Looped star polymers show conformational transition from spherical to flat toroidal shapes

Molecular Dynamics Simulation of a Feather-Boa Model of a Bacterial Chromosome

The chromosome of a bacterium consists of a mega-base pair-long circular DNA, which self-organizes within the micron-sized bacterial cell volume, compacting itself by three orders of magnitude. Unlike eukaryotic chromosomes, it lacks a nuclear membrane and freely floats in the cytosol confined by the cell membrane. It is believed that strong confinement, cross-linking by associated proteins, and molecular crowding all contribute to determine chromosome size and morphology. Modelling the chromosome simply as a circular polymer decorated with closed side loops in a cylindrical confining volume has been shown to already recapture some of the salient properties observed experimentally. Here we describe how a computer simulation can be set up to study structure and dynamics of bacterial chromosomes using this model.

Mesoscale Simulation of Bacterial Chromosome and Cytoplasmic Nanoparticles in Confinement

In this study we investigated, using a simple polymer model of bacterial chromosome, the subdiffusive behaviors of both cytoplasmic particles and various loci in different cell wall confinements. Non-Gaussian subdiffusion of cytoplasmic particles as well as loci were obtained in our Langevin dynamic simulations, which agrees with fluorescence microscope observations. The effects of cytoplasmic particle size, locus position, confinement geometry, and density on motions of particles and loci were examined systematically. It is demonstrated that the cytoplasmic subdiffusion can largely be attributed to the mechanical properties of bacterial chromosomes rather than the viscoelasticity of cytoplasm. Due to the randomly positioned bacterial chromosome segments, the surrounding environment for both particle and loci is heterogeneous. Therefore, the exponent characterizing the subdiffusion of cytoplasmic particle/loci as well as Laplace displacement distributions of particle/loci can be reproduced by this simple model. Nevertheless, this bacterial chromosome model cannot explain the different responses of cytoplasmic particles and loci to external compression exerted on the bacterial cell wall, which suggests that the nonequilibrium activity, e.g., metabolic reactions, play an important role in cytoplasmic subdiffusion.

Cell Boundary Confinement Sets the Size and Position of the E. coli Chromosome

Although the spatiotemporal structure of the genome is crucial to its biological function, many basic questions remain unanswered on the morphology and segregation of chromosomes. Here, we experimentally show in Escherichia coli that spatial confinement plays a dominant role in determining both the chromosome size and position. In non-dividing cells with lengths increased to 10 times normal, single chromosomes are observed to expand > 4-fold in size. Chromosomes show pronounced internal dynamics but exhibit a robust positioning where single nucleoids reside robustly at mid-cell, whereas two nucleoids self-organize at 1/4 and 3/4 positions. The cell-size-dependent expansion of the nucleoid is only modestly influenced by deletions of nucleoid-associated proteins, whereas osmotic manipulation experiments reveal a prominent role of molecular crowding. Molecular dynamics simulations with model chromosomes and crowders recapitulate the observed phenomena and highlight the role of entropic effects caused by confinement and molecular crowding in the spatial organization of the chromosome.

Molecular Dynamics Simulation of a Feather-Boa Model of a Bacterial Chromosome

The chromosome of a bacterium consists of a mega-base pair long circular DNA, which self-organizes within the micron-sized bacterial cell volume, compacting itself by three orders of magnitude. Unlike in eukaryotes, it lacks a nuclear membrane, and freely floats in the cytosol confined by the cell membrane. It is believed that strong confinement, cross-linking by associated proteins, and molecular crowding all contribute to determine chromosome size and morphology. Modeling the chromosome simply as a circular polymer decorated with closed side-loops in a cylindrical confining volume, has been shown to already recapture some of the salient properties observed experimentally. Here, we describe how a computer simulation can be set up to study structure and dynamics of bacterial chromosomes using this model.

Confinement and crowding control the morphology and dynamics of a model bacterial chromosome

Motivated by recent experiments probing the shape, size and dynamics of bacterial chromosomes in growing cells, we consider a polymer model consisting of a circular backbone to which side-loops are attached, confined to a cylindrical cell. Such a model chromosome spontaneously adopts a helical shape, which is further compacted by molecular crowders to occupy a nucleoid-like sub-volume of the cell. With increasing cell length, the longitudinal size of the chromosome increases in a non-linear fashion until finally saturating, its morphology gradually opening up while displaying a changing number of helical turns. For shorter cells, the chromosome extension varies non-monotonically with cell size, which we show is associated with a radial to longitudinal spatial reordering of the crowders. Confinement and crowders constrain chain dynamics leading to anomalous diffusion. While the scaling exponent for the mean squared displacement of center of mass grows and saturates with cell length, that of individual loci displays a broad distribution with a sharp maximum.

The shape of pinned forced polymer loops

Loop geometry is a frequent encounter in synthetic and biological polymers. Here we provide an analytical theory to characterize the shapes of polymer loops subjected to an external force field. We show how to calculate the polymer density, gyration radius and its distribution. Interestingly, the distribution of the gyration radius shows a non-monotonic behavior as a function of the external force. Furthermore, we analyzed the gyration tensor of the polymer loop characterizing its overall shape. Two parameters called asphericity and the nature of asphericity derived from the gyration tensor, along with the gyration radius, can be used to quantify the shape of polymer loops in theory and experiments.

The role of loops on the order of eukaryotes and prokaryotes

The study of the three-dimensional organization of chromatin has recently gained much focus in the context of novel techniques for detecting genome-wide contacts using next-generation sequencing. These chromosome conformation capture-based methods give a deep topological insight into the architecture of the genome inside the nucleus. Several recent studies observe a compartmentalization of chromatin interactions into spatially confined domains. This structural feature of interphase chromosomes is not only supported by conventional studies assessing the interaction data of millions of cells, but also by analysis on the level of a single cell. We first present and examine the different models that have been proposed to elucidate these topological domains in eukaryotes. Then we show that a model which relies on the dynamic formation of loops within domains can account for the experimentally observed contact maps. Interestingly, the topological domain structure is not only found in mammalian genomes, but also in bacterial chromosomes.

Spontaneous helicity of a polymer with side loops confined to a cylinder

Inspired by recent experiments on the spatial organization of bacterial chromosomes, we consider a type of "bottle-brush" polymer consisting of a flexible backbone chain, to which flexible side loops are connected. We show that such a model with an open linear backbone spontaneously adopts a helical structure with a well-defined pitch when confined to small cylindrical volume. This helicity persists over a range of sizes and aspect ratios of the cylinder, provided the packing fraction of the chain is suitably large. We analyze these results in terms of the interplay between the effective stiffness and actual intrachain packing effects caused by the side loops in response to the confinement.