Youngkyun Jung

Ring polymers as model bacterial chromosomes: confinement, chain topology, single chain statistics, and how they interact

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.

Effect of long-range interactions in the conserved Kardar-Parisi-Zhang equation

The conserved Kardar-Parisi-Zhang equation in the presence of long-range nonlinear interactions is studied by the dynamic renormalization group method. The long-range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions, depending on both the long-range interaction strength and the substrate dimension

Elasticity of flexible polymers under cylindrical confinement: appreciating the blob scaling regime in computer simulations

d

Velocity inversion in nanochannel flow.

. The long-range interaction makes the surface width less rough than that of the short-range interaction. In particular, the surface becomes a smooth one with a negative roughness exponent at the physical dimension d=2.

A ring-polymer model shows how macromolecular crowding controls chromosome-arm organization in Escherichia coli

Despite much renewed interest in cylindrically confined polymers with linear or nonlinear topology, often considered as model chromosomes, their scaling predictions, especially on chain elasticity and relaxation, have not been reconciled with numerical data. Of particular interest is their “effective spring constant” given in the scaling form of keff ∼ N−αD−γ, where N is the number of monomers and D the diameter of the cylindrical space. If the blob-scaling approach produces α = 1 and γ = 2 − 1/ν = 1/3 with ν = 3/5 the Flory exponent, a series of numerical studies indicate α ≈ 0.75 and unexpectedly large γ ≈ 0.9. Using computer simulations, we show that there exists a crossover from the formerly called unexpected to blob-scaling regime at a certain value of D ≈ 10 (in units of monomer sizes) for sufficiently large N (>Ncr). Our results suggest that Ncr ≈ 1000, if the farthermost distance is used as the chain size: a quantity relevant in single-chain manipulations or for ring polymers (e.g., bacterial chromosomes). Accordingly, chain relaxation dynamics is expected to show a similar crossover. Our results imply that the applicability of the blob scaling approach depends on how confined chains are characterized.

How are molecular crowding and the spatial organization of a biopolymer interrelated

The nanoscale cylindrical Couette flow is investigated by means of molecular dynamics simulations, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. We find that the tangential velocity of the flow is inverted when the fluid-wall interaction near the outer cylinder is weak and the fluid density is low. The unusual velocity inversion behavior is shown to be strongly related to the degree of the slip between the fluid and the outer cylinder, which is determined by the presence or absence of the layering of the fluid near the outer wall.

Slow relaxation of randomly packed hard spheres

Macromolecular crowding influences various cellular processes such as macromolecular association and transcription, and is a key determinant of chromosome organization in bacteria. The entropy of crowders favors compaction of long chain molecules such as chromosomes. To what extent is the circular bacterial chromosome, often viewed as consisting of “two arms”, organized entropically by crowding? Using computer simulations, we examine how a ring polymer is organized in a crowded and cylindrically-confined space, as a coarse-grained bacterial chromosome. Our results suggest that in a wide parameter range of biological relevance crowding is essential for separating the two arms in the way observed with Escherichia coli chromosomes at fast-growth rates, in addition to maintaining the chromosome in an organized collapsed state. Under different conditions, however, the ring polymer is centrally condensed or adsorbed onto the cylindrical wall with the two arms laterally collapsed onto each other. We discuss the relevance of our results to chromosome-membrane interactions.

Molecular dynamics on nonequilibrium motion of a colloidal particle driven by an external torque

In a crowded cellular interior, dissolved biomolecules or crowders exert excluded volume effects on other biomolecules, which in turn control various processes including protein aggregation and chromosome organization. As a result of these effects, a long chain molecule can be phase-separated into a condensed state, redistributing the surrounding crowders. Using computer simulations and a theoretical approach, we study the interrelationship between molecular crowding and chain organization. In a parameter space of biological relevance, the distributions of monomers and crowders follow a simple relationship: the sum of their volume fractions rescaled by their size remains constant. Beyond a physical picture of molecular crowding it offers, this finding explains a few key features of what has been known about chromosome organization in an E. coli cell.

Crossover of the behavior of surface waves in a vibrated granular material

We discover that the apparent weight and the electrical resistance of randomly packed stainless steel balls exhibit unusually slow relaxation behavior. It is found experimentally that these relaxations are due to structural change of the packing. Simultaneous measurements of the apparent weight and the electrical resistance show correlated time dependence. We have also performed two-dimensional molecular dynamics simulations and studied a possible mechanism for the slow relaxation behavior observed in experiments.

Self-avoiding polymer trapped inside a cylindrical pore: Flory free energy and unexpected dynamics

We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use the molecular dynamics simulation that is alternative to the numerical integration approach based on the Langevin equation and is expected to mimic an experiment more realistically. We choose a heat bath composed of thousands of particles interacting to each other through the Lennard-Jones potential and impose the Langevin thermostat to maintain it in equilibrium. We prepare a single colloidal particle to interact with the particles of the heat bath also by the Lennard-Jones potential while any dissipative force and noise are not employed. We prepare the simulation protocol fit to the overdamped limit in real experiments by increasing the size and mass of the colloidal particle. We study the stochastic properties of the nonequilibrium fluctuations for work and heat produced incessantly in time. We accurately confirm the fluctuation theorem for the work production. We show our results to agree accurately with those from the numerical integration of the Langevin equation.