Topological conditions for propagation of spatially-distributed neural activity

An important task of the nervous system is to transmit information faithfully and reliably across brain regions, a process that involves the coordinated activity of a relatively large population of neurons. In topographically organized networks, where the entering and exiting axons of neurons terminate in confined areas, successful propagation depends on the spatial patterns of activity: the firing neurons in a presynaptic or source layer must be located sufficiently close to each other to ensure that cells in the postsynaptic or target layer receive the requisite number of convergent inputs to fire. Here, we use principles of topology to define the conditions for transmitting information across layers. We show that simplicial complexes formed by source neurons can be used to: 1) determine whether target neurons receive suprathreshold inputs; 2) identify neurons within the active population that contribute to firing; and 3) discriminate between single and multiple active clusters of neurons.