A discrete time neural network model with spiking neurons II. Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.Comment: 43 pages - revised version - to appear il Journal of Mathematical Biolog

Genetic Basis of Growth Adaptation of Escherichia coli after Deletion of pgi, a Major Metabolic Gene

Bacterial survival requires adaptation to different environmental perturbations such as exposure to antibiotics, changes in temperature or oxygen levels, DNA damage, and alternative nutrient sources. During adaptation, bacteria often develop beneficial mutations that confer increased fitness in the new environment. Adaptation to the loss of a major non-essential gene product that cripples growth, however, has not been studied at the whole-genome level. We investigated the ability of Escherichia coli K-12 MG1655 to overcome the loss of phosphoglucose isomerase (pgi) by adaptively evolving ten replicates of E. coli lacking pgi for 50 days in glucose M9 minimal medium and by characterizing endpoint clones through whole-genome re-sequencing and phenotype profiling. We found that 1) the growth rates for all ten endpoint clones increased approximately 3-fold over the 50-day period; 2) two to five mutations arose during adaptation, most frequently in the NADH/NADPH transhydrogenases udhA and pntAB and in the stress-associated sigma factor rpoS; and 3) despite similar growth rates, at least three distinct endpoint phenotypes developed as defined by different rates of acetate and formate secretion. These results demonstrate that E. coli can adapt to the loss of a major metabolic gene product with only a handful of mutations and that adaptation can result in multiple, alternative phenotypes