Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2008 Apr 9;28(15):4047-56.
doi: 10.1523/JNEUROSCI.5559-05.2008.

Functional trade-offs in white matter axonal scaling

Samuel S-H Wang  1 , Jennifer R Shultz, Mark J Burish, Kimberly H Harrison, Patrick R Hof, Lex C Towns, Matthew W Wagers, Krysta D Wyatt
Affiliations

Functional trade-offs in white matter axonal scaling

Samuel S-H Wang et al. J Neurosci. .

Abstract

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.

PubMed Disclaimer

Figures

Figure 1.
Figure 1.
Long-distance axons in the mammalian neocortex. a, Sagittal view of macaque brain with corpus callosum indicated in white. The gray rectangles indicate rostral (r) and caudal (c) locations sampled for transmission electron microscopy. b, Representative micrographs of callosal tissue. Scale bar, 1 μm. c, The fraction of axons that are myelinated increases with brain diameter (slope, 1.04 ± 0.14% myelination per centimeter of brain diameter). Each symbol represents pooled values from one animal. The gray bars indicate ranges of previous adult measurements. d, Volume-filling efficiency of callosal axons. The fraction of volume filled by axons was determined by measuring the fraction of each electron micrograph occupied by myelinated and unmyelinated axons. e, Distribution of axon densities. Box plots indicate median, 25th and 75th percentiles, and dots indicate measurements outside this range. The gray bar indicates the range of previous measurements (Swadlow et al., 1980; LaMantia and Rakic, 1990).
Figure 2.
Figure 2.
Cross-brain conduction times in large myelinated axons. a, Histograms of size distributions of myelinated axons for mouse and macaque. b, Cumulative histograms of myelinated axon diameter. c, Micrographs demonstrating large myelinated axons (indicated by arrowheads) at noncallosal locations in white matter. Samples were taken from macaque supramarginal gyrus and cat anterior sylvian gyrus. Scale bars, 2 μm. d, The diameters of the widest callosal axons (points) increase with brain diameter, in contrast with mean diameters of unmyelinated (●) and myelinated (○) axons. SEM error bars are smaller than the symbols. Horizontal markers indicate averages of the widest callosal axons, except for shrew, mouse, and rat, where they indicate the largest observed axon. e, Estimated cross-brain conduction times for myelinated axons (average values; open triangles, r) and the widest axons (box plots). The widest axons were taken to be the widest 10 axons per 10,000 μm2, except for shrew, mouse, and rat, in which case the widest observed axon was used.
Figure 3.
Figure 3.
Increase in widest optic nerve axon diameter with brain size. The widest reported axon in each species was plotted against brain size, giving a fitted log–log slope of +0.18 ± 0.03. Literature sources for data are listed in supplemental material (available at www.jneurosci.org).
Figure 4.
Figure 4.
Size distributions of callosal axons as determined by transmission electron microscopy. In all species, the distributions are separated by a diameter threshold of 0.4–0.5 μm.
Figure 5.
Figure 5.
Scaling of per-action potential metabolic costs. a, The estimated metabolic cost per fiber of generating an action potential for unmyelinated axons, for myelinated axons, and for all white matter axons averaged. b, The estimated metabolic cost per unit weight of white matter of generating an action potential in all fibers, GAP, decreases as the −0.31 ± 0.03 power of body weight (○). Direct measurement of white matter metabolic rates per unit time, Gt, measured by autoradiographic methods (●; for data sources see the supplemental material, available at www.jneurosci.org), gives a power law slope of −0.32 ± 0.06. c, The same quantities plotted against brain size. The GAP and Gt axes are on logarithmic scales and are aligned with one another by a factor of 14.3 spikes/s.
Figure 6.
Figure 6.
Contribution of large axons to neocortical white matter volume. a, Relative cross sections of typical unmyelinated axons, myelinated axons, and giant myelinated axons. b, Estimated cumulative fraction of callosal axon volume above a given axon diameter. For clarity, cumulative fractions for diameters smaller than 1 μm (see Fig. 4) are not shown. c, The empirical scaling relationship between white matter volume and gray matter volume (Zhang and Sejnowski, 2000) shows a power law with a log–log slope of 1.23 ± 0.01. d, The estimated total volume of white matter axons (filled squares) can account for the supralinear growth in white matter volume (open circles) relative to gray matter. Replacing the overall axon distribution with that of mouse (open squares) reduces the axon volume to an approximately linear relationship. Inset, Calculated axon volume versus actual white matter volume.
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

See all "Cited by" articles

References

    1. Attwell D, Laughlin SB. An energy budget for signaling in the grey matter of the brain. J Cereb Blood Flow Metab. 2001;21:1133–1145. - PubMed
    1. Basbaum AJ, Jessell TM. The perception of pain. In: Kandel ER, Schwartz JH, Jessell TM, editors. Principles of neural science. Ed 4. New York: McGraw-Hill; 2000. pp. 472–491.
    1. Black JA, Fields RD, Waxman SG. Macromolecular structure of axonal membrane in the optic nerve of the jimpy mouse. J Neuropathol Exp Neurol. 1988;47:588–598. - PubMed
    1. Blinkov SM, Glezer II. New York: Basic Books; 1968. The human brain in figures and tables: a quantitative handbook.
    1. Braitenberg V, Schüz A. Cortex: statistics and geometry of neuronal connectivity. Ed 2. Berlin: Springer; 1998.

Publication types

LinkOut - more resources