arXiv subjects

Bhavya Mishra

Publications and source records attributed to Bhavya Mishra.

6 recordsLinked to original sources

arXiv2026

Effective field theory of a single scalar pion field for large scale structure in the Universe

We discuss the effective field theory of large scale structure in terms of a single scalar degree of freedom, corresponding to the velocity potential of the matter fluid in a $\Lambda$CDM universe. This cosmic ``pion'' field is nonlinearly related to the overdensity and the gravitational potential, and corresponds to the Goldstone boson of spontaneously broken spacetime symmetry, allowing us to organize perturbation theory in a systematic way while keeping the symmetries manifest. We develop the effective field theory of the pion field to next-to-leading order, and we use it to calculate the corrections to the power spectrum and to check that these are consistent with the consistency relations of spontaneously broken spacetime symmetry. We compare our results against computer simulations for the evolution of large scale structure in the pion field picture, and we make use of N-body simulations to measure EFT coefficients and analyze the growth of additional degrees of freedom in the deep nonlinear regime. We conclude with a discussion of how the pion field picture may help suggest new variables for analyzing simulations and experimental surveys of large scale structure.

astro-ph.CO↗

arXiv2019

A biologically motivated three-species exclusion model: effects of leaky scanning and overlapping genes on initiation of protein synthesis

Totally asymmetric simple exclusion process (TASEP) was originally introduced as a model for the traffic-like collective movement of ribosomes on a messenger RNA (mRNA) that serves as the track for the motor-like forward stepping of individual ribosomes. In each step, a ribosome elongates a protein by a single unit using the track also as a template for protein synthesis. But, pre-fabricated, functionally competent, ribosomes are not available to begin synthesis of protein; a subunit directionally scans the mRNA in search of the pre-designated site where it is supposed to bind with the other subunit and begin the synthesis of the corresponding protein. However, because of `leaky' scanning, a fraction of the scanning subunits miss the target site and continue their search beyond the first target. Sometimes such scanners successfully identify the site that marks the site for initiation of the synthesis of a different protein. In this paper, we develop an exclusion model, with three interconvertible species of hard rods, to capture some of the key features of these biological phenomena and study the effects of the interference of the flow of the different species of rods on the same lattice. More specifically, we identify the meantime for the initiation of protein synthesis as appropriate mean {\it first-passage} time that we calculate analytically using the formalism of backward master equations. In spite of the approximations made, our analytical predictions are in reasonably good agreement with the numerical data that we obtain by performing Monte Carlo simulations. We also compare our results with a few experimental facts reported in the literature and propose new experiments for testing some of our new quantitative predictions.

cond-mat.stat-mech↗

arXiv2018

First-passage processes on a filamentous track in a dense traffic: optimizing diffusive search for a target in crowding conditions

Several important biological processes are initiated by the binding of a protein to a specific site on the DNA. The strategy adopted by a protein, called transcription factor (TF), for searching its specific binding site on the DNA has been investigated over several decades. In recent times the effects obstacles, like DNA-binding proteins, on the search by TF has begun to receive attention. RNA polymerase (RNAP) motors collectively move along a segment of the DNA during a genomic process called transcription. This RNAP traffic is bound to affect the diffusive scanning of the same segment of the DNA by a TF searching for its binding site. Motivated by this phenomenon, here we develop a kinetic model where a `particle', that represents a TF, searches for a specific site on a one-dimensional lattice. On the same lattice another species of particles, each representing a RNAP, hop from left to right exactly as in a totally asymmetric simple exclusion process (TASEP) which forbids simultaneous occupation of any site by more than one particle, irrespective of their identities. Although the TF is allowed to attach to or detach from any lattice site, the RNAPs can attach only to the first site at the left edge and detach from only the last site on the right edge of the lattice. We formulate the search as a {\it first-passage} process; the time taken to reach the target site {\it for the first time}, starting from a well defined initial state, is the search time. By approximate analytical calculations and Monte Carlo (MC) computer simulations, we calculate the mean search time. We show that RNAP traffic rectifies the diffusive motion of TF to that of a Brownian ratchet, and the mean time of successful search can be even shorter than that required in the absence of RNAP traffic. Moreover, we show that there is an optimal rate of detachment that corresponds to the shortest mean search time.

physics.bio-ph↗

arXiv2018

A biologically inspired two-species exclusion model: effects of RNA polymerase motor traffic on simultaneous DNA replication

We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles ($P$) represents RNAP motors while the other ($R$) represents replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of only two $R$ particles are allowed to enter the lattice from two opposite ends whereas the unrestricted number of $P$ particles constitute a totally asymmetric simple exclusion process (TASEP) in a segment in the middle of the lattice. Consequently, the lattice consists of three segments; the encounters of the $P$ particles with the $R$ particles are confined within the middle segment (segment $2$) whereas only the $R$ particles can occupy the sites in the segments $1$ and $3$. The model captures three distinct pathways for resolving the co-directional as well as head-collision between the $P$ and $R$ particles. Using Monte Carlo simulations and heuristic analytical arguments that combine exact results for the TASEP with mean-field approximations, we predict the possible outcomes of the conflict between the traffic of RNAP motors ($P$ particles engaged in transcription) and the replication forks ($R$ particles). The outcomes, of course, depend on the dynamical phase of the TASEP of $P$ particles. In principle, the model can be adapted to the experimental conditions to account for the data quantitatively.

q-bio.SC↗

arXiv2017

Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model

We develope a two-species exclusion process with a distinct pair of entry and exit sites for each species of rigid rods. The relatively slower forward stepping of the rods in an extended bottleneck region, located in between the two entry sites, controls the extent of interference of the co-directional flow of the two species of rods. The relative positions of the sites of entry of the two species of rods with respect to the location of the bottleneck are motivated by a biological phenomenon. However, the primary focus of the study here is to explore the effects of the interference of the flow of the two species of rods on their spatio-temporal organization and the regulations of this interference by the extended bottleneck. By a combination of mean-field theory and computer simulation we calculate the flux of both species of rods and their density profiles as well as the composite phase diagrams of the system. If the bottleneck is sufficiently stringent some of the phases become practically unrealizable although not ruled out on the basis of any fundamental physical principle. Moreover the extent of suppression of flow of the downstream entrants by the flow of the upstream entrants can also be regulated by the strength of the bottleneck. We speculate on the possible implications of the results in the context of the biological phenomenon that motivated the formulation of the theoretical model.

physics.bio-ph↗

arXiv2017

Slip of grip of a molecular motor on a crowded track: Modeling shift of reading frame of ribosome on RNA template

We develop a stochastic model for the programmed frameshift of ribosomes synthesizing a protein while moving along a mRNA template. Normally the reading frame of a ribosome decodes successive triplets of nucleotides on the mRNA in a step-by-step manner. We focus on the programmed shift of the ribosomal reading frame, forward or backward, by only one nucleotide which results in a fusion protein; it occurs when a ribosome temporarily loses its grip to its mRNA track. Special "slippery" sequences of nucleotides and also downstream secondary structures of the mRNA strand are believed to play key roles in programmed frameshift. Here we explore the role of an hitherto neglected parameter in regulating -1 programmed frameshift. Specifically, we demonstrate that the frameshift frequency can be strongly regulated also by the density of the ribosomes, all of which are engaged in simultaneous translation of the same mRNA, at and around the slippery sequence. Monte Carlo simulations support the analytical predictions obtained from a mean-field analysis of the stochastic dynamics.

physics.bio-ph↗