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Phases of Polymers and Biopolymers
Full text linkIn this thesis we develop coarse grained models aiming at understanding physical
problems arising from phase transitions which occur at the single molecule level. The
thesis will consist of two parts, grossly related to and motivated by the two subjects
dealt with above. In the first half, we will focus on critical phenomena in stretching
experiments, namely in DNA unzipping and polymer stretching in a bad solvent. In
the second part, we will develop a model of thick polymers, with the goal of understanding the origin of the protein folds and the physics underlying the folding ‘transition’,
as well as with the hope of shedding some light on some of the fundamental
questions highlighted in this Introduction.
In the first part of the thesis we will introduce a simple model of self-avoiding
walks for DNA unzipping. In this way we can map out the phase diagram in the
force vs. temperature plane. This reveals the present of an interesting cold unzipping
transition. We then go on to study the dynamics of this coarse grained model. The
main result which we will discuss is that the unzipping dynamics below the melting
temperature obeys different scaling laws with respect to the opening above thermal
denaturation, which is governed by temperature induced fluctuating bubbles.
Motivated by this and by recent results from other theoretical groups, we move on
to study the relation to DNA unzipping of the stretching of a homopolymer below the
theta point. Though also in this case a cold unzipping is present in the phase diagram,
this situation is richer from the theoretical point of view because the physics depends
crucially on dimension: the underlying phase transition indeed is second order in two
dimensions and first order in three. This is shown to be intimately linked to the failure
of mean field in this phenomena, unlike for DNA unzipping. In particular, the globule
unfolds via a series (hierarchy) of minima. In two dimensions they survive in the thermodynamic
limit whereas if the dimension, d, is greater than 2, there is a crossover
and for very long polymers the intermediate minima disappear. We deem it intriguing
that an intermediate step in this minima hierarchy for polymers of finite length in the
three-dimensional case is a regular mathematical helix, followed by a zig-zag structure.
This is found to be general and almost independent of the interaction potential
details. It suggests that a helix, one of the well-known protein secondary structure, is
a natural choice for the ground state of a hydrophobic protein which has to withstand
an effective pulling force.
In the second part, we will follow the inverse route and ask for a minimal model
which is able to account for the basic aspects of folding. By this, we mean a model
which contains a suitable potential which has as its ground state a protein-like structure
and which can account for the known thermodynamical properties of the folding
transition. The existing potential which are able to do that[32] are usually constructed
‘ad hoc’ from knowledge of the native state. We stress that our procedure here is
completely different and the model which we propose should be built up starting
from minimal assumptions. Our main result is the following. If we throw away the
usual view of a polymer as a sequence of hard spheres tethered together by a chain
(see also Chapter 1) and substitute it with the notion of a flexible tube with a given
thickness, then upon compaction our ’thick polymer’ or ’tube’ will display a rich secondary structure with protein-like helices and sheets, in sharp contrast with the
degenerate and messy crumpled collapsed phase which is found with a conventional
bead-and-link or bead-and-spring homopolymer model. Sheets and helices show up
as the polymer gets thinner and passes from the swollen to the compact phase. In this
sense the most interesting regime is a ‘twilight’ zone which consists of tubes which
are at the edge of the compact phase, and we thus identify them as ‘marginally compact
strucures’. Note the analogy with the result on stretching, in which the helices
were in the same way the ‘last compact’ structures or the ‘first extended’ ones when
the polymer is being unwinded by a force.
After this property of ground states is discussed, we proceed to characterize the
thermodynamics of a flexible thick polymer with attraction. The resulting phase diagram
is shown to have many of the properties which are usually required from protein
effective models, namely for thin polymers there is a second order collapse transition
(O collapse) followed, as the temperature is lowered, by a first order transition
to a semicrystalline phase where the compact phase orders forming long strands all
aligned preferentially along some direction. For thicker polymers the transition to
this latter phase occurs directly from the swollen phase, upon lowering T, through a
first order transition resembling the folding transition of short proteins
Nonequilibrium chromosome looping via molecular slip links
No full textWe propose a model for the formation of chromatin loops based on the diffusive sliding of molecular slip links. These mimic the behavior of cohesinlike molecules, which, along with the CTCF protein, stabilize loops which contribute to organizing the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable nonequilibrium models, we show that diffusive sliding is sufficient to account for the strong bias in favor of convergent CTCF-mediated chromosome loops observed experimentally. We also find that the diffusive motion of multiple slip links along chromatin is rectified by an intriguing ratchet effect that arises if slip links bind to the chromatin at a preferred 'loading site'. This emergent collective behavior favors the extrusion of loops which are much larger than the ones formed by single slip links.Data corresponding to Figures 1 and 2 in the paper
Thermodynamics of DNA packaging inside a viral capsid: The role of DNA intrinsic thickness
No full textWe characterize the equilibrium thermodynamics of a thick polymer
confined in a spherical region of space. This is used to gain insight
into the DNA packaging process. The experimental reference system for
the present study is the recent characterization of the loading process
of the genome. inside the phi29 bacteriophage capsid. Our emphasis is on
the modelling of double-stranded DNA as a flexible thick polymer (tube)
instead of a beads-and-springs chain. By using finite-size scaling to
extrapolate our results to genome lengths appropriate for phi29, we find
that the thickness-induced force may account for up to half the one
measured experimentally at high packing densities. An analogous
agreement is found for the total work that has to be spent in the
packaging process. Remarkably, such agreement can be obtained in the
absence of any tunable parameters and is a mere consequence of the DNA
thickness. Furthermore, we provide a quantitative estimate of how the
persistence length of a polymer depends on its thickness. The expression
accounts for the significant difference in the persistence lengths of
single and double-stranded DNA (again with the sole input of their
respective sections and natural nucleotide/base-pair spacing)
Topological patterns in two-dimensional gel electrophoresis of DNA knots
Full text linkGel electrophoresis is a powerful experimental method to probe the
topology of DNA and other biopolymers. While there is a large
body of experimental work which allows us to accurately separate
different topoisomers of a molecule, a full theoretical understanding
of these experiments has not yet been achieved. Here we show
that the mobility of DNA knots depends crucially and subtly on
the physical properties of the gel, and in particular on the presence
of dangling ends. The topological interactions between these
and DNA molecules can be described in terms of an “entanglement
number”, and yield a non-monotonic mobility at moderate fields.
Consequently, in two-dimensional electrophoresis, gel bands display
a characteristic arc pattern; this turns into a straight line when the
density of dangling ends vanishes. We also provide a novel framework
to accurately predict the shape of such arcs as a function of
molecule length and topological complexity, which may be used to
inform future experiments
Curvature-driven positioning of Turing patterns in phase-separating curved membranes
No full textWe introduce a new finite difference scheme to study the dynamics of Turing patterns of a two-species activator-inhibitor system embedded on a phase-separating curved membrane, modelling for instance a lipid bilayer. We show that the underlying binary fluid can strongly affect both the dynamical and the steady state properties of the ensuing Turing patterns. Furthermore, geometry plays a key role, as a large enough local membrane curvature can both arrest the coarsening of the lipid domains and position the patterns selectively at areas of high or small local curvature. The physical phenomena we observe are due to a minimal coupling, between the diffusivity of the Turing components and the local membrane composition. While our study is theoretical in nature, it can provide a framework within which to address intracellular pattern formation in systems of interacting membrane proteins. © 2016 The Royal Society of Chemistry
Mechanisms for destabilisation of RNA viruses at air-water and liquid-liquid interfaces
No full textUnderstanding the interactions between viruses and surfaces or interfaces is important, as they provide the principles underpinning the cleaning and disinfection of contaminated surfaces. Yet, the physics of such interactions is currently poorly understood. For instance, there are longstanding experimental observations suggesting that the presence of air-water interfaces can generically inactivate and kill viruses, yet the mechanism underlying this phenomenon remains unknown. Here we use theory
and simulations to show that electrostatics provides one such mechanism, and that this is very general. Thus, we predict that the electrostatic free energy of an RNA virus should increase by several thousands of k B T as the virion breaches an air-water interface. We also show that the fate of a virus approaching a generic liquid-liquid interface depends strongly on the detailed balance between interfacial and electrostatic forces, which can be tuned, for instance, by choosing different media to contact a virus-laden respiratory droplet. Tunability arises because both the electrostatic and interfacial forces scale similarly with viral size. We propose that these results can be used to design effective strategies for surface disinfection
Data for "Mixtures of blue phase liquid crystal with simple liquids: elastic emulsions and cubic fluid cylinders"
No full textWe numerically investigate the behavior of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, χ, setting the balance between interfacial and elastic forces. When χ and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a cubic array of fluid cylinders. For larger χ, the isotropic phase arranges primarily into liquid emulsion droplets which coarsen very slowly, rewiring the blue phase disclination lines into an amorphous elastic network. Our blue phase-simple fluid composites can be externally manipulated: an electric field can trigger a morphological transition between cubic fluid cylinder phases with different topologies.Stratford, Kevin; Juho, Lintuvuori; Marenduzzo, Davide; Cates, Mike. (2018). Data for "Mixtures of blue phase liquid crystal with simple liquids: elastic emulsions and cubic fluid cylinders", [dataset]. University of Edinburgh. http://dx.doi.org/10.7488/ds/2396
Spontaneous flow in polar active fluids: the effect of a phenomenological self propulsion-like term
No full textAbstract.: We present hybrid lattice Boltzmann simulations of extensile and contractile active fluids where we incorporate phenomenologically the tendency of active particles such as cell and bacteria, to move, or swim, along the local orientation. Quite surprisingly, we show that the interplay between alignment and activity can lead to completely different results, according to geometry (periodic boundary conditions or confinement between flat walls) and nature of the activity (extensile or contractile). An interesting generic outcome is that the alignment interaction can transform stationary active patterns into continuously moving ones: the dynamics of these evolving patterns can be oscillatory or chaotic according to the strength of the alignment term. Our results suggest that flow-polarisation alignment can have important consequences on the collective dynamics of active fluids and active gel. Graphical abstract: [Figure not available: see fulltext.
Topological gelation of reconnecting polymers
Full text linkDNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids—e.g., DNA-based complex fluids or living polymer networks—with desired topologies
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