Limits...
Neocortical axon arbors trade-off material and conduction delay conservation.

Budd JM, Kovács K, Ferecskó AS, Buzás P, Eysel UT, Kisvárday ZF - PLoS Comput. Biol. (2010)

Bottom Line: We found intracortical axons were significantly longer than optimal.The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors.Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations.

View Article: PubMed Central - PubMed

Affiliation: School of Informatics, University of Sussex, Brighton, United Kingdom. j.m.l.budd@susx.ac.uk

ABSTRACT
The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit conduction delay regulate the design of individual axon arbors in cerebral cortex. Yet the spatial and temporal communication costs of single neocortical axons remain undefined. Here, using reconstructions of in vivo labelled excitatory spiny cell and inhibitory basket cell intracortical axons combined with a variety of graph optimization algorithms, we empirically investigated Cajal's conservation laws in cerebral cortex for whole three-dimensional (3D) axon arbors, to our knowledge the first study of its kind. We found intracortical axons were significantly longer than optimal. The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors. We discovered that cortical axon branching appears to promote a low temporal dispersion of axonal latencies and a tight relationship between cortical distance and axonal latency. In addition, inhibitory basket cell axonal latencies may occur within a much narrower temporal window than excitatory spiny cell axons, which may help boost signal detection. Thus, to optimize neuronal network communication we find that a modest excess of axonal wire is traded-off to enhance arbor temporal economy and precision. Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations.

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Temporal dispersion of basket cell axon latencies was approximately half that of spiny cell axons.Inset shows normalised Gaussian profiles of relative temporal dispersion independent of conduction velocity.
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pcbi-1000711-g015: Temporal dispersion of basket cell axon latencies was approximately half that of spiny cell axons.Inset shows normalised Gaussian profiles of relative temporal dispersion independent of conduction velocity.

Mentions: To predict the effect of wire minimization on temporal dispersion, we estimated axonal latency deviation about the regression lines (green lines shown in Figure 13AB) for both axon and MST data (Figures 14 and 15). Independent of conduction velocity, spiny cell axon temporal dispersion was 5.7 times less than MSTs with axonal bifurcation vertices and 8.2 times less than MSTs without axonal bifurcations (Figure 14A, left). For basket cell axon temporal dispersion, the corresponding values were 2.9 (with) and 3.4 (without bifurcation vertices) times less (Figure 14A, right). For instance, at 0.15 m s−1 conduction velocity latencies covered a narrower temporal window than MSTs (spiny, ±5 vs. ± >20 ms, Figure 14B left; basket, ±2 vs. ±8 ms, Figure 14B right), which was maintained when conduction velocity doubled to 0.30 m s−1 (spiny, ±2 vs. ±12 ms, Figure 14C left; basket, ±1 vs. ±4 ms, Figure 14C right). Figure 15 illustrates that the relative temporal dispersion of spiny cell arbors was double that shown by basket cell axons, which generally have greater branching complexity than spiny cell axons. Moreover, this difference is likely to be enhanced from the postsynaptic somatic targeting by largely myelinated basket cell axons [8],[21] compared to the postsynaptic dendritic targeting by mainly unmyelinated spiny cell axons [6],[17]. These results suggest the design of intracortical axonal arbors supports a low degree of temporal dispersion and a close relationship between distance and latency, prerequisites for intracortical synchronization [45], fast network oscillations [46], and coincidence detection [47], yet wire-minimized arbors (with or without branch points) demonstrate much poorer temporal precision making them ill-suited for these functions.


Neocortical axon arbors trade-off material and conduction delay conservation.

Budd JM, Kovács K, Ferecskó AS, Buzás P, Eysel UT, Kisvárday ZF - PLoS Comput. Biol. (2010)

Temporal dispersion of basket cell axon latencies was approximately half that of spiny cell axons.Inset shows normalised Gaussian profiles of relative temporal dispersion independent of conduction velocity.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2837396&req=5

pcbi-1000711-g015: Temporal dispersion of basket cell axon latencies was approximately half that of spiny cell axons.Inset shows normalised Gaussian profiles of relative temporal dispersion independent of conduction velocity.
Mentions: To predict the effect of wire minimization on temporal dispersion, we estimated axonal latency deviation about the regression lines (green lines shown in Figure 13AB) for both axon and MST data (Figures 14 and 15). Independent of conduction velocity, spiny cell axon temporal dispersion was 5.7 times less than MSTs with axonal bifurcation vertices and 8.2 times less than MSTs without axonal bifurcations (Figure 14A, left). For basket cell axon temporal dispersion, the corresponding values were 2.9 (with) and 3.4 (without bifurcation vertices) times less (Figure 14A, right). For instance, at 0.15 m s−1 conduction velocity latencies covered a narrower temporal window than MSTs (spiny, ±5 vs. ± >20 ms, Figure 14B left; basket, ±2 vs. ±8 ms, Figure 14B right), which was maintained when conduction velocity doubled to 0.30 m s−1 (spiny, ±2 vs. ±12 ms, Figure 14C left; basket, ±1 vs. ±4 ms, Figure 14C right). Figure 15 illustrates that the relative temporal dispersion of spiny cell arbors was double that shown by basket cell axons, which generally have greater branching complexity than spiny cell axons. Moreover, this difference is likely to be enhanced from the postsynaptic somatic targeting by largely myelinated basket cell axons [8],[21] compared to the postsynaptic dendritic targeting by mainly unmyelinated spiny cell axons [6],[17]. These results suggest the design of intracortical axonal arbors supports a low degree of temporal dispersion and a close relationship between distance and latency, prerequisites for intracortical synchronization [45], fast network oscillations [46], and coincidence detection [47], yet wire-minimized arbors (with or without branch points) demonstrate much poorer temporal precision making them ill-suited for these functions.

Bottom Line: We found intracortical axons were significantly longer than optimal.The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors.Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations.

View Article: PubMed Central - PubMed

Affiliation: School of Informatics, University of Sussex, Brighton, United Kingdom. j.m.l.budd@susx.ac.uk

ABSTRACT
The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit conduction delay regulate the design of individual axon arbors in cerebral cortex. Yet the spatial and temporal communication costs of single neocortical axons remain undefined. Here, using reconstructions of in vivo labelled excitatory spiny cell and inhibitory basket cell intracortical axons combined with a variety of graph optimization algorithms, we empirically investigated Cajal's conservation laws in cerebral cortex for whole three-dimensional (3D) axon arbors, to our knowledge the first study of its kind. We found intracortical axons were significantly longer than optimal. The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors. We discovered that cortical axon branching appears to promote a low temporal dispersion of axonal latencies and a tight relationship between cortical distance and axonal latency. In addition, inhibitory basket cell axonal latencies may occur within a much narrower temporal window than excitatory spiny cell axons, which may help boost signal detection. Thus, to optimize neuronal network communication we find that a modest excess of axonal wire is traded-off to enhance arbor temporal economy and precision. Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations.

Show MeSH
Related in: MedlinePlus