Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure

Anomalous Dynamics of Translocation

We study the dynamics of the passage of a polymer through a membrane pore (translocation), focusing on the scaling properties with the number of monomers $N$. The natural coordinate for translocation is the number of monomers on one side of the hole at a given time. Commonly used models which assume Brownian dynamics for this variable predict a mean (unforced) passage time $\tau$ that scales as $N^2$, even in the presence of an entropic barrier. However, the time it takes for a free polymer to diffuse a distance of the order of its radius by Rouse dynamics scales with an exponent larger than 2, and this should provide a lower bound to the translocation time. To resolve this discrepancy, we perform numerical simulations with Rouse dynamics for both phantom (in space dimensions $d=1$ and 2), and self-avoiding (in $d=2$) chains. The results indicate that for large $N$, translocation times scale in the same manner as diffusion times, but with a larger prefactor that depends on the size of the hole. Such scaling implies anomalous dynamics for the translocation process. In particular, the fluctuations in the monomer number at the hole are predicted to be non-diffusive at short times, while the average pulling velocity of the polymer in the presence of a chemical potential difference is predicted to depend on $N$.Comment: 9 pages, 9 figures. Submitted to Physical Review

Entropic force of polymers on a cone tip

We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by F=A kT/h. The universal amplitude A can be related to (geometry dependent) correlation exponents of long polymers. We compute A for phantom polymers, and for self-avoiding (including star) polymers by epsilon-expansion, as well as by numerical simulations in 3 dimensions

Evolved Stereoselective Hydrolases for Broad-Spectrum G-Type Nerve Agent Detoxification

SummaryA preferred strategy for preventing nerve agents intoxication is catalytic scavenging by enzymes that hydrolyze them before they reach their targets. Using directed evolution, we simultaneously enhanced the activity of a previously described serum paraoxonase 1 (PON1) variant for hydrolysis of the toxic SP isomers of the most threatening G-type nerve agents. The evolved variants show ≤340-fold increased rates and catalytic efficiencies of 0.2-5 × 107 M−1 min−1. Our selection for prevention of acetylcholinesterase inhibition also resulted in the complete reversion of PON1's stereospecificity, from an enantiomeric ratio (E) < 6.3 × 10−4 in favor of the RP isomer of a cyclosarin analog in wild-type PON1, to E > 2,500 for the SP isomer in an evolved variant. Given their ability to hydrolyze G-agents, these evolved variants may serve as broad-range G-agent prophylactics