Stimulus information in collective response of tree networks of excitable elements

Tree-like branched myelinated dendrites characterize the morphology of certain sensory neurons with excitable nodes of Ranvier at every branch point and at leaves. Such a morphology can be modeled as tree networks of diffusively coupled excitable elements. Only the leaf nodes (the nodes at the branch endings) receive the stimulus and other random inputs from the surroundings and engender action potentials that propagate through the tree and reach the central node. We quantify the collective response generated by the central node by mutual information (MI) between the stimulus and the response. We show that in the strong coupling limit, the MI is determined by the number of nodes and leaves. At the same time, it is insensitive to the particular connectivity and the distribution of the stimulus among the leaf nodes. In an intermediate coupling regime, however, MI may strongly depend on the distribution of the stimulus. We identify a mechanism behind the competition between the leaf nodes and show that the background firing of unstimulated branches can occlude a localized stimulus. Furthermore, we show that the MI can be enhanced by proper stimulus localization and tuning of coupling.