M. C. Lemos

A Hh-driven gene network controls specification, pattern and size of the Drosophila simple eyes

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.

Periodical forcing for the control of chaos in a chemical reaction.

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.

Monte Carlo simulation of a surface reaction model with local interaction

Influence of the interaction between nearest‐neighbor adatoms in a reaction of catalyzed oxidation of carbon monoxide has been studied by Monte Carlo simulation. The transition probabilities are chosen in the Arrhenius form, and the activation energy is divided into two additive terms, corresponding to the action of the substrate and to the interaction between nearest adatoms, respectively. When the interaction makes desorption easier or hinders adsorption the behavior is similar: Three steady state regimes or phases were observed; in the first phase, the surface is poisoned by oxygen; in the second phase there is a reactive steady state in which carbon dioxide is continuously produced, and in the third phase, the surface is poisoned by carbon monoxide. The transition from the O‐poisoned phase to the reactive phase is continuous, or second order, and the transition from the reaction to the CO‐poisoned phase is first order. The same occurs when the interaction is not considered. The interaction makes the s...

Influence of the interaction on oscillatory behavior in a surface reaction model

Bistability and oscillations of temperature and concentrations are observed in a kinetic model, based on the oxidation of carbon monoxide on a solid surface. The macroscopic kinetic equations, which govern the reaction, are obtained by applying a closure approximation of mean-field type. With the aim of studying how the interaction affects the oscillatory behavior in the reaction, we have explicitly considered the interaction between nearest-neighbor adsorbed species, CO–CO, CO–O, and O–O. Interactions favoring CO2 production are analyzed.

Far from equilibrium phase transitions in competitive adsorption: Dimension and closure approximation

Competitive adsorption of two species on a square lattice is considered, starting from a master equation. A doublet closure approximation is applied to obtain the kinetic equations; a Monte Carlo simulation is also performed. Unlike the results for a linear chain, multistability results, and thus there are far from equilibrium phase transitions. In this problem, the importance of the dimension of the system and the way the spatial correlations are treated in the approximation used is made clear.

Core regulatory network motif underlies the ocellar complex patterning in Drosophila melanogaster

Abstract During organogenesis, developmental programs governed by Gene Regulatory Networks (GRN) define the functionality, size and shape of the different constituents of living organisms. Robustness, thus, is an essential characteristic that GRNs need to fulfill in order to maintain viability and reproducibility in a species. In the present work we analyze the robustness of the patterning for the ocellar complex formation in Drosophila melanogaster fly. We have systematically pruned the GRN that drives the development of this visual system to obtain the minimum pathway able to satisfy this pattern. We found that the mechanism underlying the patterning obeys to the dynamics of a 3-nodes network motif with a double negative feedback loop fed by a morphogenetic gradient that triggers the inhibition in a French flag problem fashion. A Boolean modeling of the GRN confirms robustness in the patterning mechanism showing the same result for different network complexity levels. Interestingly, the network provides a steady state solution in the interocellar part of the patterning and an oscillatory regime in the ocelli. This theoretical result predicts that the ocellar pattern may underlie oscillatory dynamics in its genetic regulation.

A cellular automaton for a surface reaction: Stabilization from chaotic to periodical states

The chaotic behavior in a chemical reaction can be controlled by means of the method of external forcing. This technique, which is based on the resonance phenomenon, converts chaotic behavior into periodical one through application of a sinusoidal modulation. This paper analyzes the influence of a periodical perturbation on the environment temperature in a model of cellular automaton for the catalytic oxidation of CO. The model includes the variation of the catalyst temperature in order to analyze the oscillatory behavior of the reaction. The results of the simulations show chaotic and quasiperiodical behaviors. We point out that the periodical forcing can remove the chaotic dynamics through the stabilization of periodical solutions.

A cellular automaton for the modeling of oscillations in a surface reaction

The reaction of CO and O over a catalytic surface is studied with a cellular automata (CA) model. We extend the CA model proposed by Mai and von Niessen [Phys. Rev. A 44 R6165 (1991)] taking into account the variation of the temperature of the catalyst with the aim of analyzing the existence of oscillations in this reaction. The rate constants for different processes which govern the reaction are chosen in the Arrhenius form. Quasiperiodic, aperiodic, O-poisoned, and CO-poisoned regimes are observed depending on the temperature relaxation parameter. The results from the CA model presented are in agreement with several oscillatory behaviors which the catalyzed oxidation of CO exhibits.

Multistability of steady states in competitive adsorption of two species

Competitive adsorption of two species on a linear chain is considered. The adsorption–desorption probabilities are chosen in the Arrhenius form and it is assumed that the activation energies are partially due to interaction between nearest neighboring adatoms. Multistability can occur for an attractive interaction greater than a critical value, depending on the values of other parameters, and the least critical value corresponding to an interaction energy of ≂0.3 kcal mol−1 for room temperature. Up to seven steady states can result, three being stable. The relaxation times tend to infinitum at the critical points and the exponent α, where τJ→Jcritical∼(Jcritical−J)−α and J being a parameter gauging the strength of the interaction, has been determined for a number of cases. The analysis has been extended to two‐dimensional lattices and similar results have been obtained, although Jcritical is less than that for the linear chain. Next a dimerization reaction between adatoms has been considered jointly with ...

Competitive adsorption of two species: Doublet closure approximation and simulation

Starting from a master equation, competitive adsorption of two kinds of interacting particles on a linear chain is considered. The transition probabilities are chosen in the Arrhenius form, and the activation energy is split into two additive terms, corresponding, respectively, to the action of the substratum and to interactions between nearest neighbor adatoms. The kinetic equations are obtained by using a doublet closure approximation, writing triplet densities in terms of doublet and singlet densities. In this approximation, for the range of parameters being considered, only one stable steady state results, unlike in the case of the mean field approximation (where up to three stable steady states can exist). In view of the disagreement between the results of both approximations, a Monte Carlo simulation is carried out and results similar to those of doublet closure approximation are obtained. In neither of these two models interactions between nearest adatoms produce multistability. Thus, one may concl...