Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

A Model of Anomalous Chain Translocation Dynamics

A model of polymer translocation based on the stochastic dynamics of the number of monomers on one side of a pore-containing surface is formulated in terms of a one-dimensional generalized Langevin equation, in which the random force is assumed to be characterized by long-ranged temporal correlations. The model is introduced to rationalize anomalies in measured and simulated values of the average time of passage through the pore, which in general cannot be satisfactorily accounted for by simple Brownian diffusion mechanisms. Calculations are presented of the mean first passage time for barrier crossing and of the mean square displacement of a monomeric segment, in the limits of strong and weak diffusive bias. The calculations produce estimates of the exponents in various scaling relations that are in satisfactory agreement with available data.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

Noise-spike-induced escape in a bistable system driven by colored noise: Noise with long correlation times

An escape mechanism in a bistable system driven by colored noise of large but finite correlation time (tau) is analyzed. It is shown that the fluctuating potential theory [Phys. Rev. A 38, 3749 (1988)] becomes invalid in a region around the inflection points of the bistable potential, resulting in the underestimation of the mean first passage time at finite tau by this theory. It is shown that transitions at large but finite tau are caused by noise spikes, with edges rising and falling exponentially in a time of O(tau). Simulation of the dynamics of the bistable system driven by noise spikes of the above-mentioned nature clearly reveal the physical mechanism behind the transition.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Catalysis of tRNA Aminoacylation: Single Turnover to Steady-State Kinetics of tRNA Synthetases

Aminoacyl-tRNA synthetases (aaRS) catalyze the bimolecular association reaction between amino acid and tRNA by specifically and unerringly choosing the cognate amino acid and tRNA. There are two classes of such synthetases that perform tRNA-aminoacylation reaction. Interestingly, these two classes of aminoacyl-tRNA synthetases differ not only in their structures but they also exhibit remarkably distinct kinetics under pre-steady-state condition. The class I synthetases show initial burst of product formation followed by a slower steady-state rate. This has been argued to represent the influence of slow product release. In contrast, there is no burst in the case of class H enzymes. The tight binding of product with enzyme for class I enzymes is correlated with the enhancement of rate in presence of elongation factor. EF-TU. In spite of extensive experimental studies, there is no detailed theoretical analysis that can provide a quantitative understanding of this important problem. In this article, we present a theoretical investigation of enzyme kinetics for both classes of aminoacyl-tRNA synthetases. We present an augmented kinetic scheme and then employ the methods of time-dependent probability statistics to obtain expressions for the first passage time distribution that gives both the time-dependent and the steady-state rates. The present study quantitatively explains all the above experimental observations. We propose an alternative path way in the case of class II enzymes showing the tRNA-dependent amino acid activation and the discrepancy between the single-turnover and steady-state rate.

Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

The complex kinetics of protein folding in wide temperature ranges

The complex protein folding kinetics in wide temperature ranges is studied through diffusive dynamics on the underlying energy landscape. The well-known kinetic chevron rollover behavior is recovered from the mean first passage time, with the U-shape dependence on temperature. The fastest folding temperature T-0 is found to be smaller than the folding transition temperature T-f. We found that the fluctuations of the kinetics through the distribution of first passage time show rather universal behavior, from high-temperature exponential Poissonian kinetics to the relatively low-temperature highly nonexponential kinetics. The transition temperature is at T-k and T-0, T-k, T-f. In certain low-temperature regimes, a power law behavior at long time emerges. At very low temperatures ( lower than trapping transition temperature T< T-0/(4&SIM;6)), the kinetics is an exponential Poissonian process again.

Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments ( for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier.

Diffusion and single molecule dynamics on biomolecular interface binding energy landscape

We propose a new approach to study the diffusion dynamics on biomolecular interface binding energy landscape. The resulting mean first passage time (MFPT) has 'U'curve dependence on the temperature. It is shown that the large specificity ratio of gap to roughness of the underlying binding energy landscape not only guarantees the thermodynamic stability and the specificity [P.A. Rejto, G.M. Verkhivker, in: Proc. Natl. Acad. Sci. 93 (1996) 8945; C.J. Tsai, S. Kumar, B. Ma, R. Nussinov, Protein Sci. 8 (1999) 1181; G.A. Papoian, P.G. Wolynes, Biopolymers 68 (2003) 333; J. Wang, G.M. Verkhivker, Phys. Rev. Lett. 90 (2003) 198101] but also the kinetic accessibility. The complex kinetics and the associated fluctuations reflecting the structures of the binding energy landscape emerge upon temperature changes. The theory suggests a way of connecting the models/simulations with single molecule experiments by analysing the kinetic trajectories.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

Statistics and kinetics of single-molecule electron transfer dynamics in complex environments: A simulation model study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments ( for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.

Dinâmica de modelos minimalistas de solvente em reações de transferência de elétrons: aplicação à experimentos de única molécula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)