Motivated by recent experimental studies of Hg and Pb monolayers on Cu(001) we introduce a zero temperature model of a monolayer adsorbed on a square substrate. Lennard-Jones potentials are used to describe the interaction between pairs of adlayer-adlayer and adlayer-substrate atoms. We study a special case in which the monolayer atoms form a perfect square structure and the lattice constant, position and orientation with respect to the substrate can vary to minimize the energy. We introduce a rule based on the Farey tree construction to generate systematically the most energetically favored phases and use it to calculate the phase diagram in this model.
The standard analysis of reaction networks based on deterministic rate equations fails in confined geometries, commonly encountered in fields such as astrochemistry, thin film growth and cell biology. In these systems the small reactant population implies anomalous behavior of reaction rates, which can be accounted for only by following the full distribution of reactant numbers.
We present a computer simulation study of a disordered two-dimensional system of localized interacting electrons in thermal equilibrium. It is shown that the configuration of occupied sites within the Coulomb gap persistently changes at temperatures much less than the gap width. This is accompanied by large time-dependent fluctuations of the site energies. The observed thermal equilibration at low temperatures suggests a possible glass transition only at T = 0. We interpret the strong fluctuations in the occupation numbers and site energies in terms of the drift of the system between multiple energy minima, which implies mobility of electrons within the Coulomb gap down to very low temperatures. Insulating properties, such as hopping conduction, appear as a result of long equilibration times associated with glassy dynamics. This may shed new light on the relation between the metal-insulator transition and glassy behavior.
Competing endogenous RNAs (ceRNAs) were recently introduced as RNA transcripts that affect each other's expression level through competition for their microRNA (miRNA) coregulators. This stems from the bidirectional effects between miRNAs and their target RNAs, where a change in the expression level of one target affects the level of the miRNA regulator, which in turn affects the level of other targets. By the same logic, miRNAs that share targets compete over binding to their common targets and therefore also exhibit ceRNA-like behavior. Taken together, perturbation effects could propagate in the posttranscriptional regulatory network through a path of coregulated targets and miRNAs that share targets, suggesting the existence of distant ceRNAs. Here we study the prevalence of distant ceRNAs and their effect in cellular networks. Analyzing the network of miRNA-target interactions deciphered experimentally in HEK293 cells, we show that it is a dense, intertwined network, suggesting that many nodes can act as distant ceRNAs of one another. Indeed, using gene expression data from a perturbation experiment, we demonstrate small, yet statistically significant, changes in gene expression caused by distant ceRNAs in that network. We further characterize the magnitude of the propagated perturbation effect and the parameters affecting it by mathematical modeling and simulations. Our results show that the magnitude of the effect depends on the generation and degradation rates of involved miRNAs and targets, their interaction rates, the distance between the ceRNAs and the topology of the network. Although demonstrated for a miRNA-mRNA regulatory network, our results offer what to our knowledge is a new view on various posttranscriptional cellular networks, expanding the concept of ceRNAs and implying possible distant cross talk within the network, with consequences for the interpretation of indirect effects of gene perturbation.
Context. Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux, these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. Aims. We evaluate the formation rates of H2, HD and D2 molecules on dust grain surfaces and their abundances in the gas phase under interstellar conditions. Methods. We incorporate the moment equations into the Meudon PDR code and compare the results with those obtained from the rate equations. Results. We find that within the experimental constraints on the energy barriers for di usion and desorption and for the density of adsorption sites on the grain surface, H2, HD and D2 molecules can be formed e ciently on dust grains. Conclusions. Under a broad range of conditions, the moment equation results coincide with those obtained from the rate equations. However, in a range of relatively high grain temperatures, there are significant deviations. In this range, the rate equations fail while the moment equations provide accurate results. The incorporation of the moment equations into the PDR code can be extended to other reactions taking place on grain surfaces.
