound azide in the active site.

Ultrafast dynamics in reverse micelles

Recent advances in ultrafast laser technology have spurred investigations of microheterogeneous solutions. In particular, researchers have explored details of reverse micelles (RMs), which present isolated droplets of polar solvent sequestered from a continuous nonpolar phase by a surfactant layer. This review explores recent studies utilizing a variety of ultrafast laser techniques to uncover details about structure and dynamics in various RMs. Using ultrafast vibrational spectroscopy, researchers have probed hydrogen-bond dynamics and vibrational energy relaxation in RMs. These studies have developed our understanding of reverse micellar structure, identifying varying water environments in the RMs. In a plethora of experiments employing probe molecules, researchers have explored the confined environment presented by RMs and their impact on a range of chemical reactions. These studies have shown that confinement, rather than the specific interactions with surfactants, is an important factor determining the impact of the reverse micellar environment on the chemistry.

Native and unfolded cytochrome c--comparison of dynamics using 2D-IR vibrational echo spectroscopy

Unfolded vs native CO-coordinated horse heart cytochrome c (h-cyt c) and a heme axial methionine mutant cyt c552 from Hydrogenobacter thermophilus ( Ht-M61A) are studied by IR absorption spectroscopy and ultrafast 2D-IR vibrational echo spectroscopy of the CO stretching mode. The unfolding is induced by guanidinium hydrochloride (GuHCl). The CO IR absorption spectra for both h-cyt c and Ht-M61A shift to the red as the GuHCl concentration is increased through the concentration region over which unfolding occurs. The spectra for the unfolded state are substantially broader than the spectra for the native proteins. A plot of the CO peak position vs GuHCl concentration produces a sigmoidal curve that overlays the concentration-dependent circular dichroism (CD) data of the CO-coordinated forms of both Ht-M61A and h-cyt c within experimental error. The coincidence of the CO peak shift curve with the CD curves demonstrates that the CO vibrational frequency is sensitive to the structural changes induced by the denaturant. 2D-IR vibrational echo experiments are performed on native Ht-M61A and on the protein in low- and high-concentration GuHCl solutions. The 2D-IR vibrational echo is sensitive to the global protein structural dynamics on time scales from subpicosecond to greater than 100 ps through the change in the shape of the 2D spectrum with time (spectral diffusion). At the high GuHCl concentration (5.1 M), at which Ht-M61A is essentially fully denatured as judged by CD, a very large reduction in dynamics is observed compared to the native protein within the approximately 100 ps time window of the experiment. The results suggest the denatured protein may be in a glassy-like state involving hydrophobic collapse around the heme.

Classical nonlinear response of a chaotic system. I. Collective resonances

We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.