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We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis–Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies by using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme–substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit. [ABSTRACT FROM AUTHOR]

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture, discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)], possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A–type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features such as glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity. [ABSTRACT FROM AUTHOR]

We investigate statistics of dynamical exchange events in coarse-grained models of supercooled liquids in spatial dimensions d=1, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange-time distributions are shown to be particularly sensitive to the model parameters and dimensions, and exhibit more structured and richer behavior than persistence-time distributions. Mean exchange times are shown to be Arrhenius, regardless of models and spatial dimensions. Specifically, 〈tx〉∼c-2, with c being the excitation concentration. Different dynamical exchange processes are identified and characterized from the underlying trajectories. We discuss experimental possibilities to test some of our theoretical findings. [ABSTRACT FROM AUTHOR]

We survey the current status of single-molecule spectroscopy in the view point of theoretical aspects. After an explanation of basic concepts in single-molecule spectroscopy, we focus on the following topics: (1) line shape phenomena in disordered media, (2) photon counting statistics for time-dependent fluctuations in single-molecule spectroscopy, (3) fluorescence intensity fluctuations for nonergodic systems, (4) time-resolved single-molecule fluorescence for conformational dynamics of single biomolecules, (5) single-molecule reaction dynamics at room temperature, and (6) quantum jump method of single quantum system. We conclude this paper with some open questions and perspectives of single-molecule spectroscopy. [ABSTRACT FROM AUTHOR]

Electron transfer processes in Debye solvents are studied using a spectral analysis method recently proposed. Spectral structure of a nonadiabatic two-state diffusion equation is investigated to reveal various kinetic regimes characterized by a broad range of physical parameters; electronic coupling, energy bias, reorganization energy, and solvent relaxation rate. Within this unified framework, several kinetic behaviors of the electron transfer kinetics, including adiabatic Rabi oscillation, crossover from the nonadiabatic to adiabatic limits, transition from the incoherent to coherent kinetic limits, and dynamic bath effect, are demonstrated and compared with results from previous theoretical models. Dynamics of the electron transfer system is also calculated with the spectral analysis method. It is pointed out that in the large reorganization energy case the nonadiabatic diffusion equation exhibits a nonphysical behavior, yielding a negative eigenvalue. [ABSTRACT FROM AUTHOR]

The recombination reaction of radicals photolytically produced in solution proceeds via two distinguishable kinetic phases. At short times recombination between geminate radicals predominates, while at long times recombination between nongeminate radicals that have diffused away from their geminate counterparts to the bulk solution takes place. In most previous theories dealing with the effect of added scavenger molecules on the radical recombination reaction, only the geminate recombination phase has been considered. However, if the concentration of radical pairs generated is high, the interplay of bulk recombination in the dynamics needs to be considered. In the present paper, we formulate a theory that deals with the scavenging effect in both the geminate and bulk recombination phases within a unified framework. We show that the scavenger concentration CS and the scavenging rate coefficient kS have independent effects on the reaction, in general. In contrast, conventional theories involve these two quantities only as a product kSCS, usually in the form of a Laplace transformation variable. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A spectral analysis method is proposed to characterize multiple time scales in electron transfer processes, including vibrational relaxation, electronic coherence, activated curve crossing, or barrier crossing. Within this unified framework, observed rate behavior, biexponential and multiexponential decay, and population recurrences and oscillations are different components of the same kinetic spectrum; thus, several existing theoretical models, developed for limiting cases of electron transfer, can be analyzed, tested, and extended. In particular, the rate constant extracted from the analysis does not saturate as the electronic coupling increases but shows a crossover from the nonadiabatic to adiabatic limits, and the kinetic spectrum in the large coupling regime reveals the nature of the localization-delocalization transition as the consequence of two competing mechanisms. Though the analysis is presented in the context of electron transfer, this approach provides a different perspective for understanding dissipative dynamics and hence can be applied to study condensed-phase laser spectroscopy, quantum coherence control, energy transfer, and other charge transfer processes. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]