Finite-size and correlation-induced effects in Mean-field Dynamics

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system

Mosaic DNA imports with interspersions of recipient sequence after natural transformation of Helicobacter pylori

Helicobacter pylori colonizes the gastric mucosa of half of the human population, causing gastritis, ulcers, and cancer. H. pylori is naturally competent for transformation by exogenous DNA, and recombination during mixed infections of one stomach with multiple H. pylori strains generates extensive allelic diversity. We developed an in vitro transformation protocol to study genomic imports after natural transformation of H. pylori. The mean length of imported fragments was dependent on the combination of donor and recipient strain and varied between 1294 bp and 3853 bp. In about 10% of recombinant clones, the imported fragments of donor DNA were interrupted by short interspersed sequences of the recipient (ISR) with a mean length of 82 bp. 18 candidate genes were inactivated in order to identify genes involved in the control of import length and generation of ISR. Inactivation of the antimutator glycosylase MutY increased the length of imports, but did not have a significant effect on ISR frequency. Overexpression of mutY strongly increased the frequency of ISR, indicating that MutY, while not indispensable for ISR formation, is part of at least one ISR-generating pathway. The formation of ISR in H. pylori increases allelic diversity, and contributes to the uniquely low linkage disequilibrium characteristic of this pathogen

A new hammer to crack an old nut : interspecific competitive resource capture by plants is regulated by nutrient supply, not climate

Peer reviewedPublisher PD