Functional trade-offs in white matter axonal scaling.

The brains of large mammals have lower rates of metabolism than those of small mammals, but the functional consequences of this scaling are not well understood. An attractive target for analysis is axons, whose size, speed and energy consumption are straightforwardly related. Here we show that from shrews to whales, the composition of white matter shifts from compact, slow-conducting, and energetically expensive unmyelinated axons to large, fast-conducting, and energetically inexpensive myelinated axons. The fastest axons have conduction times of 1-5 ms across the neocortex and <1 ms from the eye to the brain, suggesting that in select sets of communicating fibers, large brains reduce transmission delays and metabolic firing costs at the expense of increased volume. Delays and potential imprecision in cross-brain conduction times are especially great in unmyelinated axons, which may transmit information via firing rate rather than precise spike timing. In neocortex, axon size distributions can account for the scaling of per-volume metabolic rate and suggest a maximum supportable firing rate, averaged across all axons, of 7 +/- 2 Hz. Axon size distributions also account for the scaling of white matter volume with respect to brain size. The heterogeneous white matter composition found in large brains thus reflects a metabolically constrained trade-off that reduces both volume and conduction time.

Scaling laws in the mammalian neocortex: does form provide clues to function?

Although descriptions of form have been a mainstay of comparative neuroanatomy, less well explored is the use of quantitative approaches, especially at the cellular level. In the neocortex, many gross and cellular anatomical measures show striking regularities over a wide range of brain sizes. Here we review our recent efforts to accurately characterize these scaling trends and explain them in functional terms. We focus on the expansion of white matter volume with increasing brain size and the formation of surface folds, in addition to principles of processing speed and energetics that may explain these phenomena. We also consider exceptional cases of neocortical morphology as a means of testing putative functional principles and developmental mechanisms. We illustrate this point by describing several morphological specializations at the cellular level that may constitute functional adaptations. Taken together, these approaches illustrate the benefits of a synthesis between comparative neuroanatomy and biophysics.