Enzo Orlandini

Monte carlo study of the interacting self-avoiding walk model in three dimensions

We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.

Polymers with spatial or topological constraints: Theoretical and computational results

In this review, we provide an organized summary of the theoretical and computational results that are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide an accessible, non-specialist introduction to the main topological concepts, polymer models, and theoretical/computational methods used to investigate dense and entangled polymer systems. The main body of our review deals with (i) the effect that spatial confinement has on the equilibrium topological entanglement of one or more polymer chains and (ii) the metric and entropic properties of polymer chains with fixed topological states. These problems have important technological applications and implications for life sciences. Both aspects, especially the latter, are amply covered. A number of selected open problems are finally highlighted.

DNA–DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting

Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What is the physical basis of this organization? Here we show evidence from stochastic simulation techniques that suggests that a key element is the tendency of contacting DNA strands to order, as in cholesteric liquid crystals. This interaction favors their preferential juxtaposition at a small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect dramatically impacts the geometry and topology of DNA inside phages. Accounting for this local potential allows us to reproduce the main experimental data on DNA organization in phages, including the cryo-EM observations and detailed features of the spectrum of DNA knots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage.

SPINODAL DECOMPOSITION TO A LAMELLAR PHASE: EFFECTS OF HYDRODYNAMIC FLOW

Results are presented for the kinetics of domain growth of a two-dimensional fluid quenched from a disordered to a lamellar phase. At early times when a Lifshitz-Slyozov mechanism is operative the growth process proceeds logarithmically in time to a frozen state with locked-in defects. However, when hydrodynamic modes become important, or the fluid is subjected to shear, the frustration of the system is alleviated and the size and orientation of the lamellae attain their equilibrium values.

Interacting self-avoiding walks and polygons in three dimensions

Self-interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the -point. We consider self-avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon. We prove that these walks and polygons have the same limiting free energy if the interactions between nearest-neighbour vertices are repulsive. The attractive interaction regime is investigated using Monte Carlo methods, and we find evidence that the limiting free energies are also equal here. In particular, this means that these models have the same -point, in the asymptotic limit. The dimensions and shapes of walks and polygons are also examined as a function of the interaction strength.

Knot probability for lattice polygons in confined geometries

We study the knot probability of polygons confined to slabs or prisms, considered as subsets of the simple cubic lattice. We show rigorously that almost all sufficiently long polygons in a slab are knotted and we use Monte Carlo methods to investigate the behaviour of the knot probability as a function of the width of the slab or prism and the number of edges in the polygon. In addition we consider the effect of solvent quality on the knot probability in these confined geometries.

Structure and Dynamics of Ring Polymers: Entanglement Effects Because of Solution Density and Ring Topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intrachain entanglement is modulated by varying both solution density (from infinite dilution up to ≈40% volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected ...

The writhe of a self-avoiding walk

The writhe of a self-avoiding walk in a three-dimensional space is the average over all projections onto a plane of the sum of the signed crossings. We compute this number using a Monte Carlo simulation. Our results suggest that the average of the absolute value of the writhe of self-avoiding walks increases as nalpha , where n is the length of the walks and alpha approximately=0.5. The mean crossing number of walks is also computed and found to have a power-law dependence on the length of the walks. In addition, we consider the effects of solvent quality on the writhe and mean crossing number of walks.

The writhe of a self-avoiding polygon

We discuss the writhe of a self-avoiding polygon on a lattice, as a geometrical measure of its entanglement complexity. We prove a rigorous result about the dependence of the absolute value of the writhe on the number n of edges in the polygon, and use Monte Carlo methods to estimate the distribution of the writhe both for all polygons with n edges and for the subset of polygons that are trefoils.

Threading dynamics of ring polymers in a gel

We perform large scale three-dimensional molecular dynamics simulations of unlinked and unknotted ring polymers diffusing through a background gel, here a three-dimensional cubic lattice. Taking advantage of this architecture, we propose a new method to unambiguously identify and quantify inter-ring threadings (penetrations) and to relate these to the dynamics of the ring polymers. We find that both the number and the persistence time of the threadings increase with the length of the chains, ultimately leading to a percolating network of inter-ring penetrations. We discuss the implications of these findings for the possible emergence of a topological jammed state of very long rings.