The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

<i>P. berghei</i> telomerase subunit TERT is essential for parasite survival

Telomeres define the ends of chromosomes protecting eukaryotic cells from chromosome instability and eventual cell death. The complex regulation of telomeres involves various proteins including telomerase, which is a specialized ribonucleoprotein responsible for telomere maintenance. Telomeres of chromosomes of malaria parasites are kept at a constant length during blood stage proliferation. The 7-bp telomere repeat sequence is universal across different Plasmodium species (GGGTTT/CA), though the average telomere length varies. The catalytic subunit of telomerase, telomerase reverse transcriptase (TERT), is present in all sequenced Plasmodium species and is approximately three times larger than other eukaryotic TERTs. The Plasmodium RNA component of TERT has recently been identified in silico. A strategy to delete the gene encoding TERT via double cross-over (DXO) homologous recombination was undertaken to study the telomerase function in P. berghei. Expression of both TERT and the RNA component (TR) in P. berghei blood stages was analysed by Western blotting and Northern analysis. Average telomere length was measured in several Plasmodium species using Telomere Restriction Fragment (TRF) analysis. TERT and TR were detected in blood stages and an average telomere length of ~950 bp established. Deletion of the tert gene was performed using standard transfection methodologies and we show the presence of tert− mutants in the transfected parasite populations. Cloning of tert- mutants has been attempted multiple times without success. Thorough analysis of the transfected parasite populations and the parasite obtained from extensive parasite cloning from these populations provide evidence for a so called delayed death phenotype as observed in different organisms lacking TERT. The findings indicate that TERT is essential for P. berghei cell survival. The study extends our current knowledge on telomere biology in malaria parasites and validates further investigations to identify telomerase inhibitors to induce parasite cell death

A simple model of a vesicle drop in a confined geometry

We present the exact solution of a two-dimensional directed walk model of a drop, or half vesicle, confined between two walls, and attached to one wall. This model is also a generalisation of a polymer model of steric stabilisation recently investigated. We explore the competition between a sticky potential on the two walls and the effect of a pressure-like term in the system. We show that a negative pressure ensures the drop/polymer is unaffected by confinement when the walls are a macroscopic distance apart

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Invloed van luchtvochtigheid op het scheuren van radijs

Referaat Veel gescheurde radijs bij hoge RV tijdens knolvorming In de winter geeft een hoge luchtvochtigheid tijdens de knolvormingsfase duidelijk meer gescheurde radijsknollen. Dit gebeurt met name als de luchtvochtigheid in de eerste teeltfase juist laag is geweest. Dit bleek uit onderzoek bij Wageningen UR Glastuinbouw in Bleiswijk. Bij oogst in januari scheuren radijsknollen veel gemakkelijker dan bij oogst in februari of maart. Vooral bij een knoldiameter van circa 8 mm zijn radijsjes gevoelig voor een hoge luchtvochtigheid. Om in de wintermaanden gescheurde radijs te voorkomen is het dus gewenst dat telers proberen om de luchtvochtigheid tijdens de knolvormingsfase te verlagen door meer te ventileren en/of wat te verwarmen. Abstract High humidity causes more splitting of radish tubers In winter season, high humidity in the greenhouse causes more cracking or splitting of the tubers of radish. This happens especially when humidity in the first growing phase is low. This became clear in a research by Wageningen UR Greenhouse Horticulture in Bleiswijk. Harvesting in January gives far more splitting of radish tubers than harvesting in February or March. Especially tubers with a diameter around 8 mm seems susceptible for splitting at circumstances with a high humidity. Growers are being advised to try to decrease the humidity in glasshouses by ventilating and or heating

Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl

Forcing Adsorption of a Tethered Polymer by Pulling

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled