During development, extracellular signaling molecules interact with intracellular gene networks to control the specification, pattern and size of organs. One such signaling molecule is Hedgehog (Hh). Hh is known to act as a morphogen, instructing different fates depending on the distance to its source. However, how Hh, when signaling across a cell field, impacts organ-specific transcriptional networks is still poorly understood. Here, we investigate this issue during the development of the Drosophila ocellar complex. The development of this sensory structure, which is composed of three simple eyes (or ocelli) located at the vertices of a triangular patch of cuticle on the dorsal head, depends on Hh signaling and on the definition of three domains: two areas of eya and so expression – the prospective anterior and posterior ocelli – and the intervening interocellar domain. Our results highlight the role of the homeodomain transcription factor engrailed (en) both as a target and as a transcriptional repressor of hh signaling in the prospective interocellar region. Furthermore, we identify a requirement for the Notch pathway in the establishment of en maintenance in a Hh-independent manner. Therefore, hh signals transiently during the specification of the interocellar domain, with en being required here for hh signaling attenuation. Computational analysis further suggests that this network design confers robustness to signaling noise and constrains phenotypic variation. In summary, using genetics and modeling we have expanded the ocellar gene network to explain how the interaction between the Hh gradient and this gene network results in the generation of stable mutually exclusive gene expression domains. In addition, we discuss some general implications our model may have in some Hh-driven gene networks.

By employing an extension of the Glauber–Ising model, the kinetics of the desorption of paired adatoms from a linear chain is studied. Three competitive mechanisms for changing a state of the system are allowed, namely desorption from or readsorption onto the chain or migration of the adatoms from site to site on the chain. The transition probabilities depend on an external field, on the interaction between nearest neighbors, and on three proper rate constants characterizing desorption, readsorption, and migration processes. An infinite set of coupled kinetic equations is obtained from the master equation. In order to compute the adsorption degree ϑ and the fraction of adjacent adatom pairs η, a ’’closure’’ approximation is taken. The steady‐state solution is in agreement with the exact result of the equilibrium statistical mechanics. We find that relaxation far from equilibrium is, in general, not describable by a single exponential. The relaxation is slower when mobility does not exist than when adatoms are mobile, though the system behavior is similar in both cases. Equilibrium state is reached most quickly when lateral interaction does not exist and the final adsorption degree is 0.5. Attractive lateral interaction yields relaxation slower than when interaction is null, while repulsive interaction favors an initial relaxation very quickly, and the system reaches an adsorption degree lower than the final one, passes through a minimum and tends to equilibrium state slowly.

Control of the chaotic behavior of a chemical system can be achieved perturbing periodically some control parameters of the system. This procedure based on external forcing, which is based on the phenomenon of resonance, can change a chaotic behavior into a periodical one by means of the application of a sinusoidal perturbation. In this paper, the influence of a periodical modulation added to the parameter controlling the oxygen adsorption rate in a cellular automaton (CA) model studying CO oxidation is analyzed. This CA model considers the oxidation reaction of CO on a catalytic surface, taking into account the catalyst temperature variation in order to analyze the reaction time oscillatory behavior. Simulations of the CA model exhibit chaotic and quasiperiodical behaviors, and it can be shown that the periodical forcing strategy can suppress the chaotic dynamics by means of the stabilization of periodical solutions.

A new experimental system to measure the equivalent thermal conductivity of a liquid with regard to the Bénard–Rayleigh problem was constructed. The liquid is enclosed within walls of polymethylmethacrylate between two copper plates in which there are thermocouples to measure the difference in temperature between the lower and upper surfaces of the layer of liquid. Heat flux is measured by means of a linear heat fluxmeter consisting of 204 thermocouples in series. The fluxmeter was calibrated and the linear relationship that exists between the heat flux and the emf generated was verified. The thermal conductivity of the polymethylmethacrylate employed was measured and measurements of the equivalent conductivity in cylindrical boundaries of two silicone oils were made. The critical value of the temperature difference and the contribution of the convective process to the transmission of heat were determined.