Nonexponential Kinetics Research Articles

Two-Dimensional Fluctuation Correlation Spectroscopy (2D-FlucCS): A Method to Determine the Origin of Relaxation Rate Dispersion.

Relaxation rate dispersion, i.e., nonexponential or multicomponent kinetics, is observed in complex systems when measuring relaxation kinetics. Often, the origin of rate dispersion is associated with the heterogeneity in the system. However, both homogeneous (where all molecules experience the same rate but inherently nonexponential) and heterogeneous (where all molecules experience different rates) systems can exhibit rate dispersion. A multidimensional correlation analysis method has been demonstrated to detect and quantify rate dispersion observed in molecular rotation, diffusion, solvation, and reaction kinetics. One-dimensional (1D) autocorrelation function detects rate dispersion and measures its extent. Two-dimensional (2D) autocorrelation function measures the origin of rate dispersion and distinguishes homogeneous from heterogeneous. In a heterogeneous system, implicitly there exist subensembles of molecules experiencing different rates. A three-dimensional (3D) autocorrelation function measures subensemble exchange if present and reveals if the system possesses static or dynamic heterogeneity. This perspective discusses the principles, applications, and potential and also presents a future outlook of two-dimensional fluctuation correlation spectroscopy (2D-FlucCS). The method is applicable to any experiment or simulation where a time series of fluctuation in an observable (emission, scattering, current, etc.) around a mean value can be obtained in steady state (equilibrium or nonequilibrium), provided the system is ergodic.

Symmetry-breaking charge transfer in an excited acridine-dione derivative: Effects of hydrogen bonding, clustering, and cooperativity in mixtures of methanol and dimethylformamide

A theory of fluorescence quenching of photoexcited centrosymmetric acridine-dione derivative induced by H-bonding interactions with solvent in mixtures of methanol (MeOH) and N,N-dimethylformamide (DMF) is developed. The theory takes into account both dynamic and static mechanisms of the quenching. An unusual threshold-type dependence of the quenching efficiency on the concentration of methanol in the mixture observed earlier in experiment is analyzed theoretically under the following assumptions: (i) individual MeOH molecules and their short hydrogen-bonded clusters form weak complexes with the dye in solution and these interactions do not affect fluorescence kinetics significantly, (ii) long clusters form strongly bound complexes with the dye and thus induce symmetry-breaking intramolecular charge transfer and efficient quenching of fluorescence. These assumptions are consistent with the cooperative character of H-bonding in alcohols and allow one to explain the observed absence of quenching at MeOH concentrations below ∼9 M. A model of H-bond clustering in mixtures of alcohols and H-bond-accepting solvents is developed. The suggested approach gives a quantitative description of the observed concentration dependence of the fluorescence yield and well reproduces the non-exponential kinetics of the fluorescence decay measured in experiments. Since the degree of the charge transfer dissymmetry in these processes is sensitive to interactions between the dye and solvent, new possibilities emerge for experimental studies on details of H-bond clustering in protic solvents.

Branching mechanism of photoswitching in an Fe(II) polypyridyl complex explained by full singlet-triplet-quintet dynamics

It has long been known that irradiation with visible light converts Fe(II) polypyridines from their low-spin (singlet) to high-spin (quintet) state, yet mechanistic interpretation of the photorelaxation remains controversial. Herein, we simulate the full singlet-triplet-quintet dynamics of the [Fe(terpy)2]2+ (terpy = 2,2’:6’,2”-terpyridine) complex in full dimension, in order to clarify the complex photodynamics. Importantly, we report a branching mechanism involving two sequential processes: a dominant 3MLCT→3MC(3T2g)→3MC(3T1g)→5MC, and a minor 3MLCT→3MC(3T2g)→5MC component. (MLCT = metal-to-ligand charge transfer, MC = metal-centered). While the direct 3MLCT→5MC mechanism is considered as a relevant alternative, we show that it could only be operative, and thus lead to competing pathways, in the absence of 3MC states. The quintet state is populated on the sub-picosecond timescale involving non-exponential dynamics and coherent Fe-N breathing oscillations. The results are in agreement with the available time-resolved experimental data on Fe(II) polypyridines, and fully describe the photorelaxation dynamics.

A Long Journey into the Investigation of the Structure–Dynamics–Function Paradigm in Proteins through the Activities of the Palermo Biophysics Group

An overview of the biophysics activity at the Department of Physics and Chemistry Emilio Segrè of the University of Palermo is given. For forty years, the focus of the research has been on the protein structure–dynamics–function paradigm, with the aim of understanding the molecular basis of the relevant mechanisms and the key role of solvent. At least three research lines are identified; the main results obtained in collaboration with other groups in Italy and abroad are presented. This review is dedicated to the memory of Professors Massimo Ugo Palma, Maria Beatrice Palma Vittorelli, and Lorenzo Cordone, which were the founders of the Palermo School of Biophysics. We all have been, directly or indirectly, their pupils; we miss their enthusiasm for scientific research, their deep physical insights, their suggestions, their strict but always constructive criticisms, and, most of all, their friendship. This paper is dedicated also to the memory of Prof. Hans Frauenfelder, whose pioneering works on nonexponential rebinding kinetics, protein substates, and energy landscape have inspired a large part of our work in the field of protein dynamics.

Isotope effects on the structural transformation and relaxation of deeply supercooled water.

We have examined the structure of supercooled liquid D2O as a function of temperature between 185 and 255K using pulsed laser heating to rapidly heat and cool the sample on a nanosecond timescale. The liquid structure can be represented as a linear combination of two structural motifs, with a transition between them described by a logistic function centered at 218K with a width of 10K. The relaxation to a metastable state, which occurred prior to crystallization, exhibited nonexponential kinetics with a rate that was dependent on the initial structural configuration. When the temperature is scaled by the temperature of maximum density, which is an isostructural point of the isotopologues, the structural transition and the non-equilibrium relaxation kinetics of D2O agree remarkably well with those for H2O.

Involvement of structural dynamics in charge-glass formation in strongly frustrated molecular metals

We present a combined study of thermal expansion and resistance fluctuation spectroscopy measurements exploring the static and dynamic aspects of the charge-glass formation in the quasi-two-dimensional organic conductors $\ensuremath{\theta}\text{\ensuremath{-}}({\mathrm{BEDT-TTF})}_{2}M{M}^{\ensuremath{'}}{(\mathrm{SCN})}_{4}$ with $M$ = Cs and ${M}^{\ensuremath{'}}$ = Co,Zn. In these materials, the emergence of a novel charge-glass state so far has been interpreted in purely electronic terms by considering the strong frustration of the Coulomb interactions on a triangular lattice. Contrary to this view, we provide comprehensive evidence for the involvement of a structural glasslike transition at ${T}_{\text{g}}\ensuremath{\sim}90\ensuremath{-}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This glassy transition can be assigned to the freezing of structural conformations of the ethylene endgroups in the donor molecule with an activation energy of ${E}_{\mathrm{a}}\ensuremath{\approx}0.32\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, and the concomitant slowing down of the charge-carrier dynamics is well described by a model of nonexponential kinetics. These findings disclose an important aspect of the phase diagram and calls for revisiting the present views of the glassy dynamics in the whole family of $\ensuremath{\theta}\text{\ensuremath{-}}({\mathrm{BEDT-TTF})}_{2}M{M}^{\ensuremath{'}}{(\mathrm{SCN})}_{4}$. Our results suggest that the entanglement of slow structural and charge-cluster dynamics due to the intimate coupling of lattice and electronic degrees of freedom determine the charge-glass formation under geometric frustration.

Dynamics of Strongly Interacting Fermi Gases with Time-Dependent Interactions: Consequence of Conformal Symmetry.

In this Letter, we investigate the effects of a time-dependent, short-ranged interaction on the long-time expansion dynamics of Fermi gases. We show that the effects of the interaction on the dynamics is dictated by how it changes under a conformal transformation, and derive an explicit criterion for the relevancy of time-dependent interactions near both the strongly and noninteracting scale invariant limits. In addition, we show that it is possible to engineer interactions that give rise to nonexponential thermalization dynamics in trapped Fermi gases. To supplement the symmetry analysis, we perform hydrodynamic simulations to show that the moment of inertia of the trapped gas indeed follows a universal time dependence that is determined jointly by the conformal symmetry and time-dependent scattering length a(t). Our results should also be relevant to the dynamics of other systems that are nearly scale invariant and that are governed by a nonrelativistic conformal symmetry.

Nonexponential kinetics captured in sequential unfolding of polyproteins over a range of loads.

While performing under mechanical loads in vivo, polyproteins are vitally involved in cellular mechanisms such as regulation of tissue elasticity and mechano-transduction by unfolding their comprising domains and extending them. It is widely thought that the process of sequential unfolding of polyproteins follows an exponential kinetics as the individual unfolding events exhibit identical and identically distributed (iid) Poisson behavior. However, it was shown that under high loads, the sequential unfolding kinetics displays nonexponential kinetics that alludes to aging by a subdiffusion process. Statistical order analysis of this kinetics indicated that the individual unfolding events are not iid, and cannot be defined as a Poisson (memoryless) process. Based on numerical simulations it was argued that this behavior becomes less pronounced with lowering the load, therefore it is to be expected that polyproteins unfolding under lower forces will follow a Poisson behavior. This expectation serves as the motivation of the current study, in which we investigate the effect of force lowering on the unfolding kinetics of Poly-L8 under varying loads, specifically high (150, 100 ​pN) and moderate-low (45, 30, 20 ​pN) forces. We found that a hierarchy among the unfolding events still exists even under low loads, again resulting in nonexponential behavior. We observe that analyzing the dwell-time distributions with stretched-exponentials and power laws give rise to different phenomenological trends. Using statistical order analysis, we demonstrated that even under the lowest load, the sequential unfolding cannot be considered as iid, in accord with the power law distribution. Additional free energy analysis revealed the contribution of the unfolded segments elasticity that scales with the force on the overall one-dimensional contour of the energy landscape, but more importantly, it discloses the hierarchy within the activation barriers during sequential unfolding that account for the observed nonexponentiality.

Polymer looping kinetics in active heterogeneous environments.

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

On the role of non-diagonal system-environment interactions in bridge-mediated electron transfer.

Bridge-mediated electron transfer (ET) between a donor and an acceptor is prototypical for the description of numerous most important ET scenarios. While multi-step ET and the interplay of sequential and direct superexchange transfer pathways in the donor-bridge-acceptor (D-B-A) model are increasingly understood, the influence of off-diagonal system-bath interactions on the transfer dynamics is less explored. Off-diagonal interactions account for the dependence of the ET coupling elements on nuclear coordinates (non-Condon effects) and are typically neglected. Here, we numerically investigate with quasi-adiabatic propagator path integral simulations the impact of off-diagonal system-environment interactions on the transfer dynamics for a wide range of scenarios in the D-B-A model. We demonstrate that off-diagonal system-environment interactions can have profound impact on the bridge-mediated ET dynamics. In the considered scenarios, the dynamics itself does not allow for a rigorous assignment of the underlying transfer mechanism. Furthermore, we demonstrate how off-diagonal system-environment interaction mediates anomalous localization by preventing long-time depopulation of the bridge B and how coherent transfer dynamics between donor D and acceptor A can be facilitated. The arising non-exponential short-time dynamics and coherent oscillations are interpreted within an equivalent Hamiltonian representation of a primary reaction coordinate model that reveals how the complex vibronic interplay of vibrational and electronic degrees of freedom underlying the non-Condon effects can impose donor-to-acceptor coherence transfer on short timescales.

Nonexponential Photoluminescence Dynamics in an Inhomogeneous Ensemble of Excitons in WSe2 Monolayers

The spectral and spatiotemporal dynamics of photoluminescence in monolayers of transition metal dichalcogenide WSe2 obtained by mechanical exfoliation on a Si/SiO2 substrate is studied over a wide range of temperatures and excitation powers. It is shown that the dynamics is nonexponential and, for times t exceeding ∼50 ps after the excitation pulse, is described by a dependence of the form 1/(t + t0). Photoluminescence decay is accelerated with a decrease in the temperature and in the energy of emitting states. It is shown that the observed dynamics cannot be described by a bimolecular recombination process, such as exciton—exciton annihilation. A model that describes the nonexponential photoluminescence dynamics by taking into account the spread of radiative recombination times of localized exciton states in a random potential gives good agreement with experimental data.

Capturing nonexponential dynamics in the presence of two decay channels

The most unstable quantum states and elementary particles possess more than a single decay channel. At the same time, it is well known that typically the decay law is not simply exponential. Therefore, it is natural to ask how to spot the non-exponential decay when (at least) two decay channels are opened. In this work, we study the tunneling phenomenon of an initially localized particle in two spatially opposite directions through two different barriers, mimicking two decay channels. In this framework, through a specific quantum mechanical examples which can be accurately solved, we study general properties of a two-channel decay that apply for various unstable quantum states (among which also for unstable particles). Apart from small deviations at early times, the survival probability and the partial tunneling probability along the chosen direction are very well described by the exponential-decay model. In contrast, the ratios of the decay probabilities and probability currents are evidently not a simple constant (as they would be in the exponential limit) but display time-persisting oscillations. Hence, these ratios are optimal witnesses of deviations from the exponential decay law.

The interplay between chromophore and protein determines the extended excited state dynamics in a single-domain phytochrome

Phytochromes are a diverse family of bilin-binding photoreceptors that regulate a wide range of physiological processes. Their photochemical properties make them attractive for applications in optogenetics and superresolution microscopy. Phytochromes undergo reversible photoconversion triggered by the Z ⇄ E photoisomerization about the double bond in the bilin chromophore. However, it is not fully understood at the molecular level how the protein framework facilitates the complex photoisomerization dynamics. We have studied a single-domain bilin-binding photoreceptor All2699g1 (Nostoc sp. PCC 7120) that exhibits photoconversion between the red light-absorbing (Pr) and far red-absorbing (Pfr) states just like canonical phytochromes. We present the crystal structure and examine the photoisomerization mechanism of the Pr form as well as the formation of the primary photoproduct Lumi-R using time-resolved spectroscopy and hybrid quantum mechanics/molecular mechanics simulations. We show that the unusually long excited state lifetime (broad lifetime distribution centered at ∼300 picoseconds) is due to the interactions between the isomerizing pyrrole ring D and an adjacent conserved Tyr142. The decay kinetics shows a strongly distributed character which is imposed by the nonexponential protein dynamics. Our findings offer a mechanistic insight into how the quantum efficiency of the bilin photoisomerization is tuned by the protein environment, thereby providing a structural framework for engineering bilin-based optical agents for imaging and optogenetics applications.

Estimation of seroconversion rates for infectious diseases: Effects of age and noise.

The presence of serum antibodies is a biomarker of past infection. Instead of seroclassification aimed at measuring seroprevalence a population sample of serum antibody levels may be used to estimate the incidence of seroconversion. This article expands an earlier study into seroincidence estimation, employing models of the seroresponse that include probability of escaping infection, as well as nonexponential decay kinetics and different sources of noise. As previously, a constant force of infection is assumed. When the seroconversion rate is low, a substantial fraction of the population may not be old enough to have experienced any seroconversions, causing underestimation of seroconversion rates that may be substantial at young ages. A correction is given that can be shown to remove such age dependent bias. Simulation studies show that the updated models provide accurate estimates of seroconversion rates, but also that the presence of noise, when unaccounted for, may introduce considerable bias, especially at low (< 0.1/yr) seroconversion rates and young ages. The revised serocalculator scripts can be used to update the R package "seroincidence."

How different are the dynamics of nanoconfined water?

We unravel the combined effects of confinement and surface interactions by studying the position dependent, time-resolved dynamic response functions in nano-containers of different shapes. Spectroscopic signatures are additionally studied through solvation dynamics by placing ionic and dipolar probes at varying distances from the enclosing surface. We find that the confined water molecules exhibit exotic dynamical features and stark differences from that in the bulk liquid. We employ atomistic molecular dynamics simulation to obtain the solvation time correlation function, non-Gaussian parameter, and non-linear response function that reveal the existence of heterogeneous and non-exponential dynamics with a strong sensitivity to both the size and the shape of the enclosure. Importantly, the slower long-time decay constant exhibits a non-monotonic spatial dependence. The initial ultrafast component is reminiscent of the same in the bulk, but it is found to have a different origin in the present systems. We perform shell-wise analyses to understand the microscopic origin of these observations and the range of the propagation of the surface induced effects.

Decay Kinetics of CeF3 under VUV and X-ray Synchrotron Radiation

Characteristic dimensions and evolution times of regions of secondary electronic excitations created by the interaction of ionizing radiation with matter cannot be measured directly. At the same time these are essential parameters both for engineering of nanostructured composite materials defining optimal layer thickness and nanoparticles radii and for the development of optimized scintillators. The paper demonstrates how such spatial and temporal data can be extracted from luminescence decay kinetics excited by vacuum ultraviolet (VUV) and X-ray photons at modern sources of synchrotron radiation MAX IV and PETRA III. Specific features of energy-band structure of self-activated crystal CeF3 are discussed, and its potential for a super-fast detection of ionizing radiation evaluated. Diffusion-controlled dipole–dipole interaction of Frenkel excitons is demonstrated to account well for the luminescence non-exponential decay kinetics providing information on the scales of excited regions created by photons of different energy. For 20 eV photons the radius of excited regions is estimated to be 10 nm, and for 200 eV photons it increases to 18 nm. Effective radius of excited regions of complicated shape created by 19 keV is as large as 80 nm and the diffusion length of Frenkel excitons over radiative time is 14 nm.

Vibrational Relaxation Dynamics of an Azido-Cobalt(II) Complex from Femtosecond UV-Pump/MIR-Probe Spectroscopy and Model Simulations with Ab Initio Anharmonic Couplings.

Vibrational energy relaxation is of critical importance for the light-controlled reactivity of transition-metal complexes. In time-resolved optical spectroscopies, it gives rise to pronounced spectral redistributions with complex band shifts and thus to nonexponential kinetics, all of which are very difficult to quantify. Here we study the vibrational relaxation dynamics of a pentacoordinated azido-cobalt(II) complex in liquid solution following its ultrafast charge-transfer excitation in the near-ultraviolet (UV). The complex is photochemically remarkably stable and returns within the experimental time resolution back to its quartet electronic ground state via internal conversion. The nonadiabatic transition effectively instantaneously converts the entire photon energy into kinetic energy of the vibrational degrees of freedom. The ensuing relaxation dynamics of the vibrationally highly excited complex are monitored as a function of time using femtosecond mid-infrared (MIR) spectroscopy in the antisymmetric stretching region of the azido ligand and occur on a time scale of a few tens of picoseconds. The dynamic evolution of the MIR spectrum due to vibrational cooling of the complex can be understood quantitatively within the framework of an anharmonic coupling model, which relies on an ab initio intramolecular cubic/quartic force field from density functional theory combined with second-order vibrational perturbation theory. The simulations suggest that the primary internal conversion preferentially dumps the excess energy into the low-frequency bending modes of the azido ligand, whereas its high-frequency stretching modes are barely affected by the initial nonadiabatic transition. Surprisingly, the two bending vibrations appear to relax independently of one another, each with its own characteristic cooling time.

Kinetics of escape of ssDNA molecules from α-hemolysin nanopores: a dynamic disorder study

Experimental studies of the escape events of single-stranded DNA (ssDNA) molecules from the membrane embedded α-hemolysin nanopores exhibited the non-exponential kinetics. The data for homopolymers of adenine (dA27) and cytosine (dC27) revealed the profound influence of the sequence dependent DNA–pore interactions and the applied potentials on the escape kinetics. The non-exponential behavior is a signature of the presence of disorder in biochemical reactions. Here, we rationalize the experimental results with a dynamic disorder approach based on Zwanzig’s fluctuating bottleneck (FB) model as a general mechanism where the rate of the reaction is controlled by the passage of a molecule through the cross-sectional area of the vestibule of the α-hemolysin channel (the bottleneck). The stochastic fluctuations of the radius of the latter is represented by the fluctuations of the intersegment distance of a Rouse chain, the dynamics of which is described using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our analytical results essentially capture the effects of underlying energetics due to the sequence-dependent nature and applied potentials in reproducing the measured survival probabilities for dA27 and dC27 in an excellent way, thereby validating the application of a simple coarse-grained theory to address the thermal escape of biopolymers from bionanopores.

Kinetics of Photoluminescence Decay of Colloidal Quantum Dots: Reversible Trapping of Photogenerated Charge Carriers

A function for the analysis of the non-exponential kinetics of photoluminescence decay of colloidal quantum dots at room temperature is presented. The function takes into account trapping and detrapping of photogenerated charge carriers with physically meaningful parameters (time constant, trapping and detrapping rate constants, and average number of traps per quantum dot). Its validity is tested by time-resolved photoluminescence spectroscopy experiments with drop-cast films of CdSe/ZnS core/shell quantum dots.

Is CH3NC isomerization an intrinsic non-RRKM unimolecular reaction?

Direct dynamics simulations, using B3LYP/6-311++G(2d,2p) theory, were used to study the unimolecular and intramolecular dynamics of vibrationally excited CH3NC. Microcanonical ensembles of CH3NC, excited with 150, 120, and 100 kcal/mol of vibrational energy, isomerized to CH3CN nonexponentially, indicative of intrinsic non-Rice-Ramsperger-Kassel-Marcus (RRKM) dynamics. The distribution of surviving CH3NC molecules vs time, i.e., N(t)/N(0), was described by two separate functions, valid above and below a time limit, a single exponential for the former and a biexponential for the latter. The dynamics for the short-time component are consistent with a separable phase space model. The importance of this component decreases with vibrational energy and may be unimportant for energies relevant to experimental studies of CH3NC isomerization. Classical power spectra calculated for vibrationally excited CH3NC, at the experimental average energy of isomerizing molecules, show that the intramolecular dynamics of CH3NC are not chaotic and the C-N≡C and CH3 units are weakly coupled. The biexponential N(t)/N(0) at 100 kcal/mol is used as a model to study CH3NC → CH3CN isomerization with biexponential dynamics. The Hinshelwood-Lindemann rate constant kuni(ω,E) found from the biexponential N(t)/N(0) agrees with the Hinshelwood-Lindemann-RRKM kuni(ω,E) at the high and low pressure limits, but is lower at intermediate pressures. As found from previous work [S. Malpathak and W. L. Hase, J. Phys. Chem. A 123, 1923 (2019)], the two kuni(ω,E) curves may be brought into agreement by scaling ω in the Hinshelwood-Lindemann-RRKM kuni(ω,E) by a collisional energy transfer efficiency factor βc. The interplay between the value of βc, for the actual intermolecular energy transfer, and the ways the treatment of the rotational quantum number K and nonexponential unimolecular dynamics affect βc suggests that the ability to fit an experimental kuni(ω,T) with Hinshelwood-Lindemann-RRKM theory does not identify a unimolecular reactant as an intrinsic RRKM molecule.