Static and dynamic properties of knotted biopolymers: from bulk to nanochannels and nanopores

Ropes 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

Fluctuations of rotational and translational degrees of freedom in an interacting active dumbbell system

We study the dynamical properties of a two-dimensional ensemble of self-propelled dumbbells with only repulsive interactions. After summarizing the behavior of the translational and rotational mean-square displacements in the homogeneous phase that we established in a previous study, we analyze their fluctuations. We study the dependence of the probability distribution functions in terms of the P\'eclet number, describing the relative role of active forces and thermal fluctuations, and of particle density.Comment: arXiv admin note: text overlap with arXiv:1501.0405

Motility-induced phase separation and coarsening in active matter

Active systems, or active matter, are self-driven systems which live, or function, far from equilibrium - a paradigmatic example which we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The nonequilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one which has recently been the subject of intense interest among biological and soft matter physicists is that of the so-called "motility-induced phase separation", whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions - we will briefly discuss at the end their role, which is not currently fully understood in this context.Comment: Contribution to the special issue "Coarsening dynamics", Comptes Rendus de Physique, see https://sites.google.com/site/ppoliti/crp-special-issu

Nonequilibrium thermodynamics of DNA nanopore unzipping

Using 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

Full phase diagram of active Brownian disks: from melting to motility-induced phase separation

We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with coexistence between active liquid and hexatic order, followed by a proper hexatic phase and a further transition to an active solid. As activity increases, the emergence of hexatic and solid order is shifted towards higher densities. Above a critical activity and for a certain range of packing fractions, the system undergoes MIPS and demixes into low and high density phases; the latter can be either disordered (liquid) or ordered (hexatic or solid) depending on activity

Plasma actuation for lifted flame stabilization in coaxial methane-air flow

The flame stabilization represents a relevant issue in aero-engine design. In fact, the growing demand of pollutant emissions reduction without significant losses of the combustion efficiency has driven the efforts of the scientific community towards lean flames. Lean fuel mixtures, characterized by low temperature flames, could manifest an unstable behaviour which can easily lead to the flame extinction due to the establishment of the blowout condition. This requires the implementation of control systems to avoid flame instability occurrence. The present work shows an investigation of the impact of dielectric barrier discharge (DBD) plasma actuation on lifted flame stabilization in a methane CH4-air Bunsen burner at ambient conditions. Two different plasma actuator configurations, powered with a high voltage (HV)/high frequency sinusoidal signal, have been investigated. Once the best actuator configuration was selected, the efficiency of the plasma actuation has been evaluated in terms of the flame lift-off distance, length and shape. In particular, in order to change the actuator power dissipation, different peak-to-peak voltages Vpp were tested, while the actuation frequency was kept equal to 20 kHz. The application of plasma discharges to flame stabilization leads to plasma-attached flames or plasma-enhanced lifted flames, depending on the air and fuel flow rates. At air flow rate of 1.54 g/s, plasma actuation allowed to decrease the lift-off height until the fuel jet velocity was below about 0.05 m/s thanks to the extension of the flame region upstream, toward the burner exit section. Beyond this value, it had no significant impact on the flame lift-off height, even though the amplitude of the lift-off height oscillations reduced coupled with a more stable behaviour of the lifting flame. The benefit of the plasma actuation increased by reducing the air flow rate to 1.35 g/s. In this condition, plasma-assisted flame reattachment was evident at each fuel velocity, in combination with an increasing flame height proportionally to the fuel jet velocity

3D polymer simulations of genome organization and transcription across different chromosomes and cell types

We employ the diffusing transcription factors model for numerical simulation of chromatin topology conformations and transcriptional processes of human chromatin. Simulations of a short chromatin filament reveal different possible pathways to regulate transcription: it is shown that the transcriptional activity profile can be regulated and controlled by either acting on the chain structural properties, or on external factors, such as the number of transcription factors. Additionally, comparisons between GRO-seq experimental data and large scale numerical simulation of entire chromosomes from the human umbilical vein endothelial cell and the B-lmphocyte GM12878 show that the model provides reliable and statistically significant predictions for transcription across different cell-lines.Comment: 26 pages, 10 figure