arXiv subjects

Apratim Chatterji

Publications and source records attributed to Apratim Chatterji.

At least 19 recordsLinked to original sources

arXiv2026

Modulating hydrodynamic flow by modifying the active patch of a colloid

We have developed a simulation model to study the hydrodynamic flow fields around Brownian colloidal particles with an active surface patch. Hydrodynamics is introduced by modeling low-Reynolds-number fluid flows around a colloid using multi-particle collision (MPC) dynamics and allowing momentum exchange between the MPC fluid and the colloid. This approach provides good estimates of both near- and far-field flows around the colloid. The size of the active patch is varied to generate different fluid flow fields around the colloid. In this framework, the fluid in the vicinity of the active patch is driven radially away from (or toward) the surface, and an equal and opposite momentum is imparted to the colloid to ensure momentum conservation. The resulting surface-driven flow generates self-propulsion of the particle, thereby converting an otherwise Brownian colloid into an active Brownian particle. Interestingly, as we systematically vary the surface area of the active patch on the colloid, the nature of the generated flow field changes from that of a pusher to a puller. To model such surface activity-driven flows, we developed a hybrid boundary condition that ensures a no-slip condition while incorporating momentum exchange between the flowing fluid and the colloid surface. This scheme integrates the advantages of bounce-back and stochastic boundary conditions while mitigating their respective limitations. Thus, in future studies, the effective hydrodynamic interactions between an active and a passive colloid, or between two active colloids, can be modulated by adjusting the size of the active patch.

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arXiv2026

Kinetics of segregation of topologically-modified ring polymers in cylindrical confinement

In Escherichia coli (E. coli), entropic repulsion between the two daughter DNA ring polymers under cylindrical confinement is believed to be an important factor governing chromosomal segregation. The repulsion can be enhanced by topological modifications, i.e., by the introduction of internal loops at certain locations along the contour of the circular DNA. However, the effect of topological modifications on the rate of segregation of ring polymers remains unclear. Therefore, we systematically varied the number and the contour length of loops introduced at selected locations by crosslinking monomers. The appropriate crosslinking was motivated by observations that extruded loops are located mainly near the origin of replication (ori-proximal) region of the E. coli chromosome. This resulted in the chains becoming intrinsically anisotropic. Using Langevin dynamics simulations of these topologically modified bead-spring polymers, we calculated the time required for segregation under cylinder confinement. With certain caveats, we found that increasing the number of loops resulted in a decrease in the time of segregation. In line with past work, we propose that this is due to the increase in the entropic repulsion between the polymers upon increasing the number of loops. In addition to the number of loops, the contour length of the loops and the mutual orientation of the (anisotropic) chains in the initial configurations played a role in determining the time of segregation.

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arXiv2025

Entropic alignment of topologically modified ring polymers in cylindrical confinement

Under high cylindrical confinement, segments of ring polymers can be localized along the long axis of the cylinder by introducing internal loops within the ring polymer. The emergent organization of the polymer segments occurs because of the entropic repulsion between internal loops. These principles were used to identify the underlying mechanism of bacterial chromosome organization. Here, we outline functional principles associated with entropic interactions, leading to specific orientations of the ring polymers relative to their neighbors in the cylindrical confinement. We achieve this by modifying the ring polymer topology by creating internal loops of two different sizes within the polymer, and thus create an asymmetry. This allows us to strategically manipulate polymer topology such that segments of a polymer face certain other segments of a neighboring polymer. The polymers therefore behave as if they are subjected to an `effective' entropic interaction reminiscent of interactions between Ising spins. But this emergent spatial and orientational organization is not enthalpy-driven. We consider a bead spring model of flexible polymers with only repulsive excluded volume interactions between the monomers. The polymers entropically repel each other and occupy different halves of the cylinder, and moreover, the adjacent polymers preferentially re-orient themselves along the axis of the cylinder. We further substantiate our observations by free energy calculations. To the best of our knowledge, this is the first study of the emergence of effective orientational interactions by harnessing entropic interactions in flexible polymers. The principles elucidated here could be relevant to understand the interactions between different sized loops within a large chromosome.

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arXiv2025

Entropic organization of topologically modified ring polymers in spherical confinement

It has been shown that under high cylindrical confinement, two ring polymers with excluded volume interactions between monomers, segregate to two halves of the cylinder to maximize their entropy. In contrast, two ring polymers remain mixed within a sphere, as there is no symmetry breaking direction [Nat Rev Microbiol, 8, 600-607 (2010)]. Therefore, in order to observe emergent organization of ring polymers in a sphere, we can introduce an asymmetric topological modification to the polymer architecture by creating a small loop and a big loop within the ring polymer. We consider the bead-spring model of polymers where there are only repulsive excluded volume interactions between the monomers ensuring that the organization we observe is purely entropy-driven. We find that for a single topologically modified polymer within a sphere, the monomers of the bigger loop are statistically more probable to be found closer to the periphery. However, the situation is reversed when we have multiple such topologically modified polymers in a sphere. The monomers of the small loops are found closer to the walls of the sphere. We can increase this localization and radial organization of polymer segments by increasing the number of small loops in each ring polymer. We study how these loops interact with each other within a polymer, as well as with loops of other polymers in spherical confinement. We compare contact maps of multiple such topologically modified polymers in a sphere. Finally, we discuss the plausible relevance of our studies to eukaryotic chromosomes that are confined within a spherical nucleus.

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arXiv2024

Topology mediated organization of E.coli chromosome in fast growth conditions

Recent experiments have been able to visualise chromosome organization in fast-growing E.coli cells. However, the mechanism underlying the spatio-temporal organization remains poorly understood. We propose that the DNA adopts a specific polymer topology as it goes through its cell cycle. We establish that the emergent entropic forces between polymer segments of the DNA-polymer with modified topology, leads to chromosome organization as seen in-vivo. We employ computer simulations of a replicating bead spring model of a polymer in a cylinder to investigate the problem. Our simulation of the overlapping cell cycles not only show successful segregation, but also reproduces the evolution of the spatial organization of the chromosomes as observed in experiments. This manuscript in addition to our previous work on slowly growing bacterial cells, shows that our topology-based model can explain the organization of chromosomes in all growth conditions.

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arXiv2023

Emergent helicity in free-standing semiflexible, charged polymers

Helical motifs are ubiquitious in macromolecular systems. The mechanism of spontaneous emergence of helicity is unknown, especially in cases where torsional interactions are absent. Emergence of helical order needs coordinated organization over long distances in polymeric macromolecules. We establish a very generic mechanism to obtain spontaneous helicity by inducing screened Coulomb interactions between monomers in a semiflexible heteropolymer. Due to changes in solvent conditions, different segments (monomers) of a polymeric chain can get locally charged with charges of differing polarities and magnitudes along the chain contour. This in turn leads to spontaneous emergence of transient helical structures along the chain contour for a wide range of Debye-lengths. We have avoided using torsional potentials to obtain helical structures and rely only on radially symmetric interactions. Lastly, transient helices can be made long-lived when they are subjected to geometric confinement, which can emerge in experimental realizations through a variety of conditions.

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arXiv2021

DNA-polymer architecture orchestrates the segregation and spatio-temporal organization of E. coli chromosomes during replication in slow growth

The mechanism and driving forces of chromosome segregation in the bacterial cell cycle of E. coli is one of the least understood events in its life cycle. Using principles of entropic repulsion between polymer loops confined in a cylinder, we use Monte carlo simulations to show that the segregation dynamics is spontaneously enhanced by the adoption of a certain DNA-polymer architecture as replication progresses. Secondly, the chosen polymer-topology ensures its self-organization along the cell axis while segregation is in progress, such that various chromosomal loci get spatially localized. The time evolution of loci positions quantitatively match the corresponding experimentally reported results, including observation of the cohesion time and the ter-transition. Additionally, the contact map generated using our bead-spring model reproduces the four macro-domains of the experimental Hi-C maps. Lastly, the proposed mechanism reproduces the observed universal dynamics as the sister loci separate during segregation. It was already hypothesized and expected that SMC proteins, e.g. MukBEF contribute over and above entropic repulsion between bacterial-DNA ring-polymers to aid the segregation of daughter DNAs in the E.coli cell cycle. We propose that cross-links (plausibly induced by SMC proteins) at crucial positions along the contour is enough to provide sufficient forces for segregation within reasonable time scales. A mapping between Monte Carlo diffusive dynamics time scales and real time units helps us use experimentally relevant numbers for our modeling.

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arXiv2021

The role of polymer architecture in the entropy driven segregation and spatial organization of bacterial chromosomes

Entropic repulsion between DNA ring polymers under confinement is the key mechanism governing the spatial segregation of bacterial chromosomes, although it remains incompletely understood how proteins aid the process of entropic segregation. Here we establish that `internal' loops within a modified-ring polymer architecture enhances entropic repulsion between two overlapping polymers confined in a cylinder. Moreover it also induces entropy-driven spatial organization of polymer segments as seen in-vivo. To that end, we design polymers of different architectures in our simulations, by introducing a minimal number of cross-links between particular monomers along the chain contour. This helps us to identify the underlying mechanisms which lead to faster segregation of spatially overlapping polymers as well as localization of specific polymer segments. The observed segregation dynamics of overlapping polymers is aided in our simulations by the frequent release of topological constraints, implemented by allowing chains to cross each at regular intervals. Additionally, we compare the segregation dynamics timescales with that of self-avoiding polymers and thereby highlight the significance of Topoisomerase in biological systems where DNA-strands are allowed to occasionally pass through each other. We use the blob model to provide a theoretical understanding of why or how certain architectures lead to enhanced entropic repulsive forces between loops, which in turn leads to the positional organization of segments relative to each other in confined environments. Lastly, we establish a correspondence between the C.crescentus bacterial species and our results for one particular polymer architecture.

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arXiv2020

Transient helix formation in semiflexible polymers without confinement effects

Generic interactions e.g. the Coulomb or other long ranged radially symmetric repulsive interactions between monomers of bead-spring model of a semi-flexible polymer induce instabilities in a initially straight polymer chain to form long lived helical structures. This mechanism can explain the spontaneous emergence of helices in stiff (bio-)polymers as effective charge of the chain increases. The helix formation is independent of the chemistry and torsional potentials are not used. So this method can be used to synthesize helical springs at length scales of nm-10$μ$.

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arXiv2018

Bacterial chromosome organization I: crucial role of release of topological constraints and molecular crowders

We showed in our previous studies that just $3\%$ cross-links, at special points along the contour of the bacterial DNA help the DNA-polymer to get organized at micron length scales \cite{jpcm,epl}. In this work, we investigate how does the release of topological constraints help in the organization of the DNA-polymer. Furthermore, we show that the chain compaction induced by the crowded environment in the bacterial cytoplasm contributes to the organization of the DNA-polymer. We model the DNA chain as a flexible bead-spring ring polymer, where each bead represents $1000$ base pairs. The specific positions of the cross-links have been taken from the experimental contact maps of the bacteria {\em C. crescentus} and {\em E. coli}. We introduce different extents of topological constraints in our model by systematically changing the diameter of the monomer bead. It varies from the value where the chain crossing can occur freely to the value where the chain crossing is disallowed. We also study the role of molecular crowders by introducing an effective Lennard Jones attraction between the monomers. Using Monte-Carlo simulations, we show that the release of topological constraints and the crowding environment play a crucial role to obtain a unique organization of the polymer.

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arXiv2018

Bacterial chromosome organization II: few special cross-links, cell confinement, and molecular crowders play the pivotal roles

Using a bead-spring model of bacterial DNA polymers of {\em C. crescentus} and {\em E. coli} we show that just $33$ and $38$ effective cross-links at special positions along the chain contour of the DNA can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the $33$ cross-links along the chain contour are chosen from the contact map data of {\em C. crescentus}. We represent $1000$ base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA. Thus a $4017$ beads on a flexible ring polymer represents the {\em C. crescentus} DNA with $4017$ kilo-base pairs. Choosing suitable parameters from our preceding study, we also incorporate the role of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the {\em C. crescentus} with available experimental contact map data and also give a prediction of the approximate positions of different segments within the cell in 3D. For the {\em E. coli} chromosome with $4.6$ million base pairs, we need around $38$ effective cross-links with cylindrical confinement to organize the chromosome. We also predict the 3D organization of the {\em E. coli} chromosome segments within the cylinder which represents the cell wall.

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arXiv2018

Heirarchical and synergistic self-assembly in composites of model Wormlike micellar-polymers and nanoparticles results in nanostructures with diverse morphologies

Using Monte Carlo simulations, we investigate the self-assembly of model nanoparticles inside a matrix of model equilibrium polymers (or matrix of Wormlike micelles) as a function of the polymeric matrix density and the excluded volume parameter between polymers and nanoparticles. In this paper, we show morphological transitions in the system architecture via synergistic self-assembly of nanoparticles and the equilibrium polymers. In a synergistic self-assembly, the resulting morphology of the system is a result of the interaction between both nanoparticles and the polymers, unlike the polymer templating method. We report the morphological transition of nanoparticle aggregates from percolating network-like structures to non-percolating clusters as a result of the change in the excluded volume parameter between nanoparticles and polymeric chains. In parallel with the change in the self-assembled structures of nanoparticles, the matrix of equilibrium polymers also shows a transition from a dispersed state to a percolating network-like structure formed by the clusters of polymeric chains. We show that the shape anisotropy of the nanoparticle clusters formed is governed by the polymeric density resulting in rod-like, sheet-like or other anisotropic nanoclusters. It is also shown that the pore shape and the pore size of the porous network of nanoparticles can be changed by changing the minimum approaching distance between nanoparticles and polymers. We provide a theoretical understanding of why various nanostructures with very different morphologies are obtained.

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arXiv2017

Self assembled linear polymeric chains with tuneable semiflexibility using isotropic interactions

We propose a two-body spherically symmetric (isotropic) potential such that particles interacting by the potential self assemble into linear semiflexible polymeric chains without branching. By suitable control of the potential parameters we can control the persistence length of the polymer, and can even introduce a controlled number of branches. Thus we show how to achieve effective directional interactions starting from spherically symmetric potentials. The self assembled polymers have a exponential distribution of chain lengths akin to what is observed for worm-like micellar systems. On increasing particle density the polymeric chains self-organize to an ordered line-hexagonal phase where every chain is surrounded by six parallel chains, the transition is first order. On further increase in monomer density, the order is destroyed and we get a branched gel like phase. This potential can be used to model semi-flexible equilibrium polymers with tunable semiflexibility and excluded volume. The use of the potential is computationally cheap and hence, can be used to simulate and probe complex micellar dynamics with long chains. The potential also gives a plausible method of tuning colloidal interactions in experiments such that one can obtain self-assembling polymeric chains made up of colloids and probe polymer dynamics using an optical microscope.

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arXiv2017

Role of special cross-links in structure formation of bacterial DNA polymer

Using data from contact maps of the DNA-polymer of $E. Coli$ (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. By suitable Monte Carlo Simulations, we show that the presence of these cross-links leads to a particular architecture and organization of the chain at large (micron) length scales of the DNA. We also investigate the structure of a ring polymer with an equal number of cross-links at random positions along the chain. We find that though the polymer does get organized at the large length scales, the nature of the organization is quite different from the organization observed with cross-links at specific biologically determined positions. We used the contact map of $E. Coli$ bacteria which has around $4.6$ million base pairs in a single circular chromosome. In our coarse-grained flexible ring polymer model, we used $4642$ monomer beads and observed that around $80$ cross-links are enough to induce the large-scale organization of the molecule accounting for statistical fluctuations caused by thermal energy. The length of a DNA chain of an even simple bacterial cell such as $E. Coli$ is much longer than typical proteins, hence we avoided methods used to tackle protein folding problems. We define new suitable quantities to identify large scale structure of a polymer chain with a few cross-links.

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arXiv2017

Origin of spatial organization of DNA-polymer in bacterial chromosomes

In-vivo DNA organization at large length scales ($\sim 100nm$) is highly debated and polymer models have proved useful to understand the principle of DNA-organization. Here, we show that $<2$% cross-links at specific points in a ring polymer can lead to a distinct spatial organization of the polymer. The specific pairs of cross-linked monomers were extracted from contact maps of bacterial DNA. We are able to predict the structure of 2 DNAs using Monte Carlo simulations of the bead-spring polymer with cross-links at these special positions. Simulations with cross-links at random positions along the chain show that the organization of the polymer is different in nature from the previous case.

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arXiv2016

Network formation and gelation in Telechelic star polymers

We investigate the efficiency of gelation and network formation in telechelic star polymer melt, where the tips of polymer arms are dipoles while rest of the monomers are uncharged. Our work is motivated by the experimental observations [A.Kulkarni et.al, Macromolecules, {\bf 48}, 6580 (2015)], in which rheological studies of telechelic star polymers of poly-(L-actide), a bio-degradable polymer, showed a drastic increase in elastic properties (up to $2000$ times) compared to corresponding star polymers without the telechelic arm ends. In contrast to previous studies, we avoid using effective attractive Lennard Jones potentials or dipolar potentials to model telechelic interactions. Instead we use explicit Coulomb positive and negative charges at the tip of polymer-arms of our bead-spring model of star polymers. By our simulations we show that the dipoles at the tip of star arms aggregate together to form clusters of dipoles. Each cluster has contribution from several stars, and in turn each star contributes to several clusters. Thus the entire polymer melt forms a connected network. Network forming tendencies decrease with decrease of the value of the effective charge constituting the dipole: this can be experimentally realized by choosing a different ionomer for the star tip. We systematically varied the value of dipole charges, the fraction of star-arms with dipoles at the tip and the length of the arms. The choice of explicit charges in our calculations enables us to make better quantitative predictions about the onset of gelation, moreover we get qualitatively distinct results about structural organization of dipoles within a dipole-cluster.

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arXiv2014

Heirarchical Self Assembly: Self Organized nano-structures in a nematically ordered matrix of self assembled polymeric chains

We report many different nano-structures which are formed when model nano-particles of different sizes (diameter σ n ) are allowed to aggregate in a background matrix of semi-flexible self assembled polymeric worm like micellar chains. The different nano-structures are formed by the dynamical arrest of phase-separating mixtures of micellar monomers and nano-particles. The different mor- phologies obtained are the result of an interplay of the available free volume, the elastic energy of deformation of polymers, the density (chemical potential) of the nano-particles in the polymer ma- trix and, of course, the ratio of the size of self assembling nano-particles and self avoidance diameter of polymeric chains. We have used a hybrid semi-grand canonical Monte Carlo simulation scheme to obtain the (non-equilibrium) phase diagram of the self-assembled nano-structures. We observe rod-like structures of nano-particles which get self assembled in the gaps between the nematically ordered chains as well as percolating gel-like network of conjoined nanotubes. We also find a totally unexpected interlocked crystalline phase of nano-particles and monomers, in which each crytal plane of nanoparticles is separated by planes of perfectly organized polymer chains. We identified the con- dition which leads to such interlocked crystal structure. We suggest experimental possibilities of how the results presented in this paper could be used to obtain different nano-structures in the lab.

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arXiv2013

Self assembly of monodisperse CdS nano-cylinders with a pore

We present investigate the self assembly and growth of an array of $CdS$ nanotubes: a consequence of a fine balance of directed motion, diffusion and aggregation of reacting ${\rm Cd^{+2}}$ and ${\rm S^{-2}}$ ions. In a previous communication [J. Kiruthiga, A. Chatterji, J. Chem. Phys., {\bf 138} 024905 (2013)], we identified the mechanism of a unexpected growth of a very uniform $CdS$ nano-cylinder from the end of a nano-channel. Furthermore, the cylinder had a pore along the axis but were closed at one end. This unique phenomenon of self assembly of {\em monodisperse} CdS nano-cylinders had been observed in a rather simple experiment where two chambers containing 0.1 M ${\rm Cd Cl_2}$ and 0.1 M ${\rm Na_2 S}$ solutions were joined by an array of anodized aluminium oxide (AAO) nano-channels [A. Varghese, S. Datta, Phys. Rev. E., {\bf 85}, 056104 (2012)]. Our previous study identified the principles governing the growth of a single nano-tube at the exit point of a single AAO-nano-channel. In this communication, we identify factors affecting the self-assembly process for nano-tubes growing out an array of closely spaced AAO nano-channel exits. Our model is not $Cd^{+2}$ or $S^{2-}$ specific, the experimental scheme can be extended to self assemble a general class of reacting-diffusing A and B ions with A (${\rm Cd^{+2}}$) selectively migrating out from a nano-channel. In particular, we note that after the initial prolonged growth of nanotubes, there can arise a severe deficiency of B-ions (${\rm S^{-2}}$) ions near the AAO-nano-channel exits, the points where the reaction and aggregation occurs to form the $CdS$ nanotube, thus impeding further growth of uniform CdS nano-tubes. Thereby we predict the necessary characteristics of reacting systems which can be self assembled using suitable adaptations of previous experiments.

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