arXiv subjects

S. Burov

Publications and source records attributed to S. Burov.

10 recordsLinked to original sources

arXiv2024

Telomeres in Lamin-A Depleted Cells Exhibit Directed Motion and Dynamic Coherence

Investigating the dynamics of chromatin loci and the factors that influence them provides valuable insights into the organization and functionality of the genome within the cell nucleus. We control the expression of Lamin-A, an important organizer of chromatin and nuclear structure. By simultaneously tracking hundreds of telomeres in Lamin-A knocked-out (KO) and wild-type (WT) nuclei, we find that telomere motion in Lamin-A depleted cells is both faster and more directed on micrometer scales, comparable to the size of chromosome territories. In contrast, telomere trajectories in WT cells exhibit pronounced anti-persistent behavior, consistent with caging by the surrounding chromatin environment. We further observe correlated motion between distinct telomeres in both WT and KO cells, with significantly stronger correlations in the KO case, indicating enhanced collective behavior. These correlations reflect cross-correlations among different loci rather than temporal correlations along individual trajectories. Together, these findings highlight the central role of Lamin-A in regulating both local confinement and collective telomere dynamics.

physics.bio-ph↗

arXiv2021

Cusp of non-Gaussian density of particles for a diffusing diffusivity model

We study a two state ``jumping diffusivity'' model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times Gaussian behavior with an effective diffusion coefficient is recovered. We show that for equilibrium initial conditions and when the limit of the diffusion coefficient $D_-\to0$ is taken, the short time behavior leads to a cusp, namely a non - analytical behavior, in the distribution of the displacements $P(x,t)$ for $x\longrightarrow 0$. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state $D_{+}$ to a $δ$-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non - analyticity in $P(x,t)$. We demonstrate how super - statistical framework is a zeroth order short time expansion of $P(x,t)$, in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.

cond-mat.stat-mech↗

arXiv2011

Residence time statistics for $N$ blinking quantum dots and other stochastic processes

We present a study of residence time statistics for $N$ blinking quantum dots. With numerical simulations and exact calculations we show sharp transitions for a critical number of dots. In contrast to expectation the fluctuations in the limit of $N \to \infty$ are non-trivial. Besides quantum dots our work describes residence time statistics in several other many particle systems for example $N$ Brownian particles. Our work provides a natural framework to detect non-ergodic kinetics from measurements of many blinking chromophores, without the need to reach the single molecule limit.

cond-mat.stat-mech↗

arXiv2010

Time transformation for random walks in the quenched trap model

Diffusion in the quenched trap model is investigated with an approach we call weak subordination breaking. We map the problem onto Brownian motion and show that the operational time is ${\cal S}_α= \sum_{x=-\infty} ^\infty (n_x)^α$ where $n_x$ is the visitation number at site $x$ . In the limit of zero temperature we recover the renormalization group (RG) solution found by Monthus. Our approach is an alternative to RG capable of dealing with any disorder strength.

cond-mat.stat-mech↗

arXiv2010

Generalized Khinchin Theorem for a Class of Aging Processes

The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by non-stationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and provide a generalization of Khinchin's theorem. Our work quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics.

cond-mat.stat-mech↗

arXiv2010

Non-Universal Extinction Transition for Boundary Active Site

We present a generalized model of a diffusion-reaction system where the reaction occurs only on the boundary. This model reduces to that of Barato and Hinrichsen when the occupancy of the boundary site is restricted to zero or one. In the limit when there is no restriction on the occupancy of the boundary site, the model reduces to an age dependent Galton-Watson branching process and admits an analytic solution. The model displays a boundary-induced phase transition into an absorbing state with rational critical exponents and exhibits aging at criticality below a certain fractal dimension of the diffusion process. Surprisingly the behavior in the critical regime for intermediate occupancy restriction $N$ varies with $N$. In fact, by varying the lifetime of the active boundary particle or the diffusion coefficient in the bulk, the critical exponents can be continuously modified.

cond-mat.stat-mech↗

arXiv2008

Random Time-Scale Invariant Diffusion and Transport Coefficients

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{δ^2}$ of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that $\overline{δ^2}$ differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable $\overline{δ^2}$. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.

cond-mat.stat-mech↗

arXiv2008

Fractional Langevin Equation: Over-Damped, Under-Damped and Critical Behaviors

The dynamical phase diagram of the fractional Langevin equation is investigated for harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) $α_c=0.402\pm 0.002$ marks a transition to a non-monotonic under-damped phase, (ii) $α_R=0.441...$ marks a transition to a resonance phase when an external oscillating field drives the system, (iii) $α_{χ_1}=0.527...$ and (iv) $α_{χ_2}=0.707...$ marks transition to a double peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over-damped, under-damped regimes, motion and resonances, show behaviors different from normal.

cond-mat.stat-mech↗

arXiv2007

The Critical Exponent of the Fractional Langevin Equation is $α_c\approx 0.402$

We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent $α_c= 0.402\pm 0.002$ marks a transition to a non-monotonic under-damped phase. The critical exponent $α_{R}=0.441...$ marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the under-damped, the over-damped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal.

cond-mat.stat-mech↗

arXiv2006

Occupation Time Statistics in the Quenched Trap Model

We investigate the distribution of occupation times for a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field $U^{\rm det}(x)$. When the distribution of energy traps is exponential with a width $T_g$ we find that the occupation time statistics behaves according to (i) the canonical Boltzmann theory when $T>T_g$, (ii) while for $T<T_g$ they are distributed according to the Lamperti distribution with the asymmetry of the distribution determined by the Boltzmann factor $\exp(-U^{\rm det}(x)/T_g)$ with $T_g$ and not $T$ being the effective temperature. We explain how our results describe occupation times in other systems with quenched disorder, when the underlying partition function of the problem is a random variable distributed according to Lévy statistics.

cond-mat.stat-mech↗