Nonequilibrium patterns and shape fluctuations in reactive membranes

A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and curvature is proposed. When the two components are not miscible, linear stability analysis predicts, and numerical simulations show, the formation of stationary nonequilibrium composition/curvature patterns whose typical size is determined by the reactive process. For miscible components, a linearization of the dynamic equations is performed in order to evaluate the correlation function for shape fluctuations from which the behavior of these systems in micropipet aspiration experiments can be predicted.

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Multilevel control of arabidopsis 3-hydroxy-3-methylglutaryl coenzyme A reductase by protein phosphatase 2A

Plants synthesize a myriad of isoprenoid products that are required both for essential constitutive processes and for adaptive responses to the environment. The enzyme 3-hydroxy-3-methylglutaryl-CoA reductase (HMGR) catalyzes a key regulatory step of the mevalonate pathway for isoprenoid biosynthesis and is modulated by many endogenous and external stimuli. In spite of that, no protein factor interacting with and regulating plant HMGR in vivo has been described so far. Here, we report the identification of two B99 regulatory subunits of protein phosphatase 2A (PP2A), designated B99a and B99b, that interact with HMGR1S and HMGR1L, the major isoforms of Arabidopsis thaliana HMGR. B99a and B99b are Ca2+ binding proteins of the EF-hand type. We show that HMGR transcript, protein, and activity levels are modulated by PP2A in Arabidopsis. When seedlings are transferred to salt-containing medium, B99a and PP2A mediate the decrease and subsequent increase of HMGR activity, which results from a steady rise of HMGR1-encoding transcript levels and an initial sharper reduction of HMGR protein level. In unchallenged plants, PP2A is a posttranslational negative regulator of HMGR activity with the participation of B99b. Our data indicate that PP2A exerts multilevel control on HMGR through the fivemember B99 protein family during normal development and in response to a variety of stress conditions.

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas¿low-density-liquid (LDL) critical point, and the other in a gas¿high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

Alternation and Cooperation in a Two-party System: Implications for Resource-Based Developing Economies

This paper studies cooperation in a political system dominated by two opportunistic parties competing in a resource-based economy. Since a binding agreement as an external solution might be difficult to enforce due to the close association between the incumbent party and the government, the paper explores the extent to which co-operation between political parties that alternate in office can rely on self-enforcing strategies to provide an internal solution. We show that, for appropriate values of the probability of re-election and the discount factor cooperation in maintaining the value of a state variable is possible, but fragile. Another result is that, in such political framework, debt decisions contain an externality element linked to electoral incentives that creates a bias towards excessive borrowing.

Extremal principle of entropy production in the climate system

Paltridge found reasonable values for the most significant climatic variables through maximizing the material transport part of entropy production by using a simple box model. Here, we analyse Paltridge's box model to obtain the energy and the entropy balance equations separately. Derived expressions for global entropy production, which is a function of the radiation field, and even its material transport component, are shown to be different from those used by Paltridge. Plausible climatic states are found at extrema of these parameters. Feasible results are also obtained by minimizing the radiation part of entropy production, in agreement with one of Planck's results, Finally, globally averaged values of the entropy flux of radiation and material entropy production are obtained for two dynamical extreme cases: an earth with uniform temperature, and an earth in radiative equilibrium at each latitudinal point

Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

Segregation of regulatory polymorphisms with effects on the gluteus medius transcriptome in a purebred pig population

Background: The main goal of the present study was to analyse the genetic architecture of mRNA expression in muscle, a tissue with an outmost economic importance for pig breeders. Previous studies have used F2 crosses to detect porcine expression QTL (eQTL), so they contributed with data that mostly represents the between-breed component of eQTL variation. Herewith, we have analysed eQTL segregation in an outbred Duroc population using two groups of animals with divergent fatness profiles. This approach is particularly suitable to analyse the within-breed component of eQTL variation, with a special emphasis on loci involved in lipid metabolism. Methodology/Principal Findings: GeneChip Porcine Genome arrays (Affymetrix) were used to determine the mRNA expression levels of gluteus medius samples from 105 Duroc barrows. A whole-genome eQTL scan was carried out with a panel of 116 microsatellites. Results allowed us to detect 613 genome-wide significant eQTL unevenly distributed across the pig genome. A clear predominance of trans- over cis-eQTL, was observed. Moreover, 11 trans-regulatory hotspots affecting the expression levels of four to 16 genes were identified. A Gene Ontology study showed that regulatory polymorphisms affected the expression of muscle development and lipid metabolism genes. A number of positional concordances between eQTL and lipid trait QTL were also found, whereas limited evidence of a linear relationship between muscle fat deposition and mRNA levels of eQTL regulated genes was obtained. Conclusions/Significance: Our data provide substantial evidence that there is a remarkable amount of within-breed genetic variation affecting muscle mRNA expression. Most of this variation acts in trans and influences biological processes related with muscle development, lipid deposition and energy balance. The identification of the underlying causal mutations and the ascertainment of their effects on phenotypes would allow gaining a fundamental perspective about how complex traits are built at the molecular level.