Topological phases and curvature-driven pattern formation in cholesteric shells.

We study the phase behaviour of cholesteric liquid crystal shells with different geometries. We compare the cases of tangential anchoring and no anchoring at the surface, focussing on the former case, which leads to a competition between the intrinsic tendency of the cholesteric to twist and the anchoring free energy which suppresses it. We then characterise the topological phases arising close to the isotropic-cholesteric transition. These typically consist of quasi-crystalline or amorphous tessellations of the surface by half-skyrmions, which are stable at lower and larger shell sizes, respectively. For ellipsoidal shells, defects in the tessellation couple to a local curvature, and according to the shell size, they either migrate to the poles or distribute uniformly on the surface. For toroidal shells, the variations in the local curvature of the surface stabilise heterogeneous phases where cholesteric or isotropic patterns coexist with hexagonal lattices of half-skyrmions.

Circular Polycatenanes: Supramolecular Structures with Topologically Tunable Properties.

Polycatenanes, 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 twist in the system, significantly altering 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 Calugareanu-White-Fuller theorem Tw+Wr=const, originally proved for ribbonlike structures such as double stranded DNA. Our results suggest that circular polycatenanes with storable and tunable twist can form a new category of highly designable multiscale structures with potential applications in supramolecular chemistry and material science.

Cholesteric Shells: Two-Dimensional Blue Fog and Finite Quasicrystals.

We study the phase behavior of a quasi-two-dimensional cholesteric liquid crystal shell. We characterize 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 of 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 stabilizes heterogeneous phases where cholesteric patterns coexist with hexagonal lattices of half-skyrmions. Quasicrystals and amorphous and heterogeneous structures could be sought experimentally by self-assembling cholesteric shells on the surface of emulsion droplets.

Investigating site-selection mechanisms of retroviral integration in supercoiled DNA braids.

We theoretically study the integration of short viral DNA in a DNA braid made up by two entwined double-stranded DNA molecules. We show that the statistics of single integration events substantially differ in the straight and buckled, or plectonemic, phase of the braid and are more likely in the latter. We further discover that integration is most likely close to plectoneme tips, where the larger bending energy helps overcome the associated energy barrier and that successive integration events are spatio-temporally correlated, suggesting a potential mechanistic explanation of clustered integration sites in host genomes. The braid geometry we consider provides a novel experimental set-up to quantify integration in a supercoiled substrate in vitro, and to better understand the role of double-stranded DNA topology during this process.

Phase diagrams of confined square lattice linked polygons.

The phase diagrams of two models of two confined and dense two-dimensional ring polymers are examined numerically. The ring polymers are modeled by square lattice polygons in a square cavity and are placed to be either unlinked or linked in the plane. The phase diagrams of the two models are found to be a function of the placement of the ring polymers and include multicritical points where first-order and continuous phase boundaries meet. We estimate numerically the critical exponents associated with the phase boundaries and the multicritical points.

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 integration 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.

Lamellar ordering, droplet formation and phase inversion in exotic active emulsions.

We study numerically the behaviour of a two-dimensional mixture of a passive isotropic fluid and an active polar gel, in the presence of a surfactant favouring emulsification. Focussing on parameters for which the underlying free energy favours the lamellar phase in the passive limit, we show that the interplay between nonequilibrium and thermodynamic forces creates a range of multifarious exotic emulsions. When the active component is contractile (e.g., an actomyosin solution), moderate activity enhances the efficiency of lamellar ordering, whereas strong activity favours the creation of passive droplets within an active matrix. For extensile activity (occurring, e.g., in microtubule-motor suspensions), instead, we observe an emulsion of spontaneously rotating droplets of different size. By tuning the overall composition, we can create high internal phase emulsions, which undergo sudden phase inversion when activity is switched off. Therefore, we find that activity provides a single control parameter to design composite materials with a strikingly rich range of morphologies.

Epigenetic Transitions and Knotted Solitons in Stretched Chromatin.

The spreading and regulation of epigenetic marks on chromosomes is crucial to establish and maintain cellular identity. Nonetheless, the dynamic mechanism leading to the establishment and maintenance of tissue-specific, epigenetic pattern is still poorly understood. In this work we propose, and investigate in silico, a possible experimental strategy to illuminate the interplay between 3D chromatin structure and epigenetic dynamics. We consider a set-up where a reconstituted chromatin fibre is stretched at its two ends (e.g., by laser tweezers), while epigenetic enzymes (writers) and chromatin-binding proteins (readers) are flooded into the system. We show that, by tuning the stretching force and the binding affinity of the readers for chromatin, the fibre undergoes a sharp transition between a stretched, epigenetically disordered, state and a crumpled, epigenetically coherent, one. We further investigate the case in which a knot is tied along the chromatin fibre, and find that the knotted segment enhances local epigenetic order, giving rise to "epigenetic solitons" which travel and diffuse along chromatin. Our results point to an intriguing coupling between 3D chromatin topology and epigenetic dynamics, which may be investigated via single molecule experiments.

Entropic elasticity and dynamics of the bacterial chromosome: A simulation study.

We study the compression and extension dynamics of a DNA-like polymer interacting with non-DNA binding and DNA-binding proteins, by means of computer simulations. The geometry we consider is inspired by recent experiments probing the compressional elasticity of the bacterial nucleoid (DNA plus associated proteins), where DNA is confined into a cylindrical container and subjected to the action of a "piston"-a spherical bead to which an external force is applied. We quantify the effect of steric interactions (excluded volume) on the force-extension curves as the polymer is compressed. We find that non-DNA-binding proteins, even at low densities, exert an osmotic force which can be a lot larger than the entropic force exerted by the compressed DNA. The trends we observe are qualitatively robust with respect to changes in protein sizes and are similar for neutral and charged proteins (and DNA). We also quantify the dynamics of DNA expansion following removal of the "piston": while the expansion is well fitted by power laws, the apparent exponent depends on protein concentration and protein-DNA interaction in a significant way. We further highlight an interesting kinetic process which we observe during the expansion of DNA interacting with DNA-binding proteins when the interaction strength is intermediate: the proteins bind while the DNA is packaged by the compression force, but they "pop-off" one-by-one as the force is removed, leading to a slow unzipping kinetics. Finally, we quantify the importance of supercoiling, which is an important feature of bacterial DNA in vivo.

Switching dynamics in cholesteric liquid crystal emulsions.

In this work we numerically study the switching dynamics of a 2D cholesteric emulsion droplet immersed in an isotropic fluid under an electric field, which is either uniform or rotating with constant speed. The overall dynamics depend strongly on the magnitude and on the direction (with respect to the cholesteric axis) of the applied field, on the anchoring of the director at the droplet surface and on the elasticity. If the surface anchoring is homeotropic and a uniform field is parallel to the cholesteric axis, the director undergoes deep elastic deformations and the droplet typically gets stuck into metastable states which are rich in topological defects. When the surface anchoring is tangential, the effects due to the electric field are overall less dramatic, as a small number of topological defects form at equilibrium. The application of the field perpendicular to the cholesteric axis usually has negligible effects on the defect dynamics. The presence of a rotating electric field of varying frequency fosters the rotation of the defects and of the droplet as well, typically at a lower speed than that of the field, due to the inertia of the liquid crystal. If the surface anchoring is homeotropic, a periodic motion is found. Our results represent a first step to understand the dynamical response of a cholesteric droplet under an electric field and its possible application in designing novel liquid crystal-based devices.

Shear dynamics of an inverted nematic emulsion.

Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet in a nematic liquid crystal under a shear flow. We find a large repertoire of possible nonequilibrium steady states as a function of the shear rate and of the anchoring of the nematic director field at the droplet surface. We first discuss homeotropic anchoring. For weak anchoring, we recover the typical behaviour of a sheared isotropic droplet in a binary fluid, which rotates, stretches and can be broken by the applied flow. For intermediate anchoring, new possibilities arise due to elastic effects in the nematic fluid. We find that in this regime the 2D droplet can tilt and move in the flow, or tumble incessantly at the centre of the channel. For sufficiently strong anchoring, finally, one or both of the topological defects which form close to the surface of the isotropic droplet in equilibrium detach from it and get dragged deep into the nematic state by the flow. In 3D, instead, the Saturn ring associated with the normal anchoring disclination line can be deformed and shifted downstream by the flow, but remains always localized in the proximity of the droplet, at least for the parameter range we explored. Tangential anchoring in 2D leads to a different dynamic response, as the boojum defects characteristic of this situation can unbind from the droplet under a weaker shear with respect to the normal anchoring case. Our results should stimulate further experiments with inverted liquid crystal emulsions under shear, as most of the predictions can be testable in principle by monitoring the evolution of liquid crystalline orientation patterns or by tracking the position and shape of the droplet over time.

Analysis of measles-related hospitalizations in Tuscany from 2000 to 2014.

To evaluate measles incidence and its relevant changes over a 14-year period (2000-2014), we analysed data from the regional hospital discharge database on children and adults hospitalized in Tuscany, Italy. A total of 181 paediatric and 413 adult cases were identified. Despite all the efforts towards regional measles elimination, we observed that the overall measles hospitalization rates for children and adults living in Tuscany globally increased from 0·45 to 0·85/100 000 during the study period (P = 0·001) showing fluctuations due to periodic measles outbreaks. Data stratified by age group showed that the hospitalization rate significantly increased in young adults over the study period, confirming an increase in susceptibility to measles in this subpopulation. Conversely, no statistically significant difference was observed in the hospitalization rate in the other age groups. However, children aged <1 year still exhibit the highest hospitalization rate. Pneumonia represented the most common complication in both the adult and children subsets. No death was reported. Measles still represents a public health problem, and national strategies should be implemented, focusing on emergent susceptible subsets, such as infants and young adults.

Electric field controlled columnar and planar patterning of cholesteric colloids.

We study how dispersions of colloidal particles in a cholesteric liquid crystal behave under a time-dependent electric field. By controlling the amplitude and shape of the applied field wave, we show that the system can be reproducibly driven out of equilibrium through different kinetic pathways and navigated through a glassylike free energy landscape encompassing many competing metastable equilibria. Such states range from simple Saturn rings to complex structures featuring amorphous defect networks, or stacks of disclination loops. A nonequilibrium electric field can also trigger the alignment of particles into columnar arrays, through defect-mediated force impulses, or their repositioning within a plane. Our results are promising in terms of providing new avenues towards controlled patterning and self-assembly of soft colloid-liquid crystal composite materials.

Interacting elastic lattice polymers: a study of the free energy of globular rings.

We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of "interacting elastic lattice polymers" and allows a sufficiently good sampling of long and compact configurations, an essential prerequisite to study the scaling behavior of free energies. By simulating interacting self-avoiding rings at several temperatures in the collapsed phase, we estimate both the bulk and the surface free energy. Moreover from the corresponding estimate of the entropic exponent α-2 we provide evidence that, unlike for swollen and Θ-point rings, the hyperscaling relation is not satisfied for globular rings.

Hospitalization rates of complicated pneumococcal community-acquired pneumonia is increasing in Tuscan children.

To provide epidemiological data on community-acquired pneumonia (CAP) and complicated CAP, a retrospective study was conducted on a partially vaccinated paediatric population. Data from children hospitalized for CAP in Tuscan hospitals between January 1st, 1999 and December 31st, 2009 were analysed. A total of 5,450 children with CAP were hospitalized. Annual hospitalization rates for CAP did not change significantly over the study period (X2 for trend= 0.652; p=0.419). The total annual hospitalization rate for pneumococcal CAP varied according to age (28.04 per 100,000 children aged less than 5 years, 10.06 per 100,000 children aged 6-12 years and 0.98 per 100,000 children aged greater than13years). Hospitalization rates for pneumococcal CAP increased from12.84 (95 percent CI:7.35-18.34) in 2001 to 45.4 (95 percent CI:35.93-54.90) per 100,000 children aged less than 5 years in 2009 (p less than 0.0001). In addition, a significant increase of hospitalization rates for complicated CAP (from 6.07 in 1999 to 13.66 in 2009 per 100,000 children; P less than 0.0001) and pneumococcal complicated CAP (from 0.19 in 1999 to 3.41 in 2009 per 100,000 children) over the study period were highlighted. Our epidemiological data confirm the decision to introduce the PCV13 vaccine, to satisfy the need to prevent a wider group of pneumococcal serotypes.

Universal properties of knotted polymer rings.

By performing Monte Carlo sampling of N-steps self-avoiding polygons embedded on different Bravais lattices we explore the robustness of universality in the entropic, metric, and geometrical properties of knotted polymer rings. In particular, by simulating polygons with N up to 10(5) we furnish a sharp estimate of the asymptotic values of the knot probability ratios and show their independence on the lattice type. This universal feature was previously suggested, although with different estimates of the asymptotic values. In addition, we show that the scaling behavior of the mean-squared radius of gyration of polygons depends on their knot type only through its correction to scaling. Finally, as a measure of the geometrical self-entanglement of the self-avoiding polygons we consider the standard deviation of the writhe distribution and estimate its power-law behavior in the large N limit. The estimates of the power exponent do depend neither on the lattice nor on the knot type, strongly supporting an extension of the universality property to some features of the geometrical entanglement.

TTR fibril formation inhibitors: is there a SAR?

Transthyretin is a homotetrameric protein that carries thyroxine and retinol binding protein in plasma and is associated with a variety of amyloid diseases. One approach to the potential treatment of TTR amyloidosis is the stabilization of the native tetramer, over the dissociative transition state, through the binding of small molecules; this increases the kinetic barrier for tetramer dissociation and prevents protein misfolding. Several molecules discovered through focused screening, or created utilizing the structure-based design, were studied to identify the structural features that could make up for a good candidate drug. In this review, we examine several different chemical classes of TTR fibril formation inhibitors, highlighting the structural modifications that have led to an improvement or to a decrease of their potency and/or selectivity.

Facilitated diffusion on confined DNA.

In living cells, proteins combine three-dimensional bulk diffusion and one-dimensional sliding along the DNA to reach a target faster. This process is known as facilitated diffusion and we investigate its dynamics in the physiologically relevant case of confined DNA. The confining geometry and DNA elasticity are key parameters: We find that facilitated diffusion is most efficient inside an isotropic volume and on a flexible polymer. By considering the typical copy numbers of proteins in vivo, we show that the speedup due to sliding becomes insensitive to fine tuning of parameters, rendering facilitated diffusion a robust mechanism to speed up intracellular diffusion-limited reactions. The parameter range we focus on is relevant for in vitro systems and for facilitated diffusion on yeast chromatin.

Bistable defect structures in blue phase devices.

Blue phases are liquid crystals made up by networks of defects, or disclination lines. While existing phase diagrams show a striking variety of competing metastable topologies for these networks, very little is known as to how to kinetically reach a target structure, or how to switch from one to the other, which is of paramount importance for devices. We theoretically identify two confined blue phase I systems in which by applying an appropriate series of electric field it is possible to select one of two bistable defect patterns. Our results may be used to realize new generation and fast switching energy-saving bistable devices in ultrathin surface treated blue phase I wafers.

Shearing self-propelled suspensions: arrest of coarsening and suppression of giant density fluctuations.

We study the effect of a linear shear flow on a collection of interacting active, self-propelled particles modeled via the Vicsek model. The imposed flow has a dramatic effect on the behavior of the model. We find that in the presence of shear there is no order-disorder transition, and that coarsening of the domains is arrested. Shear also suppresses the so-called giant density fluctuations that are observed in the quiescent limit.