Intrachain Ordering and Segregation of Polymers under Confinement

Proceedings of the National Academy of Sciences, 2006

Despite recent progress in visualization experiments, the mechanism underlying chromosome segregation in bacteria still remains elusive. Here we address a basic physical issue associated with bacterial chromosome segregation, namely the spatial organization of highly confined, self-avoiding polymers (of nontrivial topology) in a rod-shaped cell-like geometry. Through computer simulations, we present evidence that, under strong confinement conditions, topologically distinct domains of a polymer complex effectively repel each other to maximize their conformational entropy, suggesting that duplicated circular chromosomes could partition spontaneously. This mechanism not only is able to account for the spatial separation per se but also captures the major features of the spatiotemporal organization of the duplicating chromosomes observed in Escherichia coli and Caulobacter crescentus.

We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.

Soft Matter, 2012

Chromosomes in living cells are strongly confined but show a high level of spatial organization. Similarly, confined polymers display intriguing organizational and segregational properties. Here, we discuss how ring topology influences self-avoiding polymers confined in a cylindrical space, i.e. individual polymers as well as the way they interact. Our molecular dynamics simulations suggest that a ring polymer can be viewed as a ''parallel connection'' of two linear subchains, each trapped in a narrower imaginary tube. As a consequence, ring topology ''stiffens'' individual chains about fivefold and enhances their segregation appreciably, as if it induces extra linear ordering. Using a ''renormalized'' Flory approach, we show how ring topology influences individual chains in the long chain limit. Our polymer model quantitatively explains the long-standing observations of chromosome organization and segregation in E. coli.

Physical Biology

We investigate the motion of two overlapping polymers confined in a 2D box. A statistical model is constructed using blob-free-energy arguments. We find spontaneous segregation under the condition L > R(∥), and mixing under L < R(∥), where L is the length of the box and R(∥) is the polymer extension in an infinite slit. The segregation time (τ) is determined by solving a mean first-passage time problem and by performing Monte Carlo simulations. Both show a minimum in τ as a function of L. Although our results are restricted to 2D, the basic mechanism of competition between entropy and confinement leading to the minimum is suggestive of an evolutionary driving force for size selection.

The Journal of Chemical Physics

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 [1, 2]. 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 C. crescentus and 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.

We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semidilute solutions. Our main result is that the free energy for overlapping n chains is independent of chain length and scales as n 9=4 , slowly crossing over to n 3 , as n increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an additional free energy. Our results imply that, during cell cycle, global reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.

Soft Matter, 2009

... His research interests include the theory and modelling of transport properties of macromolecules and nano-particles and topological effects in macromolecular conformation and ... the aforementioned mix of moves and at regular intervals shrinkages of the simulation cell are ...

Nucleic Acids Research, 2013

Using numerical simulations of pairs of long polymeric chains confined in microscopic cylinders, we investigate consequences of double-strand DNA breaks occurring in independent topological domains, such as these constituting bacterial chromosomes. Our simulations show a transition between segregated and mixed state upon linearization of one of the modelled topological domains. Our results explain how chromosomal organization into topological domains can fulfil two opposite conditions: (i) effectively repulse various loops from each other thus promoting chromosome separation and (ii) permit local DNA intermingling when one or more loops are broken and need to be repaired in a process that requires homology search between broken ends and their homologous sequences in closely positioned sister chromatid.

The Journal of Chemical Physics

Using a coarse-grained bead-spring model of bacterial chromosomes of Caulobacter crescentus and Escherichia coli, we show that just 33 and 38 effective cross-links in 4017 and 4642 monomer chains at special positions along the chain contour 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 33/38 cross-links along the chain contour are chosen from the Hi-C contact map of bacteria C. crescentus and E. coli. We represent 1000 base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA polymer. Thus, 4017/4642 beads on a flexible ring polymer represent the C. crescentus/E. coli DNA polymer with 4017/4642 kilo-base pairs. Choosing suitable parameters from Paper I, we also incorporate the role of compaction of the polymer coil due to the presence of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the bacterial chromosomes with available experimental data and also give a prediction of the approximate positions of different segments within the cell. In the absence of confinement, the minimal number of effective cross-links required to organize the DNA chains of 4017/4642 monomers was 60/82 [

Chemical Physics Letters, 2000

Lattice-field calculations are performed on a Gaussian polymer chain confined to move within the region defined by two fused spheres. The results of the calculations are in accord with recent experimental measurements and computer simulations, and suggest that current theoretical understanding of polymer partitioning phenomena is not adequate when excluded volume interactions between the monomers are present. It is also shown that the notion of ground state dominance can fail even in the large monomer limit.