The Role of Spin Anisotropy in the Unbinding of Interfaces

We study the ground state of a classical X-Y model with $p \ge 3$-fold spin anisotropy $D$ in a uniform external field, $H$. An interface is introduced into the system by a suitable choice of boundary conditions. For large $D$, as $H \to 0$, we prove using an expansion in $D^{-1}$ that the interface unbinds from the surface through an infinite series of layering transitions. Numerical work shows that the transitions end in a sequence of critical end points.Comment: 7 pages RevTeX, plus 1 postscript figure available from the authors OUTP-94-41

Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore

The advent of solid state nanodevices allows for interrogating the physico-chemical properties of a polyelectrolyte chain by electrophoretically driving it through a nanopore. Salient dynamical aspects of the translocation process have been recently characterized by theoretical and computational studies of model polymer chains free from self-entanglement. However, sufficiently long equilibrated chains are necessarily knotted. The impact of such topological "defects" on the translocation process is largely unexplored, and is addressed in this study. By using Brownian dynamics simulations on a coarse-grained polyelectrolyte model we show that knots, despite being trapped at the pore entrance, do not "per se" cause the translocation process to jam. Rather, knots introduce an effective friction that increases with the applied force, and practically halts the translocation above a threshold force. The predicted dynamical crossover, which is experimentally verifiable, is of relevance in applicative contexts, such as DNA nanopore sequencing.Comment: 6 pages; 7 figure

Depletion effects and loop formation in self-avoiding polymers

Langevin dynamics is employed to study the looping kinetics of self-avoiding polymers both in ideal and crowded solutions. A rich kinetics results from the competition of two crowding-induced effects: the depletion attraction and the enhanced viscous friction. For short chains, the enhanced friction slows down looping, while, for longer chains, the depletion attraction renders it more frequent and persistent. We discuss the possible relevance of the findings for chromatin looping in living cells.Comment: 4 pages, 3 figure

Surface spin-flop phases and bulk discommensurations in antiferromagnets

Phase diagrams as a function of anisotropy D and magnetic field H are obtained for discommensurations and surface states for a model antiferromagnet in which $H$ is parallel to the easy axis. The surface spin-flop phase exists for all $D$. We show that there is a region where the penetration length of the surface spin-flop phase diverges. Introducing a discommensuration of even length then becomes preferable to reconstructing the surface. The results are used to clarify and correct previous studies in which discommensurations have been confused with genuine surface spin-flop states.Comment: 4 pages, RevTeX, 2 Postscript figure

Tuning Knotted Copolyelectrolyte Conformations via Solution Properties

We used Langevin dynamics simulations to study coarse-grained knotted copolyelectrolytes, composed by a neutral and a charged segment, in solutions of different salt concentrations, valency, and solvent screening power. We show that the facile variation of these parameters allows for tuning the length and position of the knotted region, which in turn controls the overall metric properties. Specifically, adding either monovalent or divalent ions causes the knot to swell at the expense of the copolyelectrolyte overall size. However, the knot typically straddles the charged-neutral interface in the presence of monovalent counterions, whereas it is attracted on the charged segment with divalent ones. Notably, similar modulations of knot size and position can also be achieved by varying the dielectric constant of the solvent. Our results demonstrate the feasibility of harnessing the solution-mediated balance of electrostatics and conformational entropy toward a facile external tuning of the conformational properties of knotted polymers

Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment

We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints

RNA Pore Translocation with Static and Periodic Forces: Effect of Secondary and Tertiary Elements on Process Activation and Duration

We use MD simulations to study the pore translocation properties of a pseudoknotted viral RNA. We consider the 71-nucleotide-long xrRNA from the Zika virus and establish how it responds when driven through a narrow pore by static or periodic forces applied to either of the two termini. Unlike the case of fluctuating homopolymers, the onset of translocation is significantly delayed with respect to the application of static driving forces. Because of the peculiar xrRNA architecture, activation times can differ by orders of magnitude at the two ends. Instead, translocation duration is much smaller than activation times and occurs on time scales comparable at the two ends. Periodic forces amplify significantly the differences at the two ends, for both activation times and translocation duration. Finally, we use a waiting-times analysis to examine the systematic slowing downs in xrRNA translocations and associate them to the hindrance of specific secondary and tertiary elements of xrRNA. The findings provide a useful reference to interpret and design future theoretical and experimental studies of RNA translocation

A complete devil's staircase in the Falicov-Kimball model

We consider the neutral, one-dimensional Falicov-Kimball model at zero temperature in the limit of a large electron--ion attractive potential, U. By calculating the general n-ion interaction terms to leading order in 1/U we argue that the ground-state of the model exhibits the behavior of a complete devil's staircase.Comment: 6 pages, RevTeX, 3 Postscript figure