Nonexponential Kinetics Research Articles

Simulation of the kinetics of ligand binding to a protein by molecular dynamics: geminate rebinding of nitric oxide to myoglobin.

We have begun to use molecular dynamics to simulate the kinetics of nitric oxide rebinding to myoglobin after photodissociation. Rebinding was simulated using a potential function that switches smoothly between a nonbinding potential and a binding potential as a function of the position and orientation of the ligand, with no barrier arising from the crossing of potential surfaces of different electron spin. In 96 of 100 trajectories, the ligand rebound in < 15 ps. The kinetic progress curve was obtained by determining the time in each trajectory at which the ligand rebound and then calculating the fraction of unbound ligands as a function of time. The curve can be well reproduced by a simple model based on the dynamics of a Langevin particle moving on a one-dimensional potential of mean force calculated from nonreactive protein trajectories. The rate of escape from the energy well adjacent to the heme is in good agreement with the value calculated from experimental data, suggesting that a multiple-well model provides a plausible explanation for the nonexponential rebinding kinetics. A transition-state analysis suggests that protein conformational relaxation coupled to the displacement of the iron from the heme plane is an unlikely cause for the nonexponential rebinding of nitric oxide.

Nonexponential generation-recombination dynamics in doped semiconductors as a possible source of high-frequency 1/f noise.

We present a theoretical study of generation-recombination processes from shallow impurities which includes self-consistently the contribution of the impurity excited levels. Making use of an original Monte Carlo simulation which accounts for both the kinetic energy of the carrier and its potential energy near the impurity, we have solved the semiclassical Boltzmann equation to investigate the dynamics of generation-recombination processes on a kinetic level. Calculations performed for the case of p-type Si clearly evidence a nonexponential distribution of the microscopic times spent by the carriers in the impurity centers and in the conducting band. This in turn leads to the impossibility of a rigorous definition of a carrier lifetime and therefore to a possible source of high-frequency 1/f noise. The theory is found to compare favorably with available experiments.

Non-exponential structural relaxation, anomalous light scattering and nanoscale inhomogeneities in glass-forming liquids

Light scattering from glass-forming liquids exhibits an anomalous time dependence in the glass transition region, e.g. maxima in the scattering intensity versus temperature curves during heating. It is shown that this behavior is consistent with the presence of nanoscale inhomogeneities (density fluctuations) which relax at different rates. It is suggested that this could be the source of non-exponential structural relaxation kinetics. An expression relating the size of these regions to structural relaxation kinetic parameters has been developed and predicts sizes in excellent agreement with those determined by other methods.

Phenylalanine fluorescence and phosphorescence used as a probe of conformation for cod parvalbumin

The fluorescence emission and triplet absorption properties of phenylalanine in cod fish parvalbumin type II, a protein that contains no Trp or Tyr, was examined in the time scale ranging from nanoseconds to microseconds at 25°C in aqueous buffer (pH 7.0). In the presence of Ca(II), the decay of fluorescence gave two lifetimes (5.9 and 53 ns) and the triplet lifetime was 425 μs. Upon removal of Ca, the fluorescence intensity decreased to values approaching that for free Phe, while the longest fluorescence decay component was 17 ns. At the same time, the decay of triplet showed complex nonexponential kinetics with decay rates faster than in the presence of Ca. Quenching and denaturation analyses suggest that the Phe's are present in a hydrophobic environment in the Ca-bound protein but that the Ca-free protein is relatively unstructured. It is concluded that Phe luminescence in proteins is sensitive to conformation and that the long lifetime of Phe excited states needs to be considered when studying its photochemistry in proteins.

Structural relaxation and nonexponential kinetics of CO-binding to horse myoglobin. Multiple flash photolysis experiments

The geminate recombination kinetics of CO-myoglobin strongly deviates from single exponential behavior in contrast to what is expected for unimolecular reactions (1). At low temperatures, this result was attributed to slowly exchanging conformational states which differ substantially in barrier height for ligand binding. Above 160 K the kinetics apparently slow down with temperature increase. Agmon and Hopfield (2) explain this result in terms of structural relaxation perpendicular to the reaction coordinate, which enhances the activation energy. In their model, structural relaxation homogenizes the kinetic response. Recently, Steinbach et al. (3) proposed a relaxation model which conserves the kinetic inhomogeneity. Below we test these conjectures by single and multiple excitation experiments. This method allows for discrimination between parallel (inhomogeneous) and sequential (homogeneous) kinetic schemes. The kinetic anomaly above 160 K is shown to result from a homogeneous, structurally relaxed intermediate. However a second anomaly is found above 210 K concerning the inhomogeneous phase which may indicate either a shift in activation energy or entropy.

Capture of hot holes by shallow acceptors in p-type GaAs studied by picosecond infrared spectroscopy.

Picosecond recombination of free holes with shallow acceptors in p-doped GaAs is directly monitored via spectrally and temporally resolved infrared studies. Neutral Zn impurities are photoionized by picosecond excitation in the wavelength range around 5 \ensuremath{\mu}m. The recombination dynamics of the free carriers with ionized acceptors is measured via transient changes of the acceptor deionization band at photon energies close to the band gap. Hole capture is observed on a time scale of up to 100 ps following nonexponential kinetics. The data are analyzed with the help of model calculations considering single-step as well as multiple-step trapping mechanisms. Emission of single longitudinal-optical phonons is found to be the main mechanism of picosecond recombination.

Excited states of tryptophan in cod parvalbumin. Identification of a short-lived emitting triplet state at room temperature

The fluorescence and phosphorescence spectra of model indole compounds and of cod parvalbumin III, a protein containing a single tryptophan and no tyrosine, were examined in the time scale ranging from subnanoseconds to milliseconds at 25 degrees C in aqueous buffer. For both Ca- bound and Ca-free parvalbumin and for model indole compounds that contained a proton donor, a phosphorescent species emitting at 450 nm with a lifetime of approximately 20-40 ns could be identified. A longer-lived phosphorescence is also apparent; it has approximately the same absorption and emission spectrum as the short-lived triplet molecule. For Ca parvalbumin, the decay of the long-lived triplet tryptophan is roughly exponential with a lifetime of 4.7 ms at 25 degrees C whereas for N-acetyltryptophanamide in aqueous buffer the decay lifetime was 30 microseconds. In contrast, the lifetime of the long-lived tryptophan species is much shorter in the Ca-free protein compared with Ca parvalbumin, and the decay shows complex nonexponential kinetics over the entire time range from 100 ns to 1 ms. It is concluded that the photochemistry of tryptophan must take into account the existence of two excited triplet species and that there are quenching moieties within the protein matrix that decrease the phosphorescence yield in a dynamic manner for the Ca-depleted parvalbumin. In contrast, for Ca parvalbumin, the tryptophan site is rigid on the time scale of milliseconds.

Using saturation-recovery EPR to measure exchange couplings in proteins: application to ribonucleotide reductase

The stable tyrosine radical of ribonucleotide reductase (RNR) from Escherichia coli, Tyr 122 of the B2 subunit, exhibits single-exponential spin-lattice relaxation lunetics for T≤16 K and nonexponential spin-lattice relaxation kinetics at higher temperatures. Saturation-recovery transients of the tyrosine radical are analyzed using a model developed to treat the interaction of two paramagnets in a rigid lattice at a fixed distance apart but with a randon orientation in the static magnetic field

Picosecond capture of photoexcited holes by shallow acceptors in p-type GaAs.

Ultrafast recombination of holes with shallow acceptors in a III-V semiconductor is directly observed for the first time, by means of picosecond infrared spectroscopy. Neutral impurities in p-doped GaAs at low temperature are photoionized by picosecond infrared excitation. The recombination of free holes with negatively charged acceptors---monitored via absorption changes below the band edge---occurs on a time scale of several tens of picoseconds, following a nonexponential kinetics. Emission of longitudinal-optical phonons by the free holes is found to be the dominant mechanism of recombination.

Inhomogeneous broadening and kinetic carbon monoxide isotope effects in low-temperature carbon monoxide recombination with myoglobin and hemoglobin.

We have analyzed the non-exponential kinetics, the temperature variation, and the CO isotope effects of the CO recombination reactions with myoglobin and single-chain hemoglobin. The analysis rests on multiphonon quantum-mechanical chemical-rate theory combined with static inhomogeneous broadening of either the reorganization free energy or the reaction Gibbs free energy. The simplest specific model which can account for all the data contains an inhomogeneous distribution function of width 0.2-0.3 eV, independent of temperature down to the tunnel transition at about 20 K, two discrete nuclear coordinates of low vibrational frequency (60-150 cm-1) representing iron-heme and CO bending motion, the CO stretching motion of frequency about 2000 cm-1, and additional inhomogeneous broadening of the protein and CO bending configuration below the tunnel transition temperature. The model appears somewhat involved but in return provides corresponding insight in the dynamics of this important class of processes.

PHOTOCHEMISTRY ON SURFACES. EXCITED STATE BEHAVIOR OF RUTHENIUM TRIS(BATHOPHENANTHROLINE DISULFONATE) ON COLLOIDAL ALUMINA-COATED SILICA PARTICLES

Abstract— The excited state behavior of an anionic ruthenium(II) complex, RuL34-(L=bathophen-anthroline disulfonate), that is electrostatically bound to positively charged alumina-coated silica particles is investigated. The apparent association constant for the binding of RuL34-to the particles is 1.2 × 104M-1. Surface photochemical processes result in decreased emission yields and multiexponential excited state decay. Excited state quenching by ground-state molecules is evident at high surface coverages. The non-exponential decay kinetics observed at low surface coverages can be attributed either to clustering of the RuL34-molecules or photoionization promoted by Lewis acid sites on the particle surface.

Heterogeneous distributions and dispersive photodissociation rates of benzo[a]pyrene diol-epoxide enantiomer-DNA and -poly (dG-dC) · poly (dG-dC) adducts

Two types of heterogeneity of adducts are illustrated and discussed utilizing non-line narrowed ( S 2← S 0 laser excitation) and line-narrowed (excitation into the (0,0) origin band) fluorescence spectra at low temperatures. The first type (type A) is due to structurally distinct and/or energetically inequivalent conformers. The second one (type B) is provided by an inhomogeneous environment of DNA and polynucleotides. In light of the above, the non-exponential photodissociation kinetics of the (±)- anti-BPDE-DNA and -polynucleotide adducts have been reanalyzed in terms of a dispersive first order chemical reaction, where the inhomogeneous effects are explicitly included. It is demonstrated that the DNA structure shows considerable inhomogeneous broadening, and that type B heterogeneity is responsible for the dispersive photodissociation process. The latter is accounted for by a Gaussian distribution of activation energies, with the center of the distribution at ≈ 600 meV and the full width at half-maximum equal to ≈ 50 meV (≈ 2 kT). Photolabile (±)- anti-BPDE- DNA and -polynucleotide adducts are identified as quasi-intercalated (site 1) (+)- and (−)- cis-BPDE. The calculated concentrations of cis-BPDE adducts in DNA and polynucleotides from the kinetic data are in very good agreement with the cis-BPDE adduct concentrations obtained from the spectral and/or chemical analysis. The average photodissociation rate and the photodissociation quantum yield of cis- and trans-BPDE adducts are also estimated.

Photochemical isomerization in the absence of a potential barrier: origin of wavelength-dependent ground-state recovery kinetics

The photophysics and isomerization dynamics in the excited state of the molecule 1,1′-diethyl-4,4′-cyanine have been investigated. Earlier studies have indicated that the isomerization of this molecule is of the barrierless type. As such, it displays some interesting properties of the excited-state relaxation dynamics. In the present work, we investigate in detail the wavelength dependence of the observed ground-state recovery lifetimes, and show that this dependence is due to a dependence on the analyzing wavelength. We believe that the origin of the effect is the admixture of non-exponential fluorescence-decay components into the ground-state recovery signal. This results in apparently faster and non-exponential ground-state recovery kinetics in the part of the absorption spectrum, overlapping with the fluorescence spectrum.

Investigation of laser-induced long-lived states of photolyzed MbCO

We present evidence from resonance Raman and absorption measurements that the extended exposure of MbCO to CW laser light at low temperatures alters the CO rebinding kinetics and leads to a significantly increased population of very long lived states of photolyzed MbCO. This optical "pumping" process is observed for samples frozen in both aqueous buffer and glycerol/buffer and exhibits power law behavior with a very weak temperature dependence. A comparison of the nonexponential rebinding kinetics of CO molecules from the pumped states with the rebinding observed in flash photolysis experiments suggests that the pumped states are distinct geminate states, not observed in flash photolysis experiments. Thus, a four-state model, with two geminate states, is implicated for MbCO. Pumped states may represent "separated geminate pair" states with the CO molecule still in the heme pocket or possibly trapped within a cavity on its way through the protein matrix, consistent with molecular dynamics simulations. The possibility of significant deoxyheme relaxation from a less domed to a more domed configuration, as a result of the multiple photolysis events associated with the pumping process, is also explored. However, the small changes observed in the Soret band line shape and position subsequent to pumping at T less than 180 K tend to rule out this explanation for the pumping process. Since the yield for creating a pumped state is small (e.g., less than 10(-7) for T greater than 100 K), pumping can be observed only after extended illumination and is absent in flash photolysis measurements, even after multiple flashes. At higher temperatures (T greater than 180 K), the escape of the CO molecule to the solvent is observed. Our data are consistent with a "phase transition" of the protein that is coupled to the surrounding matrix. The protein fluctuations are quenched below approximately 185 K for a solvent composed of 70% glycerol and below approximately 260 K for aqueous buffer. We also present the first large amplitude measurements of CO rebinding from the protein exterior, observed below 200 K after freezing the sample under laser illumination.

Temperature dependence of the initial electron-transfer kinetics in photosynthetic reaction centers of Chloroflexus aurantiacus

Absorbance changes in the near infrared were measured in photosynthetic reaction centers of the thermophilic, gliding, green bacterium Chloroflexus aurantiacus over the temperature range from 80 to 320 K, using 605-nm excitation pulses with an autocorrelation width of about 0.8 ps. Spectra collected during the first 1.5 ps after excitation show stimulated emission from the excited singlet state P*, absorbance increases at 762 and 802 nm, and absorbance decreases in the 865-nm band and at 783 and 815 nm. The absorbance changes associated with the formation of P* suggest that the electronic transitions in the ground-state spectrum are strongly mixed. Spectra collected up to 90 ps after the excitation pulse show the decay of the stimulated emission, and bleaching at 750 nm and 815 nm, reflecting the transfer of an electron from the bacteriochlorophyll dimer (P) to the initial electron acceptor(s). The electron-transfer reaction is slower in C. aurantiacus than in reaction centers of purple bacterial species; P* decays with a time-constant of 7.1±0.5 ps at 296 K and 9.0±0.1 ps at 320 K. At lower temperatures, the kinetics are non-exponential. The decay of the stimulated emission at 80 K can be fit either with a biexponential function with time constants of 3.0±0.1 and 32±12 ps, or with a stretched exponential function [exp — (t/τ0)α] with τ0 = 4.1 ± 1.2 ps and α = 0.45 ± 0.06. Several models that might account for the nonexponential decay kinetics of P* are discussed. A model based on rapid interconversion among conformational states in P* provides a simple interpretation of the temperature dependence of the kinetics.

Ligand binding and protein relaxation in heme proteins: a room temperature analysis of nitric oxide geminate recombination

Ultrafast absorption spectroscopy is used to study heme-NO recombination at room temperature in aqueous buffer on time scales where the ligand cannot leave its cage environment. While a single barrier is observed for the cage recombination of NO with heme in the absence of globin, recombination in hemoglobin and myoglobin is nonexponential. Examination of hemoglobin with and without inositol hexaphosphate points to proximal constraints as important determinants of the geminate rebinding kinetics. Molecular dynamics simulations of myoglobin and heme-imidazole subsequent to ligand dissociation were used to investigate the transient behavior of the Fe-proximal histidine coordinate and its possible involvement in geminate recombination. The calculations, in the context of the absorption measurements, are used to formulate a distinction between nonexponential rebinding that results from multiple protein conformations (substates) present at equilibrium or from nonequilibrium relaxation of the protein triggered by a perturbation such as ligand dissociation. The importance of these two processes is expected to depend on the time scale of rebinding relative to equilibrium fluctuations and nonequilibrium relaxation. Since NO rebinding occurs on the picosecond time scale of the calculated myoglobin relaxation, a time-dependent barrier is likely to be an important factor in the observed nonexponential kinetics. The general implications of the present results for ligand binding in heme proteins and its time and temperature dependence are discussed. It appears likely that, at low temperatures, inhomogeneous protein populations play an important role and that as the temperature is raised, relaxation effects become significant as well.

Electrostatic effects on the kinetics of electron transfer reactions of cytochrome c caused by binding to negatively charged lipid bilayer vesicles

The effect of binding reduced tuna mitochondrial cytochrome c to negatively charged lipid bilayer vesicles at low ionic strength on the kinetics of electron transfer to various oxidants was studied by stopped-flow spectrophotometry. Binding strongly stimulated (up to 100-fold) the rate of reaction with the positively charged cobalt phenanthroline ion, whereas the rate of reaction with the negatively charged ferricyanide ion was greatly inhibited (up to 60-fold), as compared with the same systems either at high ionic strength or at low ionic strength either in the presence of electrically neutral vesicles or in the absence of vesicles. Reactions of tuna cytochrome c with uncharged or electrically neutral oxidants such as benzoquinone and Rhodospirillum rubrum cytochrome c 2 were unaffected by binding to vesicles, suggesting little or no effect of membrane association on cytochrome structure or accessibility of the heme center. The kinetic effects were largest at lower cytochrome c to vesicle ratios, where there was a greater degree of exposure of negatively charged regions on the membrane. The reduction of cobalt phenanthroline and ferricyanide by bound cytochrome c proceeded by nonexponential kinetics, as compared with the monophasic kinetics observed in the absence of vesicles. This was probably due to the heterogeneous distribution of vesicle sizes which exists at a given lipid to protein ratio. Nonlinear oxidant concentration dependencies were observed for cobalt phenanthroline oxidation of membrane-bound cytochrome c, consistent with a (minimal) two-step kinetic mechanism involving association of the oxidant with the membrane followed by electron transfer. Based on a comparison of second-order rate constants as a function of lipid to protein mole ratio, binding of cytochrome c to the bilayer increased the efficiency of the cobalt phenanthroline reaction by a factor of approximately 500 at the highest lipid:protein ratio used. The results suggest a mechanism involving attractive and repulsive electrostatic interactions between the negatively charged bilayer and the electrically charged oxidants, which increase or decrease their effective concentrations at the membrane surface.

Nonexponential solvation dynamics of simple liquids and mixtures

Novel measurements on the microscopic solvation dynamics of coumarin probes in several simple polar solvents and solvent mixtures have been made using the time dependent fluorescence Stokes shift technique. The microscopic solvent relaxation function, C( t), is observed to be poorly modeled by a single exponential decay in many cases. The average experimental solvation times,<τ s >, for pure solvents and binary solvent mixtures are close to values predicted by dielectric continuum theory, but in many cases, the observed C( t) shape does not agree with that predicted by dielectric continuum theory. The results suggest that molecular motion of solvent molecules near the solute can be responsible for microscopic solvation components of C( t) that are not predicted using bulk dielectric data of the neat solvent and the dielectric continuum theory. In addition to the solvation dynamics results, some potential sources of probe molecule non-ideality are examined, and it is shown that these effects are not significant contributors to experimental error for these C( t) measurements.

Electron spin-lattice relaxation and spectral diffusion measurements on tyrosine radicals in proteins

The electron spin-lattice relaxation and spectral diffusion properties at 22 K have been examined for three tyrosine radicals: the stable tyrosine radical Y D + in photosystem II (PSII), the tyrosine radical in the B2 subunit of ribonucleotide reductase from Escherichia coli, and a model L-tyrosine radical prepared in a frozen glass by UV irradiation at 77 K. The relaxation transients obtained by the method of saturation recovery, where recovery from saturation following a microwave pulse is detected by a low continuous observation microwave level, were compared to those obtained by the inversion-recovery and spin-echo-detected saturation-recovery techniques. The same values for the electron spin-lattice relaxation rate 1 T 1 were obtained by saturation recovery and spin-echo-detected saturation recovery provided that spectral diffusion channels were saturated by a sufficiently long microwave pulse. The inversion-recovery spin-echo method produced relaxation transients that were more rapidly decaying than those of either of the saturation-recovery methods, owing to the presence of spectral diffusion. Two contributions to spectral diffusion were observed. For the UV-generated model L-tyrosine radical, the dominant contribution to spectral diffusion occurred on the time scale of the electron spin-spin relaxation time T 2 and was saturated with a microwave pulse lasting only 50 μs. The spectral diffusion processes for the tyrosine radicals in the proteins occurred on the time scale of T 1; a saturating microwave pulse of duration greater than 3–5 ms was required to completely saturate these spectral diffusion processes. These slow spectral diffusion processes are likely to involve electron-nuclear spin-spin interactions. It is probable that the large separation between radicals imposed by the dimensions of the protein prevents spectral diffusion paths due to interactions between tyrosine radicals on the time scale of T 2. The UV-generated l-tyrosine radical and the tyrosine radical in ribonucleotide reductase exhibited predominantly single-exponential relaxation kinetics when very long saturating pulses were employed. The tyrosine radical in PSII, however, exhibited nonexponential relaxation kinetics even at the extrapolated limit of infinitely long saturating pulses, where contributions from spectral diffusion have been eliminated. We suggest that spin-spin interactions of the tyrosine radical with neighboring paramagnetic site (s) are the source of the deviation from exponential relaxation kinetics in PSII.

Femtosecond probing of persistent wave packet motion in dissociative reactions: up to 40 ps

Femtosecond probing of nuclear motion in an alkali halide (Na I) reaction reveals a persistent wave packet, recurring at long times up to 40 ps. The detection of both “free” Na atoms and “transient” [Na…I] ≠ * indicates non-exponential dynamics through the crossing zone of the covalent and ionic potential energy curves. These observations are related to the nature of the motion, and the level structure making the packet.