arXiv subjects

Enzo Orlandini

Publications and source records attributed to Enzo Orlandini.

At least 37 records · Page 2Linked to original sources

arXiv2022

Brownian non-Gaussian diffusion of self-avoiding walks

Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center of mass grows linearly with time (Brownian behavior), the initial probability density function is strongly non-Gaussian and crosses over to Gaussianity only at large time. Full agreement between theory and simulations is achieved without the employment of fitting parameters. We discuss simulation techniques potentially capable of addressing the study of anomalous diffusion under complex conditions like adsorption- or Theta-transition.

cond-mat.stat-mech↗

arXiv2022

Dynamic and Facilitated Binding of Topoisomerase Accelerates Topological Relaxation

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in biophysics. Most of the existing models neglect the dynamics of TopoII which is characteristics for proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

cond-mat.soft↗

arXiv2022

Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit

We link the Brownian non-Gaussian diffusion of a polymer center of mass to a microscopic cause: the polymerization/depolymerization phenomenon occurring when the polymer is in contact with a monomer chemostat. The anomalous behavior is triggered by the polymer critical point, separating the dilute and the dense phase in the grand canonical ensemble. In the mean-field limit we establish contact with queuing theory and show that the kurtosis of the polymer center of mass diverges alike a response function when the system becomes critical, a result which holds for general polymer dynamics (Zimm, Rouse, reptation). Both the equilibrium and nonequilibrium behaviors are solved exactly as a reference study for novel stochastic modeling and experimental setup.

cond-mat.stat-mech↗

arXiv2022

Polymers critical point originates Brownian non-Gaussian diffusion

We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents $γ$ and $ν$ -- depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase -- concur to determine the potential divergency of a dynamic response, epitomized by the center of mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.

cond-mat.stat-mech↗

arXiv2021

Ring-o-rings: a new category of supramolecular structures with topologically tunable properties

Macrochains of topologically interlocked rings with unique physical properties have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Most of the work has been, so far, focused on linear chains and on their variety of conformational properties compared to standard polymers. Here we go beyond the linear case and show that, by circularizing such macrochains, one can exploit the topology of the local interlockings to store torsional stress in the system, altering significantly its metric and local properties. Moreover, by properly defining the twist (Tw) and writhe (Wr) of these macrorings we show the validity of a relation equivalent to the Cǎlugǎreanu-White-Fuller theorem $Tw + Wr$=const, originally proved for ribbon like structures such as ds-DNA. Our results suggest that circular structures of topologically linked rings with storable and tunable torsion can form a new category of highly designable multiscale structures with potential applications in supramolecular chemistry and material science

cond-mat.soft↗

arXiv2021

Cholesteric shells: two-dimensional blue fog and finite quasicrystals

We study the phase behaviour of a quasi-two dimensional cholesteric liquid crystal shell. We characterise the topological phases arising close to the isotropic-cholesteric transition, and show that they differ in a fundamental way from those observed on a flat geometry. For spherical shells, we discover two types of quasi-two dimensional topological phases: finite quasicrystals and amorphous structures, both made up by mixtures of polygonal tessellations of half-skyrmions. These structures generically emerge instead of regular double twist lattices because of geometric frustration, which disallows a regular hexagonal tiling of curved space. For toroidal shells, the variations in the local curvature of the surface stabilises heterogeneous phases where cholesteric patterns coexist with hexagonal lattices of half-skyrmions. Quasicrystals, amorphous and heterogeneous structures could be sought experimentally by self assembling cholesteric shells on the surface of emulsion droplets.

cond-mat.soft↗

arXiv2021

The rise and fall of branching: a slowing down mechanism in relaxing wormlike micellar networks

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached both with thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids.

cond-mat.soft↗

arXiv2020

Modelling the deceleration of COVID-19 spreading

By characterising the time evolution of COVID-19 in term of its "velocity" (log of the new cases per day) and its rate of variation, or "acceleration", we show that in many countries there has been a deceleration even before lockdowns were issued. This feature, possibly due to the increase of social awareness, can be rationalised by a susceptible-hidden-infected-recovered (SHIR) model introduced by Barnes, in which a hidden (isolated from the virus) compartment $H$ is gradually populated by susceptible people, thus reducing the effectiveness of the virus spreading. By introducing a partial hiding mechanism, for instance due to the impossibility for a fraction of the population to enter the hidden state, we obtain a model that, although still sufficiently simple, faithfully reproduces the different deceleration trends observed in several major countries.

q-bio.PE↗

arXiv2020

Topological disentanglement of linear polymers under tension

We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semi-flexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain. Our theory is extensively benchmarked with corresponding Molecular Dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.

cond-mat.stat-mech↗

arXiv2020

Aging of living polymer networks: a model with patchy particles

Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic elementary motifs to a system of worm-like micelles, we are able to simulate its relaxation dynamics, upon a thermal quench, spanning many decades, from microseconds up to tens of seconds. After mapping the model to real units and to experimental scission energies, we show that the relaxation process develops through a sequence of non-local and energetically challenging arrangements. These adjustments remove undesired structures formed as a temporary energetic solution for stabilizing the thermodynamically unstable free caps of the network. We claim that the observed scale-free nature of this stagnant process may complicate the correct quantification of experimentally relevant time scales as the Weissenberg number.

cond-mat.soft↗

arXiv2020

Separation of Geometrical and Topological Entanglement in Confined Polymers Driven Out-Of-Equilibrium

We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nano-channels and under periodic compression. We distinguish two main forms of entanglement, geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections, and is irrespective of the physical knotted state. The key discovery of our work is that these two forms of entanglement are uncoupled and evolve with distinct dynamics. While geometrical entanglement is typically in phase with the compression-elongation cycles and it is primarily sensitive to its force f, the topological measure is mildly sensitive to cyclic modulation but strongly depends on both compression force f and duration k. The findings could assist the interpretation of experiments using fluorescence molecular tracers to track physical knots in polymers. Furthermore, we identify optimal regions in the experimentally-controllable parameter space in which to obtain more/less topological and geometrical entanglement; this may help designing polymers with targeted topology.

cond-mat.soft↗

arXiv2020

Translocation of links through a pore: effects of link complexity and size

We have used Langevin dynamics to simulate the forced translocation of linked polymer rings through a narrow pore. For fixed size (i.e. fixed number of monomers) the translocation time depends on the link type and on whether the rings are knotted or unknotted. For links with two unknotted rings, the crossings between the rings can slow down the translocation and are responsible for a delay as the crossings pass through the pore. The results fall on a set of relatively smooth curves for different link families with the translocation time not always increasing with crossings number within the same family. When one ring is knotted the results depend on whether the link is prime or composite and, for the composite case, they depend on whether the knotted or unknotted ring enters the pore first. We find a similar situation for 3-component links where the results depend on whether the link is prime or composite. These results contribute to our understanding of how the entanglement complexity between filaments impacts their translocation dynamics and should be useful for extending nanopore-sensing techniques to probe the topological properties of these systems.

cond-mat.stat-mech↗

arXiv2019

Magnetic Polymer Models for Epigenetics-Driven Chromosome Folding

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Oppositely to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes -- and hence on the expression of the underlying genes -- by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first-order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian Dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirms our mean-field predictions. Extending our models to allow for non-equilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

cond-mat.soft↗

arXiv2019

Polymerization induces non-Gaussian diffusion

Recent theoretical modeling offers a unified picture for the description of stochastic processes characterized by a crossover from anomalous to normal behavior. This is particularly welcome, as a growing number of experiments suggest the crossover to be a common feature shared by many systems: in some cases the anomalous part of the dynamics amounts to a Brownian yet non-Gaussian diffusion; more generally, both the diffusion exponent and the distribution may deviate from normal behavior in the initial part of the process. Since proposed theories work at a mesoscopic scale invoking the subordination of diffusivities, it is of primary importance to bridge these representations with a more fundamental, ``microscopic'' description. We argue that the dynamical behavior of macromolecules during simple polymerization processes provide suitable setups in which analytic, numerical, and particle-tracking experiments can be contrasted at such a scope. Specifically, we demonstrate that Brownian yet non-Gaussian diffusion of the center of mass of a polymer is a direct consequence of the polymerization process. Through the kurtosis, we characterize the early-stage non-Gaussian behavior within a phase diagram, and we also put forward an estimation for the crossover time to ordinary Brownian motion.

cond-mat.stat-mech↗

arXiv2019

Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding

Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence of specific patterns adopted by protein sequences and structures to deal with backbone self-entanglement. A large scale analysis of the Protein Data Bank shows that loops significantly intertwined with another chain portion are typically closed by weakly bound amino acids. Why is this energetic frustration maintained? A possible picture is that entangled loops are formed only toward the end of the folding process to avoid kinetic traps. Consistently, these loops are more frequently found to be wrapped around a portion of the chain on their N-terminal side, the one translated earlier at the ribosome. Finally, these motifs are less abundant in natural native states than in simulated protein-like structures, yet they appear in 32% of proteins, which in some cases display an amazingly complex intertwining.

q-bio.BM↗

arXiv2019

Plectoneme dynamics and statistics in braided polymers

Braids composed of two interwoven polymer chains exhibit a buckling transition whose origin has been explained through the onset of plectonemic structures. Here we study, by a combination of simulation and analytics, the dynamics of plectoneme formation and their statistics in steady state. The introduction of an order parameter, the plectonemic fraction, allows us to map out the phase boundary between the straight braid phase and the plectonemic one. We then monitor the formation and the growth of plectonemes, observing events typical of phase separation kinetics for liquid-gas systems (fusion, fission, 1D Ostwald ripening), but also of DNA supercoiling dynamics (plectonemic hopping). Finally, we propose a stochastic field theory for the coupled dynamics of twist and local writhe which explains the phenomenology found with Brownian dynamics simulations as well the power laws underlying the coarsening of plectonemes.

cond-mat.soft↗

arXiv2019

Synergy of Topoisomerase and Structural-Maintenance-of-Chromosomes Proteins Creates a Universal Pathway to Simplify Genome Topology

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II Topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that Structural Maintenance of Chromosomes (SMC) proteins -- such as cohesins and condensins -- can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localisation of essential crossings in turn catalysing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

cond-mat.soft↗

arXiv2018

Physical Principles of Retroviral Integration in the Human Genome

Certain retroviruses, including HIV, insert their DNA in a non-random fraction of the host genome via poorly understood selection mechanisms. Here, we develop a biophysical model for retroviral integrations as stochastic and quasi-equilibrium topological reconnections between polymers. We discover that physical effects, such as DNA accessibility and elasticity, play important and universal roles in this process. Our simulations predict that integration is favoured within nucleosomal and flexible DNA, in line with experiments, and that these biases arise due to competing energy barriers associated with DNA deformations. By considering a long chromosomal region in human T-cells during interphase, we discover that at these larger scales integration sites are predominantly determined by chromatin accessibility. Finally, we propose and solve a reaction-diffusion problem that recapitulates the distribution of HIV hot-spots within T-cells. With few generic assumptions, our model can rationalise experimental observations and identifies previously unappreciated physical contributions to retroviral integration site selection.

q-bio.SC↗