From simple to complex oscillatory behavior in metabolic and genetic control networks

We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g., the coexistence between a stable steady state and a stable limit cycle (hard excitation), or the coexistence between two simultaneously stable limit cycles (birhythmicity). We discuss mechanisms responsible for the transition from simple to complex oscillatory behavior by means of a number of models serving as selected examples. The models were originally proposed to account for simple periodic oscillations observed experimentally at the cellular level in a variety of biological systems. In a second stage, these models were modified to allow for complex oscillatory phenomena such as bursting, birhythmicity, or chaos. We consider successively (1) models based on enzyme regulation, proposed for glycolytic oscillations and for the control of successive phases of the cell cycle, respectively; (2) a model for intracellular Ca(2+) oscillations based on transport regulation; (3) a model for oscillations of cyclic AMP based on receptor desensitization in Dictyostelium cells; and (4) a model based on genetic regulation for circadian rhythms in Drosophila. Two main classes of mechanism leading from simple to complex oscillatory behavior are identified, namely (i) the interplay between two endogenous oscillatory mechanisms, which can take multiple forms, overt or more subtle, depending on whether the two oscillators each involve their own regulatory feedback loop or share a common feedback loop while differing by some related process, and (ii) self-modulation of the oscillator through feedback from the system's output on one of the parameters controlling oscillatory behavior. However, the latter mechanism may also be viewed as involving the interplay between two feedback processes, each of which might be capable of producing oscillations. Although our discussion primarily focuses on the case of autonomous oscillatory behavior, we also consider the case of nonautonomous complex oscillations in a model for circadian oscillations subjected to periodic forcing by a light-dark cycle and show that the occurrence of entrainment versus chaos in these conditions markedly depends on the wave form of periodic forcing. (c) 2001 American Institute of Physics.     

Photochemical behavior of a new long-chain UV absorber derived from 4-tert-butyl-4'-methoxydibenzoylmethane

A new UV filter, the 1-(4-tert-butylphenyl)-2-decanyl-3-(4'-methoxyphenyl)-propane-1,3-dione, called C10-DBM, was prepared by grafting a 10-carbon aliphatic chain to the alpha-carbonyl position of 4-tert-butyl-4'-methoxydibenzoylmethane (BM-DBM), a well-known and often used UV filter. The UV-A absorption efficiency of organic solutions containing the new filter was tested and compared with identical solutions containing BM-DBM with or without irradiation (xenon lamp). The originality of this new filter is that its UV-A absorbance appeared during irradiation of the molecule. Although the molar absorption coefficient of C10-DBM in the UV-A domain was lower than that of BM-DBM, the solutions absorption exhibited a much more photostable behavior under irradiation. In this study, we first demonstrated that C10-DBM was a precursor of BM-DBM (enol isomer) by means of high-performance liquid chromatography followed by mass spectrometry. Indeed, we showed that the UV-A absorption of C10-DBM solutions appearing during the irradiation of the molecule was due to a Norrish-II reaction (beta-cleavage), which induced the release of the BM-DBM enol form and 1-decene. Then, we established a kinetic model for the photochemistry of C10-DBM and fitted the variation of UV absorption spectra to confirm the proposed mechanism.     

Influence of physical parameters and lubricants on the compaction properties of granulated and non-granulated cross-linked high amylose starch

Cross-linked high amylose starch (CLA) is a pharmaceutical excipient used in direct compression for the preparation of controlled release tablets and implants. In this work the compression properties of CLA in bulk and granulated forms (without binder) were evaluated for the first time. Tablets were prepared on an instrumented single punch machine. The flow properties and the compression characteristics (compressibility, densification behavior, work of compression) of the materials as well as the mechanical strength of the finished compacts (compactibility) were systematically examined. Wet granulation was found to improve the flowability and the compressibility of CLA but concomitantly reduced its compactibility. It was demonstrated that CLA was a plastically deforming material with a plasticity index and a yield pressure value comparable to those of pregelatinized starch. The compactibility of granulated CLA was independent of particle size in the range of 75 to 500 microm, but slightly decreased when the percentage of the fine particles (<75 microm) in the bulk powder was increased. Water and colloidal silicone dioxide facilitated the consolidation of CLA, while magnesium stearate had an opposite effect on the tablet crushing force.     

Sums of unitarily equivalent positive operators

Some simple conditions on positive operators A and K ensure that A can be written as a series in the unitary orbit of K.     

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For smooth initial condition, the rescaled solution of such an equation, once averaged over the randomness, is shown to converge polynomially fast to the solution of the homogenized equation, with an explicit exponent depending only on the dimension. Polynomial rate of homogenization for the averaged heat kernel, with an explicit exponent, is then derived. Similar results for elliptic equations are also presented.     

Supramolecular Assemblies of Phosphorylated Cavitands

The recent results in the chemistry of cavitands have proved that they are very efficient molecular receptors and potential precursors of molecular devices. In this context, we have investigated the synthesis and binding properties of phosphorylated cavitands. The stereoselective synthesis and the structural studies of the new compounds showed that these bowl-shaped molecules possess a well defined aromatic cavity surrounded by four phosphoryl groups (P=O or P=S). They are very efficient ligands for metal and organic cations. They are able to encapsulate cationic species by cooperative effect of the preorganized aromatic cavity and the four phosphorylated groups. Moreover, the upper and lower rim functionalitics can lead to the formation of molecular capsules and supramolecular assemblies whose properties and structures have been investigated by X-ray diffraction and NMR studies in solution.     

Exploring the uranyl organometallic chemistry: from single to double uranium-carbon bonds

Uranyl organometallic complexes featuring uranium(VI)-carbon single and double bonds have been obtained from uranyl UO(2)X(2) precursors by avoiding reduction of the metal center. X-ray diffraction and density functional theory analyses of these complexes showed that the U-C and U=C bonds are polarized toward the nucleophilic carbon.     

Effect of laser energy, substrate film thickness and bioink viscosity on viability of endothelial cells printed by Laser-Assisted Bioprinting

Biofabrication of three dimensional tissues by Laser-Assisted Bioprinting (LAB) implies to develop specific strategies for assembling the extracellular matrix (ECM) and cells. Possible strategies consist in (i) printing cells onto or in the depth of ECM layer and/or (ii) printing bioinks containing both cells and ECM-like printable biomaterial. The aim of this article was to evaluate combinatorial effects of laser pulse energy, ECM thickness and viscosity of the bioink on cell viability. A LAB workstation was used to print Ea.hy926 endothelial cells onto a quartz substrate covered with a film of ECM mimicking Matrigel™. Hence, effect of laser energy, Matrigel™ film thickness and bioink viscosity was addressed for different experimental conditions (8-24 μJ, 20-100 μm and 40-110 mPa s, respectively). Cell viability was assessed by live/dead assay performed 24 h post-printing. Results show that increasing the laser energy tends to augment the cell mortality while increasing the thickness of the Matrigel™ film and the viscosity of the bioink support cell viability. Hence, critical printing parameters influencing high cell viability have been related to the cell landing conditions and more specifically to the intensity of the cell impacts occurring at the air-ECM interface and at the ECM-glass interface.