Narrow Results

In this paper we prove the propagation of chaos property for an ensemble of interacting neurons subject to independent Brownian noise. The propagation of chaos property means that in the large network size limit, the neurons behave as if they are probabilistically independent. The model for the internal dynamics of the neurons is taken to be that of Wilson and Cowan, and we consider there to be multiple different populations. The synaptic connections are modeled with a nonlinear “electrical” model. The nonlinearity of the synaptic connections means that our model lies outside the scope of classical propagation of chaos results. We obtain the propagation of chaos result by taking advantage of the fact that the mean-field equations are Gaussian, which allows us to use Borell’s Inequality to prove that its tails decay exponentially.

Electrophysiological and ultrastructural studies have demonstrated that gap junctions connect diverse types of neurons in the central nervous system, permitting direct electrical and metabolic coupling. A member of gap junction channel subunit connexin36 (Cx36), is probed for the location of cell-to-cell communication in the mammalian retina, where gap junction networks of major classes of neurons are present. We present an analysis of the expression and localization of Cx36 protein in adult Wistar rat retina, using a newly generated polyclonal antibody against a sequence in the predicted cytoplasmic loop of the Cx36 amino acid alignment, deduced from the cDNA sequence. The affinity-purified antibody, recognizing a single 36-kDa protein, consistently labeled discrete puncta of subcellular structures likely to be associated with gap junctions in the inner plexiform layer, and also cytoplasm within somata and dendrites of retinal amacrine and ganglion cells, following examination with various fixation protocols and double labeling immuno-fluorescence. These results provide that prominent cell-to-cell communication appears in mature excitatory neurons such as retinal ganglion cells, in addition to inhibitory amacrine cells, mediated by gap junctions in the adult retina.

Alpha-type retinal ganglion cells (alpha cells) of the same class in mammalian retina are connected by gap junctions. Electrical synapses between alpha cells were examined using combined techniques of dual patch-clamp recordings, intracellular labeling and electron microscopy in the albino rat retina. In simultaneous dual whole-cell recordings from pairs of neighboring alpha cells, bidirectional electrical synapses with symmetrical junction conductance were observed in pairs with cells of the same morphological type. Regulatory domains of gap junction protein subunit connexins in electrical synapses between alpha cells by extracellular and intracellular ligands investigated by dual whole-patch clamp recordings. I examined how passage currents through electrical synapses between alpha cells are modulated by specific antibodies against connexin36 proteins, and extracellular or intracellular application of ligands. Control conditions led us to observe large passage currents between connected cells and adequate transjunctional conductance (Gj) (1.35$\pm$0.51nS). Experimental results show that high level of intracellular cyclic AMP within examined cells suppress electrical synapses between the neighboring cells. Gj between examined cells reduced to 0.15$\pm$0.04nS. Under application of dopamine (1.25$\pm$0.06nS) or intracellular cyclic GMP (0.98$\pm$0.23nS), however, Gj also remains as in the control level. Intracellular application of an antibody against the cytoplasmic loop of connexin36 reduced G_j (0.98$\pm$0.23nS). Cocktail of the antibody against cytoplasmic connexin36 and intracellular cyclic AMP leaves Gj as in the level by single involvement of the cytoplasmic antibody. The elimination of Gj by the cytoplasmic antibody was in a dose-dependent manner. These results suggest that binding domains against cyclic AMP may be present in the cytoplasmic sites of connexin proteins to regulate channel opening of gap junctions between mammalian retinal alpha ganglion cells.