arXiv subjects

Binayak Banerjee

Publications and source records attributed to Binayak Banerjee.

2 recordsLinked to original sources

arXiv2026

Resetting dynamics in a system with quenched disorder

Although resetting has widespread applicability, applying it to the dynamics in the presence of spatial quenched disorder, which is essential in many physical problems, is challenging. In this study, we consider a well-known one-dimensional model of particle hopping on a lattice with quenched disorder in the form of site-dependent hopping probabilities, drawn from a power-law distribution, and apply the resetting formalism. As a physical example, we recast the growth dynamics of microtubules with sudden catastrophic disassembly events as a resetting dynamics. We consider two distinct regimes for growth dynamics: a strongly biased case and a less biased case. Motivated by experimental results, we take a Gamma distribution for the resetting time. Our results show that occasional disassembly events are crucial for the experimentally observed distribution of reset (or catastrophe) lengths. We also analyze steady-state distributions under different resetting protocols-resetting to the initial position versus a random site. We also investigate the distribution of first-passage times to a fixed distance following reset. Finally, by considering other resetting probability distributions, we identify a regime where the mean displacement grows as slowly as $\log^2 t$. We also elucidate the role of disorder in the system properties under the resetting dynamics. Our study paves the way to treat the dynamics of complex physical systems using resetting.

cond-mat.stat-mech↗

arXiv2024

Effects of bursty synthesis in organelle biogenesis

A fundamental question of cell biology is how cells control the number of organelles. The processes of organelle biogenesis, namely de novo synthesis, fission, fusion, and decay, are inherently stochastic, producing cell-to-cell variability in organelle abundance. In addition, experiments suggest that the synthesis of some organelles can be bursty. We thus ask how bursty synthesis impacts intracellular organelle number distribution. We develop an organelle biogenesis model with bursty de novo synthesis by considering geometrically distributed burst sizes. We analytically solve the model in biologically relevant limits and provide exact expressions for the steady-state organelle number distributions and their means and variances. We also present approximate solutions for the whole model, complementing with exact stochastic simulations. We show that bursts generally increase the noise in organelle numbers, producing distinct signatures in noise profiles depending on different mechanisms of organelle biogenesis. We also find different shapes of organelle number distributions, including bimodal distributions in some parameter regimes. Notably, bursty synthesis broadens the parameter regime of observing bimodality compared to the `non-bursty' case. Together, our framework utilizes number fluctuations to elucidate the role of bursty synthesis in producing organelle number heterogeneity in cells.

physics.bio-ph↗