Metabolic and structural rearrangement during dark-induced autophagy in soybean (Glycine max L.) nodules: An electron microscopy and P-31 and C-13 nuclear magnetic resonance study

The effects of dark-induced stress on the evolution of the soluble metabolites present in senescent soybean (Glycine max L.) nodules were analysed in vitro using C-13- and P-31-NMR spectroscopy. Sucrose and trehalose were the predominant soluble storage carbons. During dark-induced stress, a decline in sugars and some key glycolytic metabolites was observed. Whereas 84% of the sucrose disappeared, only one-half of the trehalose was utilised. This decline coincides with the depletion of Gln, Asn, Ala and with an accumulation of ureides, which reflect a huge reduction of the N-2 fixation. Concomitantly, phosphodiesters and compounds like P-choline, a good marker of membrane phospholipids hydrolysis and cell autophagy, accumulated in the nodules. An autophagic process was confirmed by the decrease in cell fatty acid content. In addition, a slight increase in unsaturated fatty acids (oleic and linoleic acids) was observed, probably as a response to peroxidation reactions. Electron microscopy analysis revealed that, despite membranes dismantling, most of the bacteroids seem to be structurally intact. Taken together, our results show that the carbohydrate starvation induced in soybean by dark stress triggers a profound metabolic and structural rearrangement in the infected cells of soybean nodule which is representative of symbiotic cessation.

Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.