arXiv subjects

Angelo Rosa

Publications and source records attributed to Angelo Rosa.

At least 37 records · Page 2Linked to original sources

arXiv2022

Entanglement length scale separates threading from branching of unknotted and non-concatenated ring polymers in melts

Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single ring level, other works show pairs of rings also thread each other - a feature overlooked in the tree theories. Here we reconcile this dichotomy using Monte-Carlo simulations of the ring melts with different bending rigidity. We find that rings are double-folded (more strongly for stiffer rings) on and above the entanglement length scale, while the threadings are localized on smaller scales. The different theories disagree on the details of the tree structure, i.e the fractal dimension of the backbone of the tree. In the stiffer melts we find an indication of a self-avoiding scaling of the backbone, while more flexible chains do not exhibit such a regime. Moreover, the theories commonly neglect threadings, and assign different importance to the impact of the progressive constraint release (tube dilation) on single ring relaxation due to the motion of other rings. Despite each threading creates only a small opening in the double-folded structure, the threading loops can be numerous and their length can exceed substantially the entanglement scale. We link the threading constraints to the divergence of the relaxation time of a ring, if the tube dilation is hindered by pinning a fraction of other rings in space. Current theories do not predict such divergence and predict faster than measured diffusion of rings, pointing at the relevance of the threading constraints in unpinned systems as well. Revision of the theories with explicit threading constraints might elucidate the validity of the conjectured existence of topological glass.

cond-mat.soft↗

arXiv2021

Computer simulations of melts of ring polymers with non-conserved topology: A dynamic Monte Carlo lattice model

We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on the FCC lattice which takes explicitly into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison to standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing is responsible for fluidizing the melt provided the time scale of the process is faster than the internal relaxation of the chain, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.

cond-mat.soft↗

arXiv2021

Nanorheology of active-passive polymer mixtures is topology-sensitive

We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes {\it decelerate} with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett. 116, 058301 (2016)] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells.

cond-mat.soft↗

arXiv2020

Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality as the numerical evaluation of Marko's and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests, that our analytical expressions for the finite-chain length corrections are of similar quality. As an application of our results we discuss the possibility of inferring the changing number of nicks in a double-stranded DNA molecule in single-molecule stretching experiments from the accompanying changes in the effective chain length.

cond-mat.soft↗

arXiv2020

Merging 1D and 3D genomic information: Challenges in modelling and validation

Genome organization in eukaryotes during interphase stems from the delicate balance between non-random correlations present in the DNA polynucleotide linear sequence and the physico/chemical reactions which shape continuously the form and structure of DNA and chromatin inside the nucleus of the cell. It is now clear that these mechanisms have a key role in important processes like gene regulation, yet the detailed ways they act simultaneously and, eventually, come to influence each other even across very different length-scales remain largely unexplored. In this paper, we recapitulate some of the main results concerning gene regulatory and physical mechanisms, in relation to the information encoded in the 1D sequence and the 3D folding structure of DNA. In particular, we stress how reciprocal crossfeeding between 1D and 3D models may provide original insight into how these complex processes work and influence each other.

q-bio.GN↗

arXiv2020

Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers

The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring-linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in "chimeric" architectures. The simplest example of this family is a "tadpole"-shaped polymer - a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically-tunable bulk rheological properties.

cond-mat.soft↗

arXiv2019

Randomly branching $θ$-polymers in two and three dimensions: Average properties and distribution functions

Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers in $θ$-solvent conditions obtained by Monte Carlo computer simulations. The first part of the work focuses on polymer average properties, like the average polymer spatial size as a function of the total tree mass and the typical length of the average path length on the polymer backbone. In the second part, we move beyond average chain behavior and we discuss the complete distribution functions for tree paths and tree spatial distances, which are shown to obey the classical Redner-des Cloizeaux functional form. Our results were rationalized first by the systematic comparison to a Flory theory for branching polymers and, next, by generalized Fisher-Pincus relationships between scaling exponents of distribution functions. For completeness, the properties of $θ$-polymers were compared to their ideal (i.e.), no volume interactions) as well as good-solvent (i.e.), above the $θ$-point) counterparts. The results presented here brings to conclusion the recent work performed in our group [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016), J. Chem. Phys. 145, 164906 (2016), Phys. Rev. E 95, 012117 (2017)] in the context of the scaling properties of branching polymers.

cond-mat.soft↗

arXiv2019

Topological constraints in eukaryotic genomes and how they can be exploited to improve spatial models of chromosomes

Several orders of magnitude typically separate the contour length of eukaryotic chromosomes and the size of the nucleus where they are confined. The ensuing topological constraints can slow down the relaxation dynamics of genomic filaments to the point that mammalian chromosomes are never in equilibrium over a cell's lifetime. In this opinion article, we revisit these out-of-equilibrium effects and discuss how their inclusion in physical models can enhance the spatial reconstructions of interphase eukaryotic genomes from phenomenological constraints collected during interphase.

q-bio.QM↗

arXiv2019

Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure

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 untangled (i.e. non-concatenated and unknotted) rings, which are known to crumple and segregate. Here we study these systems using a computationally efficient multi-scale approach, where we combine massive simulations on the fiber level with the explicit construction of untangled ring melt configurations based on theoretical ideas for their large scale structure. We find (i) that topological constraints may be neglected on scales below the standard entanglement length, $L_e$, (ii) that rings with a size $1 \le L_r/L_e \le 30$ exhibit nearly ideal lattice tree behavior characterized by primitive paths which are randomly branched on the entanglement scale, and (iii) that larger rings are compact with gyration radii $\langle R_g^2(L_r) \rangle \propto L_r^{2/3}$. The detailed comparison between equilibrated and constructed ensembles allows us to perform a `Feynman test' of our understanding of untangled rings: can we convert ideas for the large-scale ring structure into algorithms for constructing (nearly) equilibrated ring melt samples? We show that most structural observables are quantitatively reproduced by two different construction schemes: hierarchical crumpling and ring melts derived from the analogy to interacting branched polymers. However, the latter fail the `Feynman test' with respect to the magnetic radius, $R_m$, which we have defined based on an analogy to magnetostatics. While $R_m$ is expected to vanish for double-folded structures, the observed values of $\langle R_m^2(L_r) \rangle \propto \langle R_g^2(L_r) \rangle$ provide a simple and computationally convenient measure of the presence of a non-negligible amount of local loop opening in crumpled rings.

cond-mat.soft↗

arXiv2018

Conformational statistics of randomly-branching double-folded ring polymers

The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore the conformational statistics of double-folded rings in the limit of tight wrapping. In particular, we relate the exponents characterizing the ring statistics to those describing the primitive trees and discuss the distribution functions $p(\vec r | \ell)$ and $p(L | \ell)$ for the spatial distance, $\vec r$, and tree contour distance, $L$, between monomers as a function of their ring contour distance, $\ell$.

cond-mat.soft↗

arXiv2016

Beyond Flory theory: Distribution functions for interacting lattice trees

While Flory theories provide an extremely useful framework for understanding the behavior of interacting, randomly branching polymers, the approach is inherently limited. Here we use a combination of scaling arguments and computer simulations to go beyond a Gaussian description. We analyse distributions functions for a wide variety of quantities characterising the tree connectivities and conformations for the four different statistical ensembles, which we have studied numerically in [Rosa and Everaers, J. Phys. A (2016, published) and J. Chem. Phys. (2016, to appear)]: (a) ideal randomly branching polymers, (b) $2d$ and $3d$ melts of interacting randomly branching polymers, (c) $3d$ self-avoiding trees with annealed connectivity and (d) $3d$ self-avoiding trees with quenched ideal connectivity. In particular, we investigate the distributions (i) $p_N(n)$ of the weight, $n$, of branches cut from trees of mass $N$ by severing randomly chosen bonds; (ii) $p_N(l)$ of the contour distances, $l$, between monomers; (iii) $p_N(\vec r)$ of spatial distances, $\vec r$, between monomers, and (iv) $p_N(\vec r|l)$ of the end-to-end distance of paths of length $l$. Data for different tree sizes superimpose, when expressed as functions of suitably rescaled observables $\vec x = \vec r/\langle r^2(N) \rangle$ or $x =l/\langle l(N) \rangle$. In particular, we observe a generalised Kramers relation for the branch weight distributions (i) and find that all the other distributions (ii-iv) are of Redner-des Cloizeaux type, $q(\vec x) = C \, |x|^θ \exp \left( -(K |x|)^t \right)$. We propose a coherent framework, including generalised Fisher-Pincus relations, relating most of the RdC exponents to each other and to the contact and Flory exponents for interacting trees.

cond-mat.stat-mech↗

arXiv2016

Computer simulations of melts of randomly branching polymers

Randomly branching polymers with {\em annealed} connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present computer simulations of melts of annealed randomly branching polymers of $3 \le N \le 1800$ segments in $d=2$ and $d=3$ dimensions. In all cases, we perform a detailed analysis of the observed tree connectivities and spatial conformations. Our results are in excellent agreement with an asymptotic scaling of the average tree size of $R \sim N^{1/d}$, suggesting that the trees behave as compact, {\it territorial} fractals. The observed swelling relative to the size of ideal trees, $R\sim N^{1/4}$, demonstrates that excluded volume interactions are only partially screened in melts of annealed trees. Overall, our results are in good qualitative agreement with the predictions of Flory theory. In particular, we find that the trees swell by the combination of modified branching and path stretching. However, the former effect is subdominant and difficult to detect in $d=3$ dimensions.

cond-mat.stat-mech↗

arXiv2016

Computer simulations of randomly branching polymers: Annealed vs. quenched branching structures

We present computer simulations of three systems of randomly branching polymers in d=3 dimensions: ideal trees and self-avoiding trees with annealed and quenched connectivities. In all cases, we performed a detailed analysis of trees connectivities, spatial conformations and statistical properties of linear paths on trees, and compare the results to the corresponding predictions of Flory theory. We confirm that, overall, the theory predicts correctly that trees with quenched ideal connectivity exhibit {\it less} overall swelling in good solvent than corresponding trees with annealed connectivity even though they are more strongly stretched on the path level. At the same time, we emphasize the inadequacy of the Flory theory in predicting the behaviour of other, and equally relevant, observables like contact probabilities between tree nodes. We show, then, that contact probabilities can be aptly characterized by introducing a novel critical exponent, $θ_{path}$, which accounts for how they decay as a function of the node-to-node path distance on the tree.

cond-mat.stat-mech↗

arXiv2016

Large scale chromosome folding is stable against local changes in chromatin structure

Characterizing the link between small-scale chromatin structure and large-scale chromosome folding during interphase is a prerequisite for understanding transcription. Yet, this link remains poorly investigated. Here, we introduce a simple biophysical model where interphase chromosomes are described in terms of the folding of chromatin sequences composed of alternating blocks of fibers with different thicknesses and flexibilities, and we use it to study the influence of sequence disorder on chromosome behaviors in space and time. By employing extensive computer simulations,we thus demonstrate that chromosomes undergo noticeable conformational changes only on length-scales smaller than $10^5$ basepairs and time-scales shorter than a few seconds, and we suggest there might exist effective upper bounds to the detection of chromosome reorganization in eukaryotes. We prove the relevance of our framework by modeling recent experimental FISH data on murine chromosomes.

cond-mat.soft↗

arXiv2015

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 density increases. Conversely, contact frequencies between chain monomers are shown to depend on solution density for both chain topologies. 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 diffusion of dispersed colloid-like particles is markedly faster in the rings case.

cond-mat.soft↗

arXiv2014

Viscoelasticity of model interphase chromosomes

We investigated the viscoelastic response of model interphase chromosomes by tracking the three-dimensional motion of hundreds of dispersed Brownian particles of sizes ranging from the thickness of the chromatin fiber up to slightly above the mesh size of the chromatin solution. In agreement with previous computational studies on polymer solutions and melts, we found that the large-time behaviour of diffusion coefficient and the experienced viscosity of moving particles as functions of particle size deviate from the traditional Stokes-Einstein relation, and agree with a recent scaling theory of diffusion of non-sticky particles in polymer solutions. Interestingly, we found that at short times large particles are temporary "caged" by chromatin spatial constraints, which thus form effective domains whose size match remarkably well recent experimental results for micro-tracers inside interphase nuclei. Finally, by employing a known mathematical relation between the time mean-square displacement of tracked particles and the complex shear modulus of the surrounding solution, we calculated the elastic and viscous moduli of interphase chromosomes.

q-bio.BM↗

arXiv2014

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 non-concatenated 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 multi-scale approach to show that melts of rings of total contour length $L_r$ can be {\it quantitatively} mapped onto melts of {\em interacting} lattice trees with gyration radii $\langle R_g^2(L_r) \rangle \propto L_r^{2ν}$ and $ν=0.32\pm0.01$.

cond-mat.soft↗

arXiv2013

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.

cond-mat.soft↗