The hypergeometric connectivity hypothesis: Divergent performance of brain circuits with different synaptic connectivity distributions

The development of connectivity among brain networks (e.g., thalamocortical, cortico-thalamic, cortico-cortical) proceeds via a combination of axon and dendrite growth followed by a later process of synaptic pruning [Purves, D., Lichtman, J.W., 1980. Elimination of synapses in the developing nervous system. Science, 210, 153-157; Oppenheim, R.W., 1991. Cell death during development of the nervous system. Annual Review of Neuroscience, 14(1), 453-501.; Oppenheim, R., Qin-Wei Y., Prevette D., Yan Q., 1992. Brain-derived neurotrophic factor rescues developing avian motoneurons from cell death. Nature, 360, 755-757]. Sparse synaptic distribution (i.e., the low probability (<0.1) of contact among neurons; [Braitenberg, V., Schüz, A., 1998. Cortex: Statistics and geometry of neuronal connectivity: Springer Berlin.] can conform to any of a range of connectivity patterns with different distributional characteristics; and different distribution patterns can yield networks with very different functional properties. We rigorously investigate a range of different connectivity characteristics, and show that different synaptic distributions can substantially affect the functional capabilities of the resulting networks. In particular, we provide formal measures of information loss in transmission from one set of neurons to another as a function of synaptic distribution, and show a set of empirical cases with different information-theoretic utility. We characterize the trade-offs among utility and costs, and their dependence on different classes of developmental strategies by which axons from one cell group are "assigned" to synapses on dendrites from a target cell group. It is shown that hypergeometric distributions minimize a range of measured costs, compared to competing synaptic distributions. It is also found that the divergent performance among differently organized brain circuits expands with brain size, rendering the effects increasingly consequential for big brains. In summary, we propose that the characteristics of hypergeometric connectivity provide a coherent explanatory hypothesis of a range of developmental and anatomical data.

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