Modular structure in C. elegans neural network and its response to external localized stimuli

Synchronization plays a key role in information processing in neuronal networks. Response of specific groups of neurons are triggered by external stimuli, such as visual, tactile or olfactory inputs. Neurons, however, can be divided into several categories, such as by physical location, functional role or topological clustering properties. Here we study the response of the electric junction C. elegans network to external stimuli using the partially forced Kuramoto model and applying the force to specific groups of neurons. Stimuli were applied to topological modules, obtained by the ModuLand procedure, to a ganglion, specified by its anatomical localization, and to the functional group composed of all sensory neurons. We found that topological modules do not contain purely anatomical groups or functional classes, corroborating previous results, and that stimulating different classes of neurons lead to very different responses, measured in terms of synchronization and phase velocity correlations. In all cases, however, the modular structure hindered full synchronization, protecting the system from seizures. More importantly, the responses to stimuli applied to topological and functional modules showed pronounced patterns of correlation or anti-correlation with other modules that were not observed when the stimulus was applied to ganglia.Comment: 23 pages, 6 figure

Counterions at charge-modulated substrates

We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.Comment: 7 page