arXiv subjects

Gennady Margolin

Publications and source records attributed to Gennady Margolin.

6 recordsLinked to original sources

arXiv2006

Analysis of a microscopic stochastic model of microtubule dynamic instability

A novel theoretical model of dynamic instability of a system of linear (1D) microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates/frequencies of larger-scale changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady state concentration of free tubulin, and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between microscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Lastly, we use a computational Monte Carlo model to provide an explanation for non-exponential MT length distributions observed in experiments. In particular, we show that appearance of such non-exponential distributions in the experiments can occur because the true steady state has not been reached, and/or due to the presence of a cell edge.

q-bio.SC↗

arXiv2006

Power Law Blinking Quantum Dots: Stochastic and Physical Models

We quantify nonergodic and aging behaviors of nanocrystals (or quantum dots) based on stochastic model. Ergodicity breaking is characterized based on time average intensity and time average correlation function, which remain random even in the limit of long measurement time. We argue that certain aspects of nonergodicity can be explained based on a modification of Onsager's diffusion model of an ion pair escaping neutralization. We explain how diffusion models generate nonergodic behavior, namely a simple mechanism is responsible for the breakdown of the standard assumption of statistical mechanics. Data analysis shows that distributions of on and off intervals in the nanocrystal blinking are almost identical, $ψ_{\pm}(τ)\propto A_{\pm}τ^{-(1+α_{\pm})}$ with $A_{+}\approx A_{-}$ and $α_{+}\approxα_{-}=α$ and $α\approx0.8$. The latter exponent indicates that a simple diffusion model with $α=0.5$ neglecting the electron-hole Coulomb interaction and/or tunneling, is not sufficient.

cond-mat.stat-mech↗

arXiv2005

Nonergodisity of a time series obeying Lévy statistics

Time-averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied. Such a process, called a Lévy walk, describes dynamical behaviors of many physical systems, fluorescence intermittency of semiconductor nanocrystals under continuous laser illumination being one example. When the mean sojourn time diverges the process is non-ergodic. In that case, the time average autocorrelation function is not equal to the ensemble averaged autocorrelation function, instead it remains random even in the limit of long measurement time. Several approximations for the distribution of this random autocorrelation function are obtained for different parameter ranges, and favorably compared to Monte Carlo simulations. Nonergodicity of the power spectrum of the process is briefly discussed, and a nonstationary Wiener-Khintchine theorem, relating the correlation functions and the power spectrum is presented. The considered situation is in full contrast to the usual assumptions of ergodicity and stationarity.

cond-mat.stat-mech↗

arXiv2005

Single Molecule Chemical Reaction: Kramers Approach Revisited

Single molecule chemical reactions yield new insight into fluctuation phenomena which are obscured in measurement of ensemble of molecules. Kramers escape problem is investigated here in a framework suitable for single molecule reactions. In particular we obtain distributions of escape times in simple limiting cases, rather than their mean, and investigate their sensitivity on initial conditions. Rich physical behaviors are observed: sub-Poissonian statistics when the dynamics is only slightly deviating from Newtonian, super-Poissonian behavior when diffusion is dominating, and Poissonian behavior when Kramers original conditions hold. By varying initial conditions escape time distributions can follow a (usual) exponential or a $τ^{-3/2}$ decay, due to regular diffusion. We briefly address experimental results which yield the $τ^{-3/2}$ behavior (with cutoffs) and propose that this behavior is universal.

cond-mat.stat-mech↗

arXiv2004

Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals

We investigate the non-ergodic properties of blinking nano-crystals using a stochastic approach. We calculate the distribution functions of the time averaged intensity correlation function and show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe non-ergodicity in systems stochastically modeled using the Levy walk framework for anomalous diffusion, for example certain types of chaotic dynamics, currents in ion-channel, and single spin dynamics to name a few.

cond-mat.stat-mech↗

arXiv2004

Aging Correlation Functions for Blinking Nano-Crystals, and Other On - Off Stochastic Processes

Following recent experiments on power law blinking behavior of single nano-crystals, we calculate two-time intensity correlation functions for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit --> h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior) (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nano-crystals). (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nano-crystals). (iv) For defected off time distribution we also find x=t+t' . Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B <--> AB, when followed on a single particle level exhibits aging behavior.

cond-mat.stat-mech↗