1,721,002 research outputs found
Static and dynamic properties of knotted biopolymers: from bulk to nanochannels and nanopores
Full text linkRopes or yarns, especially when disorderly packed, are prone to develop knots. Polymers are no exception to this rule and, in fact, rigorous mathematical results have been proved regarding the "statistical necessity" that sufficiently-long circular chains are knotted. The current surge of scientific interest in knotted polymers, and especially biopolymers, is prompted by the need to understand the profound implications that these forms of entanglement can have on the mechanical, dynamical and conformational properties of polymer chains.
For proteins, for instance, a long standing problem is how exactly the knotting properties of naturally-occurring proteins differ from those of general, non-specific, polymer models. This question has, in fact, motivated studies in several directions, from surveying and classifying systematically the repertoire of knots in peptide chains, to establishing the details of the folding route. For genomic DNA instead, it has long been known that it can be highly entangled due to the high packing degree that it attains in all organisms, from viruses to eukaryotic cells.
In this case, the advent of single-molecule manipulation techniques, which are routinely applied to DNA filaments of various length, has opened new, and still largely unexplored, perspectives for
detecting or controlling the spontaneous knotting properties of DNA.
In this thesis, I will use theoretical and computational techniques to tackle various aspects of the aforementioned issues.
In Chapter 1, I will provide a primer on knots, which sets a reference for concepts and methods used in subsequent chapters. I will in particular present a small resume of knot theory, focusing mainly on notions useful in our context. Afterwards, I will introduce some of the computational techniques used to detect and pinpoint knots along closed and open chains.
In Chapter 2, I will discuss our recent survey of the entire protein data bank, where we searched for all instances of knotted protein chains. The analysis yielded an up-to-date information about the overall knotting probability, the repertoire of knot types, as well as insight on the length and sequence position of knots in peptide chains.
In Chapter 3, I will use a general polyelectrolyte chain model, mapped to DNA, to study the dynamical mechanisms governing knot formation when DNA is confined inside a nanopore channel with size compatible with the DNA persistence length.
I will shown that the deep looping and back-folding of the chain ends will be responsible for the knot formation and destruction.
Upon increasing the chain length, the knotting probability of DNA increases due to the growing time a knot can diffuse alongside the chain. Instead unknotted lifetimes level off to a constant because they are ruled by the backfolding process.
In chapter 4, I will present the translocation of flexible and knotted polyelectrolyte chains, parametrized after single-stranded DNA, inside a pore too narrow to allow knot passage.
This out-of-equilibrium process, which can affect the polymer translocation in complex and counter-intuitive ways, depends deeply on the knot topology.
We tackled the resulting translocation compliance in a simple framework based on how the pulling force, applied only inside the pore, propagates along and past the knot, and how it is related to the structural properties of different knot types.
In chapter 5, I will discuss the translocation of double-stranded DNA chains through wide nanopores. The study is motivated by a recent experimental breakthrough, for which we provide key insight and explanations for the observed phenomenology
Exploring Different Temperature Definitions for an Athermal Tracer in an Active Bath: Out-of-Equilibrium Effects and Mass Dependence
No full textThe notion of temperature in out-of-equilibrium systems is still elusive. Here, we explore three different temperature definitions for an athermal tracer immersed in a out-of-equilibrium bath of active Brownian particles, with which it interacts solely through collisions. Temperatures are, respectively, defined from velocity fluctuations, the fluctuation-dissipation theorem and a heat fluctuation theorem, and we find their values to increase with the tracer’s mass following sigmoidal trends, the first two sharing similar values, the one defined from the fluctuation theorem showing lower ones. Notably, these trends are reminiscent of the trend of the kinetic temperature of a single free active particle as function of its mass. Using thus the latter as fit functional form, we interpret the tracer as effectively behaving like a single free active particle with the same mass but lower persistence time or activity amplitude
Nonequilibrium thermodynamics of DNA nanopore unzipping
Full text linkUsing theory and simulations, we carried out a first systematic
characterization of DNA unzipping via nanopore translocation. Starting from
partially unzipped states, we found three dynamical regimes depending on the
applied force, f: (i) heterogeneous DNA retraction and rezipping (f < 17pN),
(ii) normal (17pN 60pN) drift-diffusive
behavior. We show that the normal drift-diffusion regime can be effectively
modelled as a one-dimensional stochastic process in a tilted periodic
potential. We use the theory of stochastic processes to recover the potential
from nonequilibrium unzipping trajectories and show that it corresponds to the
free-energy landscape for single base-pairs unzipping. Applying this general
approach to other single-molecule systems with periodic potentials ought to
yield detailed free-energy landscapes from out-of-equilibrium trajectories.Comment: 6 pages, 4 figure
Unzipping of knotted DNA via nanopore translocation
No full textDNA unzipping by nanopore translocation has implications in diverse contexts, from polymer physics to single-molecule manipulation to DNA–enzyme interactions in biological systems. Here we use molecular dynamics simulations and a coarse-grained model of DNA to address the nanopore unzipping of DNA filaments that are knotted. This previously unaddressed problem is motivated by the fact that DNA knots inevitably occur in isolated equilibrated filaments and in vivo. We study how different types of tight knots in the DNA segment just outside the pore impact unzipping at different driving forces. We establish three main results. First, knots do not significantly affect the unzipping process at low forces. However, knotted DNAs unzip more slowly and heterogeneously than unknotted ones at high forces. Finally, we observe that the microscopic origin of the hindrance typically involves two concurrent causes: the topological friction of the DNA chain sliding along its knotted contour and the additional friction originating from the entanglement with the newly unzipped DNA. The results reveal a previously unsuspected complexity of the interplay of DNA topology and unzipping, which should be relevant for interpreting nanopore-based single-molecule unzipping experiments and improving the modeling of DNA transactions in vivo
Rotational and translational diffusion in an interacting active dumbbell system
Full text linkWe study the dynamical properties of a two-dimensional ensemble of self-propelled dumbbells with only repulsive interactions. This model undergoes a phase transition between a homogeneous and a segregated phase and we focus on the former. We analyze the translational and rotational mean-square displacements in terms of the Peclet number, describing the relative role of active forces and thermal fluctuations, and of particle density. We find that the four distinct regimes of the translational mean-square displacement of the single active dumbbell survive at finite density for parameters that lead to a separation of time scales. We establish the Peclet number and density dependence of the diffusion constant in the last diffusive regime. We prove that the ratio between the diffusion constant and its value for the single dumbbell depends on temperature and active force only through the Peclet number at all densities explored. We also study the rotational mean-square displacement proving the existence of a rich behavior with intermediate regimes only appearing at finite density. The ratio of the rotational late-time diffusion constant and its vanishing density limit depends on the Peclet number and density only. At low Peclet number it is a monotonically decreasing function of density. At high Peclet number it first increases to reach a maximum and then decreases as a function of density. We interpret the latter result advocating the presence of large-scale fluctuations close to the transition, at large-enough density, that favor coherent rotation inhibiting, however, rotational motion for even larger packing fractions
Fluctuations of rotational and translational degrees of freedom in an interacting active dumbbell system
Full text linkPore translocation of knotted DNA rings
No full textWe use an accurate coarse-grained model for DNA and stochastic molecular dynamics simulations to study the pore translocation of 10-kbp-long DNA rings that are knotted. By monitoring various topological and physical observables we find that there is not one, as previously assumed, but rather two qualitatively different modes of knot translocation. For both modes the pore obstruction caused by knot passage has a brief duration and typically occurs at a late translocation stage. Both effects are well in agreement with experiments and can be rationalized with a transparent model based on the concurrent tensioning and sliding of the translocating knotted chains. We also observed that the duration of the pore obstruction event is more controlled by the knot translocation velocity than the knot size. These features should advance the interpretation and design of future experiments aimed at probing the spontaneous knotting of biopolymers
Tracer motion in an active dumbbell fluid
No full textThe diffusion properties of spherical tracers coupled through a repulsive potential to a system of active dumbbells are analyzed. We model the dumbbells' dynamics with Langevin equations and the activity with a self-propulsive force of constant magnitude directed along the main axis of the molecules. Two types of tracers are considered. Thermal tracers are coupled to the same bath as the dumbbells while athermal tracers are not; both interact repulsively with the dumbbells. We focus our attention on the intruders' mean square displacement and how it compares to the one of the dumbbells. We show that the dynamics of thermal intruders, with mass similar to the one of the dumbbells, display the typical four time-lag regimes of the dumbbells' mean square displacement. The thermal tracers' late-time diffusion coefficient depends on their mass very weakly and it is close to the one of the dumbbells at low Péclet only. Athermal tracers only have ballistic and late-time diffusive regimes. The late time diffusion coefficients of athermal tracers and dumbbells have similar values at high Péclet number when their masses are of the same order, while at low Péclet number this coefficient gets close to the one of the dumbbells only when the tracers are several order of magnitude heavier than the dumbbells. We propose a generalization of the Enskog law for dilute hard disks, that describes the athermal tracers' mean square displacement in the form of a scaling law in terms of their mass
Ion Channels in Critical Membranes: Clustering, Cooperativity, and Memory Effects
Full text linkMuch progress has been made in elucidating the inner workings of voltage-gated ion channels, but less
understood is the influence of lipid rafts on gating kinetics. Here we propose that state-dependent channel
affinity for different lipid species provides a unified explanation for the experimentally observed behaviors of
clustering, cooperativity, and hysteresis. We develop models of diffusing lipids and channels engaged in Isinglike
interactions to investigate the collective behaviors driven by raft formation in critical membranes close to the
demixing transition. The model channels demonstrate lipid-mediated long-range interactions, activation curve
steepening, and long-term memory in ionic currents. These behaviors likely play a role in channel-mediated
cellular signaling and suggest a universal mechanism for self-organization of biomolecular assemblies
Work fluctuations for a harmonically confined active Ornstein-Uhlenbeck particle
Full text linkWe study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem
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