Planar lattice gases with nearest-neighbour exclusion

We discuss the hard-hexagon and hard-square problems, as well as the corresponding problem on the honeycomb lattice. The case when the activity is unity is of interest to combinatorialists, being the problem of counting binary matrices with no two adjacent 1's. For this case we use the powerful corner transfer matrix method to numerically evaluate the partition function per site, density and some near-neighbour correlations to high accuracy. In particular for the square lattice we obtain the partition function per site to 43 decimal places.Comment: 16 pages, 2 built-in Latex figures, 4 table

Identification of a Novel Binding Partner of Phospholipase Cβ1: Translin-Associated Factor X

Mammalian phospholipase Cβ1 (PLCβ1) is activated by the ubiquitous Gαq family of G proteins on the surface of the inner leaflet of plasma membrane where it catalyzes the hydrolysis of phosphatidylinositol 4,5 bisphosphate. In general, PLCβ1 is mainly localized on the cytosolic plasma membrane surface, although a substantial fraction is also found in the cytosol and, under some conditions, in the nucleus. The factors that localize PLCβ1in these other compartments are unknown. Here, we identified a novel binding partner, translin-associated factor X (TRAX). TRAX is a cytosolic protein that can transit into the nucleus. In purified form, PLCβ1 binds strongly to TRAX with an affinity that is only ten-fold weaker than its affinity for its functional partner, Gαq. In solution, TRAX has little effect on the membrane association or the catalytic activity of PLCβ1. However, TRAX directly competes with Gαq for PLCβ1 binding, and excess TRAX reverses Gαq activation of PLCβ1. In C6 glia cells, endogenous PLCβ1 and TRAX colocalize in the cytosol and the nucleus, but not on the plasma membrane where TRAX is absent. In Neuro2A cells expressing enhanced yellow and cyano fluorescent proteins (i.e., eYFP- PLCβ1 and eCFP-TRAX), Förster resonance energy transfer (FRET) is observed mostly in the cytosol and a small amount is seen in the nucleus. FRET does not occur at the plasma membrane where TRAX is not found. Our studies show that TRAX, localized in the cytosol and nucleus, competes with plasma-membrane bound Gαq for PLCβ1 binding thus stabilizing PLCβ1 in other cellular compartments

Lattice Glass Models

Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition which is very similar to that observed in other off-lattice systems and which does not depend on a specific dynamical rule. Whereas their analytic solution within the Bethe approximation shows that they do have a discontinuous glass transition compatible with the numerical observations.Comment: 4 pages, 2 figures; minor change

First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion

A lattice gas with infinite repulsion between particles separated by $\leq 1$ lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive favoring movement along one axis of the square lattice. The equilibrium (zero drive) transition to a phase with sublattice ordering, known to be continuous, shifts to lower density, and becomes discontinuous for large bias. In the ordered nonequilibrium steady state, both the particle and order-parameter densities are nonuniform, with a large fraction of the particles occupying a jammed strip oriented along the drive. The relaxation exhibits features reminiscent of models of granular and glassy materials.Comment: 8 pages, 5 figures; results due to bad random number generator corrected; significantly revised conclusion

Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions

To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only density functional theory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three-dimensional) with that of squares (two-dimensional) and rods (one-dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered cubic, and body-centered cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.Comment: 13 pages, 13 figures; needs revtex

The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovasz local lemma in probabilistic combinatorics. We show that the conclusion of the Lovasz local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovasz local lemma -- which provides a sufficient condition for this to occur -- corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer and explicitly by Dobrushin. We also present some refinements and extensions of both arguments, including a generalization of the Lovasz local lemma that allows for "soft" dependencies. In addition, we prove some general properties of the partition function of a repulsive lattice gas, most of which are consequences of the alternating-sign property for the Mayer coefficients. We conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity. To be published in J. Stat. Phy

Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two $A$ particles land onto two vacant sites at the extremities of the catalytic segment, or when any $A$ particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another $A$ particle. Non-catalytic segments are inert with respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.Comment: AMSTeX, 27 pages + 4 figure

Controlled assembly of SNAP-PNA-fluorophore systems on DNA templates to produce fluorescence resonance energy transfer

The SNAP protein is a widely used self-labeling tag that can be used for tracking protein localization and trafficking in living systems. A model system providing controlled alignment of SNAP-tag units can provide a new way to study clustering of fusion proteins. In this work, fluorescent SNAP-PNA conjugates were controllably assembled on DNA frameworks forming dimers, trimers, and tetramers. Modification of peptide nucleic acid (PNA) with the O6-benzyl guanine (BG) group allowed the generation of site-selective covalent links between PNA and the SNAP protein. The modified BG-PNAs were labeled with fluorescent Atto dyes and subsequently chemo-selectively conjugated to SNAP protein. Efficient assembly into dimer and oligomer forms was verified via size exclusion chromatography (SEC), electrophoresis (SDS-PAGE), and fluorescence spectroscopy. DNA directed assembly of homo- and hetero-dimers of SNAP-PNA constructs induced homo- and hetero-FRET, respectively. Longer DNA scaffolds controllably aligned similar fluorescent SNAP-PNA constructs into higher oligomers exhibiting homo-FRET. The combined SEC and homo-FRET studies indicated the 1:1 and saturated assemblies of SNAP-PNA-fluorophore:DNA formed preferentially in this system. This suggested a kinetic/stoichiometric model of assembly rather than binomially distributed products. These BG-PNA-fluorophore building blocks allow facile introduction of fluorophores and/or assembly directing moieties onto any protein containing SNAP. Template directed assembly of PNA modified SNAP proteins may be used to investigate clustering behavior both with and without fluorescent labels which may find use in the study of assembly processes in cells

Activation of H+-ATPase of the Plasma Membrane of Saccharomyces cerevisiae by Glucose: The Role of Sphingolipid and Lateral Enzyme Mobility

Activation of the plasma membrane H+-ATPase of the yeast Saccharomyces cerevisiae by glucose is a complex process that has not yet been completely elucidated. This study aimed to shed light on the role of lipids and the lateral mobility of the enzyme complex during its activation by glucose. The significance of H+-ATPase oligomerization for the activation of H+-ATPase by glucose was shown using the strains lcb1-100 and erg6, with the disturbed synthesis of sphyngolipid and ergosterol, respectively. Experiments with GFP-fused H+-ATPase showed a decrease in fluorescence anisotropy during the course of glucose activation, suggesting structural reorganization of the molecular domains. An immunogold assay showed that the incubation with glucose results in the spatial redistribution of ATPase complexes in the plasma membrane. The data suggest that (1) to be activated by glucose, H+-ATPase is supposed to be in an oligomeric state, and (2) glucose activation is accompanied by the spatial movements of H+-ATPase clusters in the PM