  Neural connectivity at the cellular and mesoscopic level appears very
specific and is presumed to arise from highly specific developmental
mechanisms. However, there are general shared features of connectivity in
systems as different as the networks formed by individual neurons in
Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of
cortical areas in the mouse, macaque, and human brain. In all these systems,
connection length distributions have very similar shapes, with an initial large
peak and a long flat tail representing the admixture of long-distance
connections to mostly short-distance connections. Furthermore, not all
potentially possible synapses are formed, and only a fraction of axons (called
filling fraction) establish synapses with spatially neighboring neurons. We
explored what aspects of these connectivity patterns can be explained simply by
random axonal outgrowth. We found that random axonal growth away from the soma
can already reproduce the known distance distribution of connections. We also
observed that experimentally observed filling fractions can be generated by
competition for available space at the target neurons--a model markedly
different from previous explanations. These findings may serve as a baseline
model for the development of connectivity that can be further refined by more
specific mechanisms.
