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Debashish Chowdhury

Publications and source records attributed to Debashish Chowdhury.

At least 37 records · Page 2Linked to original sources
arXiv2017

A Multispecies Exclusion Process with Fusion and Fission of Rods: a model inspired by Intraflagellar Transport

We introduce a multispecies exclusion model where length-conserving probabilistic fusion and fission of the hard rods are allowed. Although all rods enter the system with the same initial length ${\ell}=1$, their length can keep changing, because of fusion and fission, as they move in a step-by-step manner towards the exit. Two neighboring hard rods of lengths ${\ell}_{1}$ and ${\ell}_{2}$ can fuse into a single rod of longer length ${\ell}={\ell}_{1}+{\ell}_{2}$ provided ${\ell} \leq N$. Similarly, length-conserving fission of a rod of length ${\ell}' \leq N$ results in two shorter daughter rods. Based on the extremum current hypothesis, we plot the phase diagram of the model under open boundary conditions utilizing the results derived for the same model under periodic boundary condition using mean-field approximation. The density profile and the flux profile of rods are in excellent agreement with computer simulations. Although the fusion and fission of the rods are motivated by similar phenomena observed in Intraflagellar Transport (IFT) in eukaryotic flagella, this exclusion model is too simple to account for the quantitative experimental data for any specific organism. Nevertheless, the concepts of `flux profile' and `transition zone' that emerge from the interplay of fusion and fission in this model are likely to have important implications for IFT and for other similar transport phenomena in long cell protrusions.

cond-mat.stat-mech↗
arXiv2017

Strength and stability of active ligand-receptor bonds: a microtubule attached to a wall by molecular motor tethers

We develop a stochastic kinetic model of a pre-formed attachment of a mictrotuble (MT) with a cell cortex, in which the MT is tethered to the cell by a group of active motor proteins. Such an attachment is a particularly unique case of ligand-receptor bonds: The MT ligand changes its length (and thus binding sites) with time by polymerization-depolymerization kinetics, while multiple motor receptors tend to walk actively along the MT length. These processes, combined with force-mediated unbinding of the motors, result in an elaborate behavior of the MT connection to the cell cortex. We present results for the strength and lifetime of the system through the well-established force-clamp and force-ramp protocols when external tension is applied to the MT. The simulation results reveal that the MT-cell attachment behaves as a catch-bond or slip-bond depending on system parameters. We provide analytical approximations of the lifetime and discuss implications of our results on in-vitro experiments.

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

A generalized Michaelis-Menten equation in protein synthesis: effects of mis-charged cognate tRNA and mis-reading of codon

The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA. By a combination of analytical and numerical methods we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model. The corresponding exact analytical expression for the average rate of elongation of a nascent protein is a `biologically motivated' generalization of the {\it Michaelis-Menten formula} for the average rate of enzymatic reactions. This generalized Michaelis-Menten-like formula (and the exact analytical expressions for a few other quantities) that we report here display the interplay of four different branched pathways corresponding to selection of four different types of tRNA.

physics.bio-ph↗
arXiv2017

A Multispecies Exclusion Model Inspired By Transcriptional Interference

We introduce exclusion models of two distinguishable species of hard rods with their distinct sites of entry and exit under open boundary conditions. In the first model both species of rods move in the same direction whereas in the other two models they move in the opposite direction. These models are motivated by the biological phenomenon known as Transcriptional Interference. Therefore, the rules for the kinetics of the models, particularly the rules for the outcome of the encounter of the rods, are also formulated to mimic those observed in Transcriptional Interference. By a combination of mean-field theory and computer simulation of these models we demonstrate how the flux of one species of rods is completely switched off by the other. Exploring the parameter space of the model we also establish the conditions under which switch-like regulation of two fluxes is possible; from the extensive analysis we discover more than one possible mechanism of this phenomenon.

physics.bio-ph↗
arXiv2017

Michaelis-Menten at 100 and allosterism at 50: driving molecular motors in a hailstorm with noisy ATPase engines and allosteric transmission

Cytoskeletal motor proteins move on filamentous tracks by converting input chemical energy that they derive by catalyzing the hydrolysis of ATP. The ATPase site is the analog of an engine and hydrolysis of ATP is the analog of burning of chemical fuel. Moreover, the functional role of a segment of the motor is analogous to that of the transmission system of an automobile that consists of shaft, gear, clutch, etc. The operation of the engine is intrinsically "noisy" and the motor faces a molecular "hailstorm" in the aqueous medium. In this commemorative article, we celebrate the centenary of Michaelis and Menten's landmark paper of 1913 and the golden jubilee of Monod et al.'s classic paper of 1963 by highlighting their relevance in explaining the operational mechanisms of the engine and the transmission system, respectively, of cytoskeletal motors.

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↗
arXiv2017

Quantitative Connection Between Ensemble Thermodynamics and Single-Molecule Kinetics: A Case Study Using Cryogenic Electron Microscopy and Single-Molecule Fluorescence Resonance Energy Transfer Investigations of the Ribosome

At equilibrium, thermodynamic and kinetic information can be extracted from biomolecular energy landscapes by many techniques. However, while static, ensemble techniques yield thermodynamic data, often only dynamic, single-molecule techniques can yield the kinetic data that describes transition-state energy barriers. Here we present a generalized framework based upon dwell-time distributions that can be used to connect such static, ensemble techniques with dynamic, single-molecule techniques, and thus characterize energy landscapes to greater resolutions. We demonstrate the utility of this framework by applying it to cryogenic electron microscopy (cryo-EM) and single-molecule fluorescence resonance energy transfer (smFRET) studies of the bacterial ribosomal pre-translocation complex. Among other benefits, application of this framework to these data explains why two transient, intermediate conformations of the pre-translocation complex, which are observed in a cryo-EM study, may not be observed in several smFRET studies.

physics.bio-ph↗
arXiv2017

TASEP on parallel tracks: effects of mobile bottlenecks in fixed segments

We study the flux of totally asymmetric simple exclusion processes (TASEPs) on a twin co-axial square tracks. In this biologically motivated model the particles in each track act as mobile bottlenecks against the movement of the particles in the other although the particle are not allowed to move out of their respective tracks. So far as the outer track is concerned, the particles on the inner track act as bottlenecks only over a set of fixed segments of the outer track, in contrast to site-associated and particle-associated quenched randomness in the earlier models of disordered TASEP. In a special limiting situation the movement of particles in the outer track mimic a TASEP with a "point-like" immobile (i.e., quenched) defect where phase segregation of the particles is known to take place. The length of the inner track as well as the strength and number density of the mobile bottlenecks moving on it are the control parameters that determine the nature of spatio-temporal organization of particles on the outer track. Variation of these control parameters allow variation of the width of the phase-coexistence region on the flux-density plane of the outer track. Some of these phenomena are likely to survive even in the future extensions intended for studying traffic-like collective phenomena of polymerase motors on double-stranded DNA.

cond-mat.stat-mech↗
arXiv2017

First Passage Time in Computation by Tape-Copying Turing Machines: Slippage of Nascent Tape

Transcription of the genetic message encoded chemically in the sequence of the DNA template is carried out by a molecular machine called RNA polymerase (RNAP). Backward or forward slippage of the nascent RNA with respect to the DNA template strand give rise to a transcript that is, respectively, longer or shorter than the corresponding template. We model a RNAP as a "Tape-copying Turing machine" (TCTM) where the DNA template is the input tape while the nascent RNA strand is the output tape. Although the TCTM always steps forward the process is assumed to be stochastic that has a probability of occurrence per unit time. The time taken by a TCTM for each single successful forward stepping on the input tape, during which the output tape suffers lengthening or shortening by $n$ units because of backward or forward slippage, is a random variable; we report some of the statistical characteristics of this time by using the formalism for calculation of the distributions of {\it first-passage time}. The results are likely to find applications in the analysis of experimental data on "programmed" transcriptional error caused by transcriptional slippage which is a mode of "recoding" of genetic information.

physics.bio-ph↗
arXiv2015

Mixed molecular motor traffic on nucleic acid tracks: models of transcriptional interference and regulation of gene expression

RNA polymerase (RNAP) is molecular machine that polymerizes a RNA molecule, a linear heteropolymer, using a single stranded DNA (ssDNA) as the corresponding template; the sequence of monomers of the RNA is dictated by that of monomers on the ssDNA template. While polymerizing a RNA, the RNAP walks step-by-step on the ssDNA template in a specific direction. Thus, a RNAP can be regarded also as a molecular motor and the sites of start and stop of its walk on the DNA mark the two ends of the genetic message that it transcribes into RNA. Interference of transcription of two overlapping genes is believed to regulate the levels of their expression, i.e., the overall rate of the corresponding RNA synthesis, through suppressive effect of one on the other. Here we model this process as a mixed traffic of two groups of RNAP motors that are characterized by two distinct pairs of start and stop sites. Each group polymerizes identical copies of a RNA while the RNAs polymerized by the two groups are different. These models, which may also be viewed as two interfering totally asymmetric simple exclusion processes, account for all modes of transcriptional interference in spite of their extreme simplicity. A combination of mean-field theory and computer simulation of these models demonstrate the physical origin of the switch-like regulation of the two interfering genes in both co-directional and contra-directional traffic of the two groups of RNAP motors.

physics.bio-ph↗
arXiv2015

Collective cargo hauling by a bundle of parallel microtubules: bi-directional motion caused by load-dependent polymerization and depolymerization

A microtubule (MT) is a hollow tube of approximately 25 nm diameter. The two ends of the tube are dissimilar and are designated as `plus' and `minus' ends. Motivated by the collective push and pull exerted by a bundle of MTs during chromosome segregation in a living cell, we have developed here a much simplified theoretical model of a bundle of parallel dynamic MTs. The plus-end of all the MTs in the bundle are permanently attached to a movable `wall' by a device whose detailed structure is not treated explicitly in our model. The only requirement is that the device allows polymerization and depolymerization of each MT at the plus-end. In spite of the absence of external force and direct lateral interactions between the MTs, the group of polymerizing MTs attached to the wall create a load force against the group of depolymerizing MTs and vice-versa; the load against a group is shared equally by the members of that group. Such indirect interactions among the MTs gives rise to the rich variety of possible states of collective dynamics that we have identified by computer simulations of the model in different parameter regimes. The bi-directional motion of the cargo, caused by the load-dependence of the polymerization kinetics, is a "proof-of-principle" that the bi-directional motion of chromosomes before cell division does not necessarily need active participation of motor proteins.

q-bio.SC↗
arXiv2014

Single-enzyme kinetics with branched pathways: exact theory and series expansion

The progress of the successive rounds of catalytic conversion of substrates into product(s) by a single enzyme is characterized by the distribution of turnover times. Establishing the most general form of dependence of this distribution on the substrate concentration [S] is one of the fundamental challenges in single molecule enzymology. The distribution of the times of dwell of a molecular motor at the successive positions on its track is an analogous quantity. We derive approximate series expansions for the [ATP]-dependence of the first two moments of the dwell time distributions of motors that catalyze hydrolysis of ATP to draw input energy. Comparison between our results for motors with branched pathways and the corresponding expressions reported earlier for linear enzymatic pathways provides deep insight into the effects of the branches. Such insight is likely to help in discovering the most general form of [S]-dependence of these fundamental distributions.

physics.chem-ph↗
arXiv2014

Distribution of lifetimes of kinetochore-microtubule attachments: interplay of energy landscape, molecular motors and microtubule (de-)polymerization

Before a cell divides into two daughter cells, chromosomes are replicated resulting in two sister chromosomes embracing each other. Each sister chromosome is bound to a separate proteinous structure, called kinetochore (kt), that captures the tip of a filamentous protein, called microtubule (MT). Two oppositely oriented MTs pull the two kts attached to two sister chromosomes thereby pulling the two sisters away from each other. Here we theoretically study an even simpler system, namely an isolated kt coupled to a single MT; this system mimics an {\it in-vitro} experiment where a single kt-MT attachment is reconstituted using purified extracts from budding yeast. Our models not only account for the experimentally observed "catch-bond-like" behavior of the kt-MT coupling, but also make new predictions on the probability distribution of the lifetimes of the attachments. In principle, our new predictions can be tested by analyzing the data collected in the {\it in-vitro} experiments provided the experiment is repeated sufficiently large number of times. Our theory provides a deep insight into the effects of (a) size, (b) energetics, and (c) stochastic kinetics of the kt-MT coupling on the distribution of the lifetimes of these attachments.

physics.bio-ph↗
arXiv2013

First-passage problems in DNA replication: effects of template tension on stepping and exonuclease activities of a DNA polymerase motor

A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. But, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an {\it in-vitro} experiment where a single-stranded DNA, subjected to a mechanical tension $F$, is converted to a double-stranded DNA by a single DNAP. The $F$-dependence of the average rate of replication, which depends on the rates of both polymerase and exonuclease activities of the DNAP, is in good qualitative agreement with the corresponding experimental results. We introduce 9 novel distinct {\it conditional dwell times} of a DNAP. Using the methods of first-passage times, we also derive the exact analytical expressions for the probability distributions of these conditional dwell times. The predicted $F$-dependence of these distributions are, in principle, accessible to single-molecule experiments.

q-bio.SC↗
arXiv2013

Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist's perspective

A molecular motor is made of either a single macromolecule or a macromolecular complex. Just like their macroscopic counterparts, molecular motors "transduce" input energy into mechanical work. All the nano-motors considered here operate under isothermal conditions far from equilibrium. Moreover, one of the possible mechanisms of energy transduction, called Brownian ratchet, does not even have any macroscopic counterpart. But, molecular motor is not synonymous with Brownian ratchet; a large number of molecular motors execute a noisy power stroke, rather than operating as Brownian ratchet. We review not only the structural design and stochastic kinetics of individual single motors, but also their coordination, cooperation and competition as well as the assembly of multi-module motors in various intracellular kinetic processes. Although all the motors considered here execute mechanical movements, efficiency and power output are not necessarily good measures of performance of some motors. Among the intracellular nano-motors, we consider the porters, sliders and rowers, pistons and hooks, exporters, importers, packers and movers as well as those that also synthesize, manipulate and degrade "macromolecules of life". We review mostly the quantitative models for the kinetics of these motors. We also describe several of those motor-driven intracellular stochastic processes for which quantitative models are yet to be developed. In part I, we discuss mainly the methodology and the generic models of various important classes of molecular motors. In part II, we review many specific examples emphasizing the unity of the basic mechanisms as well as diversity of operations arising from the differences in their detailed structure and kinetics. Multi-disciplinary research is presented here from the perspective of physicists.

physics.bio-ph↗
arXiv2013

A theoretical model for attachment lifetimes of kinetochore-microtubules: Mechano-kinetic "catch-bond" mechanism for error-correction

Before cell division, two identical copies of chromosomes are pulled apart by microtubule (MT) filaments that approach the chromosomes from the opposite poles a mitotic spindle. Connection between the MTs and the chromosomes are mediated by a molecular complex called kinetochore. An externally applied tension can lead to detachment of the MTs from the kinetochore; the mean lifetime of such an attachment is essentially a mean first-passage time. In their in-vitro pioneering single-kinetochore experiments, Akiyoshi et al. (Nature 468, 576 (2010)), observed that the mean lifetimes of reconstituted MT-kinetochore attachments vary non-monotonically with increasing tension. The counter-intuitive stabilization of the attachments by small load forces was interpreted in terms of a catch-bond-like mechanism based on a phenomenological 2-state kinetic model. Here we develop the first detailed microscopic model for studying the dependence of the lifetime of the MT-kinetochore attachment on (a) the structure, (b) energetics, and (c) kinetics of the coupling. The catch-bond-like mechanism emerges naturally from this model. Moreover, in-silico experiments on this model reveal further interesting phenomena, arising from the subtle effects of competing sub-processes, which are likely to motivate new experiments in this emerging area of single-particle biophysics.

physics.bio-ph↗