Angelo Rosa

Looping Probabilities in Model Interphase Chromosomes

Fluorescence in-situ hybridization (FISH) and chromosome conformation capture (3C) are two powerful techniques for investigating the three-dimensional organization of the genome in interphase nuclei. The use of these techniques provides complementary information on average spatial distances (FISH) and contact probabilities (3C) for specific genomic sites. To infer the structure of the chromatin fiber or to distinguish functional interactions from random colocalization, it is useful to compare experimental data to predictions from statistical fiber models. The current estimates of the fiber stiffness derived from FISH and 3C differ by a factor of 5. They are based on the wormlike chain model and a heuristic modification of the Shimada-Yamakawa theory of looping for unkinkable, unconstrained, zero-diameter filaments. Here, we provide an extended theoretical and computational framework to explain the currently available experimental data for various species on the basis of a unique, minimal model of decondensing chromosomes: a kinkable, topologically constraint, semiflexible polymer with the (FISH) Kuhn length of l(K) = 300 nm, 10 kinks per Mbp, and a contact distance of 45 nm. In particular: 1), we reconsider looping of finite-diameter filaments on the basis of an analytical approximation (novel, to our knowledge) of the wormlike chain radial density and show that unphysically large contact radii would be required to explain the 3C data based on the FISH estimate of the fiber stiffness; 2), we demonstrate that the observed interaction frequencies at short genomic lengths can be explained by the presence of a low concentration of curvature defects (kinks); and 3), we show that the most recent experimental 3C data for human chromosomes are in quantitative agreement with interaction frequencies extracted from our simulations of topologically confined model chromosomes.

Ring polymers in the melt state: the physics of crumpling.

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for nonconcatenated unknotted rings, which are known to crumple and segregate and which have been implicated as models for the generic behavior of interphase chromosomes. Here we use a computationally efficient multiscale approach to show that melts of rings of total contour length Lr can be quantitatively mapped onto melts of interacting lattice trees with gyration radii ⟨R(g)(2)(Lr)⟩ ∝ L(r)(2ν) and ν = 0.32 ± 0.01.

Structure and Dynamics of Ring Polymers: Entanglement Effects Because of Solution Density and Ring Topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intrachain entanglement is modulated by varying both solution density (from infinite dilution up to ≈40% volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected ...

Stretching of a polymer below the theta point.

The unfolding of a polymer below the theta point when pulled by an external force is studied both in d=2 on the lattice and in d=3 off the lattice. At T=0 and for finite length chains, it is found that the globule unfolds via multiple steps, corresponding to transitions between different minima, in both cases. In d=3 one of these intermediates is a regular helix. In the infinite length limit, these steps have a qualitative effect only in d=2. The phase diagram in d=2 is determined via the transfer matrix. To rationalize these results, energy-entropy and renormalization group arguments are given.

Colocalization of coregulated genes: a steered molecular dynamics study of human chromosome 19

The connection between chromatin nuclear organization and gene activity is vividly illustrated by the observation that transcriptional coregulation of certain genes appears to be directly influenced by their spatial proximity. This fact poses the more general question of whether it is at all feasible that the numerous genes that are coregulated on a given chromosome, especially those at large genomic distances, might become proximate inside the nucleus. This problem is studied here using steered molecular dynamics simulations in order to enforce the colocalization of thousands of knowledge-based gene sequences on a model for the gene-rich human chromosome 19. Remarkably, it is found that most () gene pairs can be brought simultaneously into contact. This is made possible by the low degree of intra-chromosome entanglement and the large number of cliques in the gene coregulatory network. A clique is a set of genes coregulated all together as a group. The constrained conformations for the model chromosome 19 are further shown to be organized in spatial macrodomains that are similar to those inferred from recent HiC measurements. The findings indicate that gene coregulation and colocalization are largely compatible and that this relationship can be exploited to draft the overall spatial organization of the chromosome in vivo. The more general validity and implications of these findings could be investigated by applying to other eukaryotic chromosomes the general and transferable computational strategy introduced here.

Spontaneous Knotting and Unknotting of Flexible Linear Polymers: Equilibrium and Kinetic Aspects

We report on a computational study of the statics and dynamics of long flexible linear polymers that spontaneously knot and unknot. Specifically, the equilibrium self-entanglement properties, such as the knotting probability, knot length and position, are investigated with extensive Monte Carlo sampling of chains of up to 15,000 beads. Tens of such equilibrated chains of up to 4, 096 beads are next used as starting points for Langevin dynamics simulations. The complex interplay of chain dynamics and self-knotting is addressed by monitoring the time evolution of various metric and entanglement properties. In particular, the extensive duration of the simulations allows for observing the spontaneous formation and disappearance of prime and composite physical knots in linear chains. Notably, a sizeable fraction of self-knotting and unknotting events is found to involve regions that are far away from the chain termini. To the best of our knowledge this represents the first instance where spontaneous changes in knotting for linear homopolymers are systematically characterized using unbiased dynamics simulations.

Correlation function and generalized master equation of arbitrary age

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J. Stat. Phys. 104, 489 (2001)]. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations of the conventional Liouville treatment.

Mechanical unfolding of directed polymers in a poor solvent: critical exponents.

We study the thermodynamics of an exactly solvable model of a self-interacting, partially directed self-avoiding walk in two dimensions when a force is applied on one end of the chain. The critical force for the unfolding is determined exactly, as a function of the temperature, below the Theta transition. The transition is of second order and is characterized by new critical exponents that are determined by a careful numerical analysis. The usual polymer critical index nu on the critical line, and another one which we call zeta, takes a nontrivial value that is numerically close to 2/3.

Trajectory versus probability density entropy

We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy.

Density effects in entangled solutions of linear and ring polymers

In this paper, we employ molecular dynamics computer simulations to study and compare the statics and dynamics of linear and circular (ring) polymer chains in entangled solutions of different densities. While we confirm that linear chain conformations obey Gaussian statistics at all densities, rings tend to crumple becoming more and more compact as the density increases. Conversely, contact frequencies between chain monomers are shown to depend on solution density for both chain topologies. The relaxation of chains at equilibrium is also shown to depend on topology, with ring polymers relaxing faster than their linear counterparts. Finally, we discuss the local viscoelastic properties of the solutions by showing that the diffusion of dispersed colloid-like particles is markedly faster in the rings case.