Flow-distributed spikes for Schnakenberg kinetics

This is the post-print version of the final published paper. The final publication is available at link.springer.com by following the link below. Copyright @ 2011 Springer-Verlag.We study a system of reaction–diffusion–convection equations which combine a reaction–diffusion system with Schnakenberg kinetics and the convective flow equations. It serves as a simple model for flow-distributed pattern formation. We show how the choice of boundary conditions and the size of the flow influence the positions of the emerging spiky patterns and give conditions when they are shifted to the right or to the left. Further, we analyze the shape and prove the stability of the spikes. This paper is the first providing a rigorous analysis of spiky patterns for reaction-diffusion systems coupled with convective flow. The importance of these results for biological applications, in particular the formation of left–right asymmetry in the mouse, is indicated.RGC of Hong Kon

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Overexpression of the Mitochondrial T3 Receptor p43 Induces a Shift in Skeletal Muscle Fiber Types

In previous studies, we have characterized a new hormonal pathway involving a mitochondrial T3 receptor (p43) acting as a mitochondrial transcription factor and consequently stimulating mitochondrial activity and mitochondrial biogenesis. We have established the involvement of this T3 pathway in the regulation of in vitro myoblast differentiation.We have generated mice overexpressing p43 under control of the human α-skeletal actin promoter. In agreement with the previous characterization of this promoter, northern-blot and western-blot experiments confirmed that after birth p43 was specifically overexpressed in skeletal muscle. As expected from in vitro studies, in 2-month old mice, p43 overexpression increased mitochondrial genes expression and mitochondrial biogenesis as attested by the increase of mitochondrial mass and mt-DNA copy number. In addition, transgenic mice had a body temperature 0.8°C higher than control ones and displayed lower plasma triiodothyronine levels. Skeletal muscles of transgenic mice were redder than wild-type animals suggesting an increased oxidative metabolism. In line with this observation, in gastrocnemius, we recorded a strong increase in cytochrome oxidase activity and in mitochondrial respiration. Moreover, we observed that p43 drives the formation of oxidative fibers: in soleus muscle, where MyHC IIa fibers were partly replaced by type I fibers; in gastrocnemius muscle, we found an increase in MyHC IIa and IIx expression associated with a reduction in the number of glycolytic fibers type IIb. In addition, we found that PGC-1α and PPARδ, two major regulators of muscle phenotype were up regulated in p43 transgenic mice suggesting that these proteins could be downstream targets of mitochondrial activity. These data indicate that the direct mitochondrial T3 pathway is deeply involved in the acquisition of contractile and metabolic features of muscle fibers in particular by regulating PGC-1α and PPARδ

Intracellular Trafficking Considerations in the Development of Natural Ligand-Drug Molecular Conjugates for Cancer

Overexpressed receptors, characteristic of many cancers, have been targeted by various researchers to achieve a more specific treatment for cancer. A common approach is to use the natural ligand for the overexpressed receptor as a cancer-targeting agent which can deliver a chemically or genetically conjugated toxic molecule. However, it has been found that the therapeutic efficacy of such ligand-drug molecular conjugates can be limited, since they naturally follow the intracellular trafficking pathways of the endogenous ligands. Therefore, a thorough understanding of the intracellular trafficking properties of these ligands can lead to novel design criteria for engineering ligands to be more effective drug carriers. This review presents a few commonly used ligand/receptor systems where intracellular trafficking considerations can potentially improve the therapeutic efficacy of the ligand-drug molecular conjugates

First measurement of Bose-Einstein correlations in proton-proton collisions at √s=0.9 and 2.36 TeV at the LHC

Bose-Einstein correlations have been measured using samples of proton-proton collisions at 0.9 and 2.36 TeV center-of-mass energies, recorded by the CMS experiment at the CERN Large Hadron Collider. The signal is observed in the form of an enhancement of pairs of same-sign charged particles with small relative four-momentum. The size of the correlated particle emission region is seen to increase significantly with the particle multiplicity of the event