Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, $p_c \sim N^{-1}$, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as $\sim N$, to a smooth state with $\sim N^2$. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which $\sim N^{3/2}$. For $p>>p_c$ we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.Comment: 9 pages, 8 figure

Electrostatic Interactions of Asymmetrically Charged Membranes

We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged and planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and Pincus in which the important length scales are the inter-plate separation and the Gouy-Chapman length. In the regime of low salt and high surface charges we predict - for any ratio of the charges on the surfaces - that the attractive pressure is long-ranged as a function of the spacing. The attractive pressure is related to the decrease in counter-ion concentration as the inter-plate distance is decreased. Our theory predicts several scaling regimes with different scaling expressions for the pressure as function of salinity and surface charge densities. The pressure predictions can be related to surface force experiments of oppositely charged surfaces that are prepared by coating one of the mica surfaces with an oppositely charged polyelectrolyte

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $\rho<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.Comment: 7 page

Modelling study of dimerization in mammalian defensins

BACKGROUND: Defensins are antimicrobial peptides of innate immunity functioning by non-specific binding to anionic phospholipids in bacterial membranes. Their cationicity, amphipathicity and ability to oligomerize are considered key factors for their action. Based on structural information on human β-defensin 2, we examine homologous defensins from various mammalian species for conserved functional physico-chemical characteristics. RESULTS: Based on homology greater than 40%, structural models of 8 homologs of HBD-2 were constructed. A conserved pattern of electrostatics and dynamics was observed across 6 of the examined defensins; models backed by energetics suggest that the defensins in these 6 organisms are characterized by dimerization-linked enhanced functional potentials. In contrast, dimerization is not energetically favoured in the sheep, goat and mouse defensins, suggesting that they function efficiently as monomers. CONCLUSION: β-defensin 2 from some mammals may work as monomers while those in others, including humans, work as oligomers. This could potentially be used to design human defensins that may be effective at lower concentrations and hence have therapeutic benefits