arXiv subjects

Deepak Bhat

Publications and source records attributed to Deepak Bhat.

12 recordsLinked to original sources

arXiv2025

Theory of Semi-discontinuous DNA Replication

In biological cells, DNA replication is carried out by the replisome, a protein complex encompassing multiple DNA polymerases. DNA replication is semi-discontinuous: a DNA polymerase synthesizes one (leading) strand of the DNA continuously, and another polymerase synthesizes the other (lagging) strand discontinuously. Complex dynamics of the lagging-strand polymerase within the replisome result in the formation of short interim fragments, known as Okazaki fragments, and gaps between them. Although the semi-discontinuous replication is ubiquitous, a detailed characterization of it remains elusive. In this work, we develop a framework to investigate the semi-discontinuous replication by incorporating stochastic dynamics of the lagging-strand polymerase. Computing the size distribution of Okazaki fragments and gaps, we uncover the significance of the polymerase dissociation in shaping them. We apply the method to the previous experiment on the T4 bacteriophage replication system and identify the key parameters governing the polymerase dynamics. These results reveal that the collisions of lagging-strand polymerase with pre-synthesised Okazaki fragments primarily trigger its dissociation from the lagging strand.

physics.bio-ph↗

arXiv2023

Genome replication in asynchronously growing microbial populations

Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and genome stability. Qualitatively, in a growing cell culture, one expects that genomic regions that are replicated early should be more abundant than regions that are replicated late. This abundance pattern can be experimentally measured using deep sequencing. However, a general quantitative theory to explain these data is still lacking. In this paper, we predict the abundance of DNA fragments in asynchronously growing cultures from any given stochastic model of the DNA replication program. As key examples, we present stochastic models of the DNA replication programs in Escherichia coli and in budding yeast. In both cases, our approach leads to analytical predictions that are in excellent agreement with experimental data and permit to infer key information about the replication program. In particular, our method is able to infer the locations of known replication origins in budding yeast with high accuracy. These examples demonstrate that our method can provide insight into a broad range of organisms, from bacteria to eukaryotes.

q-bio.SC↗

arXiv2021

Search and localization dynamics of the CRISPR/Cas9 system

The CRISPR/Cas9 system acts as the prokaryotic immune system and has important applications in gene editing. The protein Cas9 is one of its crucial components. The role of Cas9 is to search for specific target sequences on the DNA and cleave them. In this Letter, we introduce a model of facilitated diffusion for Cas9 and fit its parameters to single-molecule experiments. Our model confirms that Cas9 search for targets by sliding, but shows that its sliding length is rather short. We then investigate how Cas9 explores a long stretch of DNA containing randomly placed targets. We solve this problem by mapping it into the theory of Anderson localization in condensed matter physics. Our theoretical approach rationalizes experimental evidences on the distribution of Cas9 molecules along the DNA.

q-bio.SC↗

arXiv2019

Polarization and Consensus by Opposing External Sources

We introduce a socially motivated extension of the voter model in which individual voters are also influenced by two opposing, fixed-opinion news sources. These sources forestall consensus and instead drive the population to a politically polarized state, with roughly half the population in each opinion state. Two types social networks for the voters are studied: (a) the complete graph of $N$ voters and, more realistically, (b) the two-clique graph with $N$ voters in each clique. For the complete graph, many dynamical properties are soluble within an annealed-link approximation, in which a link between a news source and a voter is replaced by an average link density. In this approximation, we show that the average consensus time grows as $N^\alpha$, with $\alpha = p\ell/(1-p)$. Here $p$ is the probability that a voter consults a news source rather than a neighboring voter, and $\ell$ is the link density between a news source and voters, so that $\alpha$ can be greater than 1. The polarization time, namely, the time to reach a politically polarized state from an initial strong majority state, is typically much less than the consensus time. For voters on the two-clique graph, either reducing the density of interclique links or enhancing the influence of news sources again promotes polarization.

physics.soc-ph↗

arXiv2019

Opinion Formation under Antagonistic Influences

We study the opinion dynamics in a generalized voter model in which voters are additionally influenced by two antagonistic news sources, whose effect is to promote political polarization. We show that, as the influence of the news sources is increased, the mean time to reach consensus is anomalously long, the time to reach a politically polarized state is quite short, and the steady-state opinion distribution exhibits a transition from a near consensus state to a politically polarized state.

physics.soc-ph↗

arXiv2019

Fixation in Fluctuating Populations

We investigate the dynamics of the voter model in which the population itself changes endogenously via the birth-death process. There are two species of voters, labeled A and B, and the population of each species can grow or shrink by the birth-death process at equal rates $b$. Individuals of opposite species also undergo voter model dynamics in which an AB pair can equiprobably become AA or BB with rate $v$---neutral evolution. In the limit $b/v\to\infty$, the distribution of consensus times varies as $t^{-3}$ and the probability that the population size equals $n$ at the moment of consensus varies as $n^{-3}$. As the birth/death rate $b$ is increased, fixation occurs more more quickly; that is, population fluctuations promote consensus.

q-bio.PE↗

arXiv2018

Non-equilibrium dynamics of the piston in the Szilard engine

We consider a Szilard engine in one dimension, consisting of a single particle of mass $m$, moving between a piston of mass $M$, and a heat reservoir at temperature $T$. In addition to an external force, the piston experiences repeated elastic collisions with the particle. We find that the motion of a heavy piston ($M \gg m$), can be described effectively by a Langevin equation. Various numerical evidences suggest that the frictional coefficient in the Langevin equation is given by $\gamma = (1/X)\sqrt{8 \pi m k_BT}$, where $X$ is the position of the piston measured from the thermal wall. Starting from the exact master equation for the full system and using a perturbation expansion in $\epsilon= \sqrt{m/M}$, we integrate out the degrees of freedom of the particle to obtain the effective Fokker-Planck equation for the piston albeit with a different frictional coefficient. Our microscopic study shows that the piston is never in equilibrium during the expansion step, contrary to the assumption made in the usual Szilard engine analysis --- nevertheless the conclusions of Szilard remain valid.

cond-mat.stat-mech↗

arXiv2017

Unusual equilibration of a particle in a potential with a thermal wall

We consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits a slow power law relaxation with a logarithmic correction towards the final equilibrium state. We extend the renewal approach to a class of confining potentials of the form $U(x) \propto x^\alpha$, $x>0$, where we find that the relaxation is $\sim t^{-(\alpha+2)/(\alpha-2)}$ for $\alpha >2$, with a logarithmic correction when $(\alpha+2)/(\alpha-2)$ is an integer. For $\alpha <2$ the relaxation is exponential. Interestingly for $\alpha=2$ (harmonic potential) the localised bath can not equilibrate the particle.

cond-mat.stat-mech↗

arXiv2017

Stall force of a cargo driven by N interacting motor proteins

We study a generic one-dimensional model for an intracellular cargo driven by N motor proteins against an external applied force. The model includes motor-cargo and motor-motor interactions. The cargo motion is described by an over-damped Langevin equation, while motor dynamics is specified by hopping rates which follow a local detailed balance condition with respect to change in energy per hopping event. Based on this model, we show that the stall force, the mean external force corresponding to zero mean cargo velocity, is completely independent of the details of the interactions and is, therefore, always equal to the sum of the stall forces of the individual motors. This exact result is arrived on the basis of a simple assumption: the (macroscopic) state of stall of the cargo is analogous to a state of thermodynamic equilibrium, and is characterized by vanishing net probability current between any two microstates, with the latter specified by motor positions relative to the cargo. The corresponding probability distribution of the microstates under stall is also determined. These predictions are in complete agreement with numerical simulations, carried out using specific forms of interaction potentials.

physics.bio-ph↗

arXiv2014

Transport of organelles by elastically coupled motor proteins

Motor-driven cargo transport is a complex phenomenon where multiple motor proteins attached on to a cargo engage in pulling activity, often leading to tug-of-war, displaying bidirectional motion. However, most mathematical and computational models ignore the details of the motor-cargo interaction. Here, we study a generic model in which N motors are elastically coupled to a cargo, which itself is subjected to thermal noise in the cytoplasm and to an additional external applied force. The motor-hopping rates are chosen to satisfy detailed balance with respect to the energy of elastic stretching. With these assumptions, an (N+1)-variable master equation is constructed for dynamics of the motor-cargo complex. By expanding the hopping rates to linear order in fluctuations in motor positions, we obtain a linear Fokker-Planck equation. The deterministic equations governing the average quantities are separated out and explicit analytical expressions are obtained for the mean velocity and diffusion coefficient of the cargo. We also study the statistical features of the force experienced by an individual motor and quantitatively characterize the load-sharing among the cargo-bound motors. The mean cargo velocity and the effective diffusion coefficient are found to be decreasing functions of the stiffness. While increase in the number of motors N does not increase the velocity substantially, it decreases the effective diffusion coefficient which falls as 1/N asymptotically. We further show that the cargo-bound motors share the force exerted on the cargo equally only in the limit of vanishing elastic stiffness; as stiffness is increased, deviations from equal load sharing are observed. Numerical simulations agree with our analytical results where expected. Interestingly, we find in simulations that the stall force of a cargo elastically coupled to motors is independent of the stiffness.

physics.bio-ph↗

arXiv2013

Memory, Bias and Correlations in Bidirectional Transport of Molecular Motor-driven Cargoes

Molecular motors are specialized proteins which perform active, directed transport of cellular cargoes on cytoskeletal filaments. In many cases, cargo motion powered by motor proteins is found to be bidirectional, and may be viewed as a biased random walk with fast unidirectional runs interspersed with slow `tug-of-war' states. The statistical properties of this walk are not known in detail, and here, we study memory and bias, as well as directional correlations between successive runs in bidirectional transport. We show, based on a study of the direction reversal probabilities of the cargo using a purely stochastic (tug-of-war) model, that bidirectional motion of cellular cargoes is, in general, a correlated random walk. In particular, while the motion of a cargo driven by two oppositely pulling motors is a Markovian random walk, memory of direction appears when multiple motors haul the cargo in one or both directions. In the latter case, the Markovian nature of the underlying single motor processes is hidden by internal transitions between degenerate run and pause states of the cargo. Interestingly, memory is found to be a non-monotonic function of the number of motors. Stochastic numerical simulations of the tug-of-war model support our mathematical results and extend them to biologically relevant situations.

q-bio.SC↗

arXiv2012

Effectiveness of a dynein team in tug-of-war helped by reduced load-sensitivity of detachment: evidence from study of bidirectional endosome transport in Dictyostelium discoideum

Bidirectional cargo transport by molecular motors in cells is a complex phenomenon, in which the cargo (usually a vesicle) alternately moves in retrograde and anterograde directions. In this case, teams of oppositely pulling motors (eg., kinesin and dynein) bind to the cargo simultaneously, and `coordinate' their activity such that the motion consists of spells of positively and negatively directed segments, separated by pauses of varying duration. A set of recent experiments have analyzed the bidirectional motion of endosomes in the amoeba D. discoideum in detail. It was found that in between directional switches, a team of 5-6 dyneins stall a cargo against a stronger kinesin in tug of war, which lasts for almost a second. As the mean detachment time of a kinesin under its stall load was also observed to be ~ 1s, we infer that the collective detachment time of the dynein assembly must also be similar. Here, we analyze this inference from a modeling perspective, using experimentally measured single-molecule parameters as inputs. We find that the commonly assumed exponential load-dependent detachment rate is inconsistent with observations, as it predicts that a 5-dynein assembly will detach under its combined stall load in less than a hundredth of a second. A modified model where the load-dependent unbinding rate is assumed to saturate at stall-force level for super-stall loads gives results which are in agreement with experimental data. Our analysis suggests that the load-dependent detachment of a dynein in a team is qualitatively different at sub-stall and super-stall loads, a conclusion which is likely to have implications in other situations involving collective effects of many motors.

q-bio.SC↗