Suckjoon Jun

Entropy-driven spatial organization of highly confined polymers: Lessons for the bacterial chromosome

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.

Entropy as the driver of chromosome segregation

We present a new physical biology approach to understanding the relationship between the organization and segregation of bacterial chromosomes. We posit that replicated Escherichia coli daughter strands will spontaneously demix as a result of entropic forces, despite their strong confinement within the cell; in other words, we propose that entropy can act as a primordial physical force which drives chromosome segregation under the right physical conditions. Furthermore, proteins implicated in the regulation of chromosome structure and segregation may in fact function primarily in supporting such an entropy-driven segregation mechanism by regulating the physical state of chromosomes. We conclude that bacterial chromosome segregation is best understood in terms of spontaneous demixing of daughter strands. Our concept may also have important implications for chromosome segregation in eukaryotes, in which spindle-dependent chromosome movement follows an extended period of sister chromatid demixing and compaction.

Physical manipulation of the Escherichia coli chromosome reveals its soft nature

Replicating bacterial chromosomes continuously demix from each other and segregate within a compact volume inside the cell called the nucleoid. Although many proteins involved in this process have been identified, the nature of the global forces that shape and segregate the chromosomes has remained unclear because of limited knowledge of the micromechanical properties of the chromosome. In this work, we demonstrate experimentally the fundamentally soft nature of the bacterial chromosome and the entropic forces that can compact it in a crowded intracellular environment. We developed a unique “micropiston” and measured the force-compression behavior of single Escherichia coli chromosomes in confinement. Our data show that forces on the order of 100 pN and free energies on the order of 105 kBT are sufficient to compress the chromosome to its in vivo size. For comparison, the pressure required to hold the chromosome at this size is a thousand-fold smaller than the surrounding turgor pressure inside the cell. Furthermore, by manipulation of molecular crowding conditions (entropic forces), we were able to observe in real time fast (approximately 10 s), abrupt, reversible, and repeatable compaction–decompaction cycles of individual chromosomes in confinement. In contrast, we observed much slower dissociation kinetics of a histone-like protein HU from the whole chromosome during its in vivo to in vitro transition. These results for the first time provide quantitative, experimental support for a physical model in which the bacterial chromosome behaves as a loaded entropic spring in vivo.

Kinetic model of DNA replication in eukaryotic organisms

We formulate a kinetic model of DNA replication that quantitatively describes recent results on DNA replication in the in vitro system of Xenopus laevis prior to the mid-blastula transition. The model describes well a large amount of different data within a simple theoretical framework. This allows one, for the first time, to determine the parameters governing the DNA replication program in a eukaryote on a genome-wide basis. In particular, we have determined the frequency of origin activation in time and space during the cell cycle. Although we focus on a specific stage of development, this model can easily be adapted to describe replication in many other organisms, including budding yeast.

The multifork Escherichia coli chromosome is a self-duplicating and self-segregating thermodynamic ring polymer

At all but the slowest growth rates, Escherichia coli cell cycles overlap, and its nucleoid is segregated to daughter cells as a forked DNA circle with replication ongoing-a state fundamentally different from eukaryotes. We have solved the chromosome organization, structural dynamics, and segregation of this constantly replicating chromosome. It is locally condensed to form a branched donut, compressed so that the least replicated DNA spans the cell center and the newest DNA extends toward the cell poles. Three narrow zones at the cell center and quarters contain both the replication forks and nascent DNA and serve to segregate the duplicated chromosomal information as it flows outward. The overall pattern is smoothly self-replicating, except when the duplicated terminus region is released from the septum and recoils to the center of a sister nucleoid. In circular cross-section of the cell, the left and right arms of the chromosome form separate, parallel structures that lie in each cell half along the radial cell axis. In contrast, replication forks and origin and terminus regions are found mostly at the center of the cross section, balanced by the parallel chromosome arms. The structure is consistent with the model in which the nucleoid is a constrained ring polymer that develops by spontaneous thermodynamics. The ring polymer pattern extrapolates to higher growth rates and also provides a structural basis for the form of the chromosome during very slow growth.

Cell-size maintenance: universal strategy revealed

How cells maintain a stable size has fascinated scientists since the beginning of modern biology, but has remained largely mysterious. Recently, however, the ability to analyze single bacteria in real time has provided new, important quantitative insights into this long-standing question in cell biology.

Compression and stretching of a self-avoiding chain in cylindrical nanopores.

Force-induced deformations of a self-avoiding chain confined inside a cylindrical cavity, with diameter D, are probed using molecular dynamics simulations, scaling analysis, and analytical calculations. We obtain and confirm a simple scaling relation -fD approximately R(-9/4) in the strong-compression regime, while for weak deformations, we find fD = -A(R/R0) + B(R/R0)(-2), where A and B are constants, f the external force, and R the chain extension (with R0 its unperturbed value). For a strong stretch, we present a universal, analytical force-extension relation. Our results can be used to analyze the behavior of biomolecules in confinement.

Bending forces plastically deform growing bacterial cell walls.

Significance Regulation of cell wall growth is a process of fundamental importance in cell biology. In this paper, to our knowledge, we demonstrate for the first time that mechanical stress directly influences cell wall synthesis of bacteria. In a series of simple experiments, we elastically and plastically deform cell walls as they grow by applying anisotropic mechanical stresses to bacteria. Using a theory of dislocation-mediated growth, we explain how growth and form of the cell walls are quantitatively related to one another in bacteria. Cell walls define a cell’s shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell’s responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.

Persistence Length of Chromatin Determines Origin Spacing in Xenopus Early-Embryo DNA Replication: Quantitative Comparisons between Theory and Experiment

In Xenopus early embryos, replication origins neither require specific DNA sequences nor is there an efficient S/M checkpoint, even though the whole genome (3 billion bases) is completely duplicated within 10-20 minutes. This leads to the “random-completion problem” of DNA replication in embryos, where one needs to find a mechanism that ensures complete, faithful, timely reproduction of the genome without any sequence dependence of replication origins. We analyze recent DNA replication data in Xenopus laevis egg extracts and find discrepancies with models where replication origins are distributed independently of chromatin structure. Motivated by these discrepancies, we have investigated the role that chromatin looping may play in DNA replication. We find that the loop-size distribution predicted from a wormlike-chain model of chromatin can account for the spatial distribution of replication origins in this system quantitatively. Together with earlier findings of increasing frequency of origin firings, our results can explain the random-completion problem. The agreement between experimental data (molecular combing) and theoretical predictions suggests that the intrinsic stiffness of chromatin loops plays a fundamental biological role in DNA replication in early-embryo Xenopus in regulating the origin spacing.

Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing

We show that Kramers rate theory gives a straightforward, accurate estimate of the closing time τc of a semiflexible polymer that is valid in cases of physical interest. The calculation also reveals how the time scales of chain relaxation and closing are intertwined, illuminating an apparent conflict between two ways of calculating τc in the flexible limit.