Waiting time distribution and nonexponential relaxation in single molecule spectroscopic studies: Realization of entropic bottleneck in a simple model

Nonexponential kinetics of ion pair dissociation in electrofreezing water

Temporally- or spatially-heterogeneous environments can participate in many kinetic processes, from chemical reactions and self-assembly to the forced dissociation of biomolecules. Here, we simulate the molecular dynamics of a model ion pair forced to dissociate in an explicit, aqueous solution. Triggering dissociation with an external electric field causes the surrounding water to electrofreeze and the ion pair population to decay nonexponentially. To further probe the role of the aqueous environment in the kinetics, we also simulate dissociation events under a purely mechanical force on the ion pair. In this case, regardless of whether the surrounding water is a liquid or already electrofrozen, the ion pair population decays exponentially with a well-defined rate constant that is specific to the medium and applied force. These simulation data, and the rate parameters we extract, suggest the disordered kinetics in an electrofreezing medium are a result of the comparable time scales of two concurrent processes, electrofreezing and dissociation.

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.

Information entropy as a measure of nonexponentiality of waiting-time distributions

It is shown that the information entropy based on waiting-time distributions (WTDs) offers a natural and robust measure of nonexponentiality of the distributions in the form of the Schrödinger-Brillouin negentropy, or equivalently the Kullback-Leibler divergence, and has a straightforward interpretation in terms of transition state theory. Other measures of nonexponentiality of WTDs, based on comparison of the standard deviation and the median with the mean waiting time, are also discussed. The theoretical analysis is illustrated with results from protein folding studies.

Theoretical model based on the memory effect for the strange photoisomerization kinetics of diarylethene derivatives dispersed on polymer films

In the present paper the authors present a theoretical model to explain the kinetics involving the induction period observed by Irie et al. [Nature (London) 420, 759 (2002)] for photoisomerization of diarylethene derivatives dispersed on polymer films at a single molecular level. In the model we assume that both ground state and excited state free energy landscapes which result from the interaction between the photochromic molecule and the surrounding polymer are rugged and have several local minima along the pathway to the critical point at which isomerization actually occurs. We assume that after one photoexcitation a fraction of the photochromic molecule moves to a new local minimum and stays there, although the other fraction returns to the original local minimum. The former effect is referred to as the memory effect. After repeated photoexcitations the photochromic molecule moves gradually from one local minimum to another in the pathway to the isomerization point. It finally reaches the isomerization point, where isomerization occurs. Their model successfully reproduces the kinetics of photoisomerization of diarylethene derivatives dispersed on polymer films observed experimentally.

Simulated data sets for single molecule kinetics: some limitations and complications of data analysis

When the fluorescence intensity of a chromophore attached to or bound in an enzyme relates to a specific reactive step in the enzymatic reaction, a single molecule fluorescence study of the process reveals a time sequence in the fluorescence emission that can be analyzed to derive kinetic and mechanistic information. Reports of various experimental results and corresponding theoretical studies have provided a basis for interpreting these data and understanding the methodology. We have found it useful to parallel experiments with Monte Carlo simulations of potential models hypothesized to describe the reaction kinetics. The simulations can be adapted to include experimental limitations, such as limited data sets, and complexities such as dynamic disorder, where reaction rates appear to change over time. By using models that are known a priori, the simulations reveal some of the challenges of interpreting finite single-molecule data sets by employing various statistical signatures that have been identified.

Theory of single-molecule spectroscopy: beyond the ensemble average

Single-molecule spectroscopy (SMS) is a powerful experimental technique used to investigate a wide range of physical, chemical, and biophysical phenomena. The merit of SMS is that it does not require ensemble averaging, which is found in standard spectroscopic techniques. Thus SMS yields insight into complex fluctuation phenomena that cannot be observed using standard ensemble techniques. We investigate theoretical aspects of SMS, emphasizing (a) dynamical fluctuations (e.g., spectral diffusion, photon-counting statistics, antibunching, quantum jumps, triplet blinking, and nonergodic blinking) and (b) single-molecule fluctuations in disordered systems, specifically distribution of line shapes of single molecules in low-temperature glasses. Special emphasis is given to single-molecule systems that reveal surprising connections to Levy statistics (i.e., blinking of quantum dots and single molecules in glasses). We compare theory with experiment and mention open problems. Our work demonstrates that the theory of SMS is a complementary field of research for describing optical spectroscopy in the condensed phase.

Nonmonotonic temperature dependence of heat capacity through the glass transition within a kinetic model

The heat capacity of a supercooled liquid subjected to a temperature cycle through its glass transition is studied within a kinetic model. In this model, the beta process is assumed to be thermally activated and described by a two-level system. The alpha process is described as a beta relaxation mediated cooperative transition in a double well. The overshoot of the heat capacity during the heating scan is well reproduced and is shown to be directly related to delayed energy relaxation in the double well. In addition, the calculated scan rate dependencies of the glass transition temperature T(g) and the limiting fictive temperature T(f) (L) show qualitative agreement with the known results. Heterogeneity is found to significantly reduce the overshoot of heat capacity. Furthermore, the frequency dependent heat capacity has been calculated within the present framework and found to be rather similar to the experimentally observed behavior of supercooled liquids.