Adaptation Reduces Variability of the Neuronal Population Code

Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable. For an ensemble of spike-frequency adapting neurons this results in the regularization of the population activity and an enhanced post-synaptic signal decoding. We confirm our theoretical results in a population of cortical neurons.Comment: 4 pages, 2 figure

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

Cardiac Function and Architecture Are Maintained in a Model of Cardiorestricted Overexpression of the Prorenin-Renin Receptor

The (pro)renin-renin receptor, (P)RR has been claimed to be a novel element of the renin-angiotensin system (RAS). The function of (P)RR has been widely studied in renal and vascular pathology but the cardio-specific function of (P)RR has not been studied in detail. We therefore generated a transgenic mouse (Tg) with cardio-restricted (P)RR overexpression driven by the alpha-MHC promotor. The mRNA expression of (P)RR was ∼170-fold higher (P<0.001) and protein expression ∼5-fold higher (P<0.001) in hearts of Tg mice as compared to non-transgenic (wild type, Wt) littermates. This level of overexpression was not associated with spontaneous cardiac morphological or functional abnormalities in Tg mice. To assess whether (P)RR could play a role in cardiac hypertrophy, we infused ISO for 28 days, but this caused an equal degree of cardiac hypertrophy and fibrosis in Wt and Tg mice. In addition, ischemia-reperfusion injury was performed in Langendorff perfused isolated mouse hearts. We did not observe differences in parameters of cardiac function or damage between Wt and Tg mouse hearts under these conditions. Finally, we explored whether the hypoxia sensing response would be modulated by (P)RR using HeLa cells with and without (P)RR overexpression. We did not establish any effect of (P)RR on expression of genes associated with the hypoxic response. These results demonstrate that cardio-specific overexpression of (P)RR does not provoke phenotypical differences in the heart, and does not affect the hearts’ response to stress and injury. It is concluded that increased myocardial (P)RR expression is unlikely to have a major role in pathological cardiac remodeling

Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings

Model calculations have been performed on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory couplings with time delay. The coupled, excitable HH neurons are assumed to receive the two kinds of spike-train inputs: the transient input consisting of $M$ impulses for the finite duration ($M$: integer) and the sequential input with the constant interspike interval (ISI). The distribution of the output ISI $T_{\rm o}$ shows a rich of variety depending on the coupling strength and the time delay. The comparison is made between the dependence of the output ISI for the transient inputs and that for the sequential inputs.Comment: 19 pages, 4 figure

Evidence for a supernova in reanalyzed optical and near-infrared images of GRB970228

We present B-, V-, R_c-, I_c-, J-, H-, K- and K'-band observations of the optical transient (OT) associated with GRB970228, based on a reanalysis of previously used images and unpublished data. In order to minimize calibration differences we have collected and analyzed most of the photometry and consistently determined the magnitude of the OT relative to a set of secondary field stars. We confirm our earlier finding that the early decay of the light curves (before March 6, 1997) was faster than that at intermediate times (between March 6 and April 7, 1997). At late times the light curves resume a fast decay (after April 7, 1997). The early-time observations of GRB970228 are consistent with relativistic blast-wave models but the intermediate- and late-time observations are hard to understand in this framework. The observations are well explained by an initial power law decay with index -1.73 +0.09 -0.12 modified at later times by a type-I_c supernova light curve. Together with the evidence for GRB980326 and GRB980425 this gives further support for the idea that at least some GRBs are associated with a possibly rare type of supernova.Comment: Submitted to the Astrophysical Journal, 9 pages including 3 figures, uses emulateapj.st