Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types

Alteration of crystalline zircon solid solutions: a case study on zircon from an alkaline pegmatite from Zomba-Malosa, Malawi

A natural, altered zircon crystal from an alkaline pegmatite from the Zomba-Malosa Complex of the Chilwa Alkaline Province in Malawi has been studied by a wide range of analytical techniques to understand the alteration process. The investigated zircon shows two texturally and chemically different domains. Whereas the central parts of the grain (zircon I) appear homogeneous in backscattered electron images and are characterised by high concentrations of trace elements, particularly Th, U, and Y, the outer regions (zircon II) contain significantly less trace elements, numerous pores, and inclusions of thorite, ytttrialite, and fergusonite. Zircon II contains very low or undetectable concentrations of non-formula elements such as Ca, Al, and Fe, which are commonly observed in high concentrations in altered radiation-damaged zircon. U-Pb dating of both zircon domains by LA-ICPMS and SHRIMP yielded statistically indistinguishable U-Pb weighted average ages of 119.3 2.1 (2r) and 118 1.2 (2r) Ma, respectively, demonstrating that the zircon had not accumulated a significant amount of self-irradiation damage at the time of the alteration event.Electron microprobe dating of thorite inclusions in zircon II yielded a Th-U-total Pb model age of 122 5 (2r) Ma, supporting the age relationship between both zircon domains. The hydrothermal solution responsible for the alteration of the investigated zircon was alkaline and rich in CO3 2-, as suggested by the occurrence of REE carbonates and CO2-bearing fluid inclusions. The alteration of the crystalline, trace element-rich zircon is explained by an interface-coupled dissolution-reprecipitation mechanism. During such a process, the congruent dissolution of the trace element-rich parent zircon I was spatially and temporally coupled to the precipitation of the trace element-poor zircon II at an inward moving dissolution-precipitation front. The driving force for such a process was merely the difference between the solubility of the trace element-rich and -poor zircon in the hydrothermal solution. The replacement process and the occurrence of mineral inclusions and porosity in the product zircon II is explained by the thermodynamics of solid solution-aqueous solution systems