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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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Excess axonal wire originates from nature of bouton distribution, ‘bouton-free’ internodal length, and branching complexity.(A) Whole arbor wire economy was negatively correlated with the proportion of boutons on first- and second-order branches (Spearman rank correlation, rs = −0.84, p<10−6, one-sided; linear regression (solid grey line), slope  = −109.21, intercept  = 183.35). (B) Whole arbor wire economy was strongly negatively correlated with the proportion of internodal wire length due to ‘bouton-free’ axonal sections (Spearman rank correlation, rs = −0.94, p<10−6, one-sided; linear regression, slope  = −1.93, intercept  = 1.75). (C) Average wire economy of axonal subtrees decreased with parent branch order towards whole arbor economy levels suggesting basket axon poorer wire economy was associated with their greater degree of branching complexity. (D) Percentage excess wire grew with branch order towards whole arbor levels implying each level of branching costs excess wire length in neocortical axons.
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pcbi-1000711-g010: Excess axonal wire originates from nature of bouton distribution, ‘bouton-free’ internodal length, and branching complexity.(A) Whole arbor wire economy was negatively correlated with the proportion of boutons on first- and second-order branches (Spearman rank correlation, rs = −0.84, p<10−6, one-sided; linear regression (solid grey line), slope  = −109.21, intercept  = 183.35). (B) Whole arbor wire economy was strongly negatively correlated with the proportion of internodal wire length due to ‘bouton-free’ axonal sections (Spearman rank correlation, rs = −0.94, p<10−6, one-sided; linear regression, slope  = −1.93, intercept  = 1.75). (C) Average wire economy of axonal subtrees decreased with parent branch order towards whole arbor economy levels suggesting basket axon poorer wire economy was associated with their greater degree of branching complexity. (D) Percentage excess wire grew with branch order towards whole arbor levels implying each level of branching costs excess wire length in neocortical axons.

Mentions: When examining how different wire-related arbor properties varied with branch order, we discovered that while the proportion of total axon length and bouton number, and bouton density all decreased with branch order, conversely, the proportion of internodal bouton-free axon length increased (see Figure 9). For example, first- and second-order branches accounted for the vast majority of boutons (spiny, 88.9±7.2% & basket, 97.1±2.1%; c.f. grouped 92±5% [43]) and axonal wire (spiny, 80.6±6.5% & basket, 76.1±3.7%; c.f. length uncorrected & grouped 82±6% [43]) (see Figure 9AB). In addition, mean bouton density (bouton-laden sections only) fell as branch order increased with, for example, basket cell first- and second-order branches having a greater density than spiny cells axons (e.g. at first-order: spiny, 0.07±0.01 & basket, 0.18±0.03 boutons per micron, or interbouton interval (ibi) 14.1 & 5.7 microns per bouton, respectively; c.f. grouped ibi 3–11 microns per bouton [43]), though thereafter bouton density declined similarly to zero by fifth-order (see Figure 9C). Importantly, we found whole arbor wire length economy was negatively correlated with the proportion of total boutons per arbor located on first- and second-order branches (Spearman rank correlation, rs = −0.84, p<10−6, one-sided; linear regression, slope  = −109.21, intercept  = 183.35; see Figure 10A) suggesting wire length economy improved when boutons were more evenly spread over an arbor.


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)

Excess axonal wire originates from nature of bouton distribution, ‘bouton-free’ internodal length, and branching complexity.(A) Whole arbor wire economy was negatively correlated with the proportion of boutons on first- and second-order branches (Spearman rank correlation, rs = −0.84, p<10−6, one-sided; linear regression (solid grey line), slope  = −109.21, intercept  = 183.35). (B) Whole arbor wire economy was strongly negatively correlated with the proportion of internodal wire length due to ‘bouton-free’ axonal sections (Spearman rank correlation, rs = −0.94, p<10−6, one-sided; linear regression, slope  = −1.93, intercept  = 1.75). (C) Average wire economy of axonal subtrees decreased with parent branch order towards whole arbor economy levels suggesting basket axon poorer wire economy was associated with their greater degree of branching complexity. (D) Percentage excess wire grew with branch order towards whole arbor levels implying each level of branching costs excess wire length in neocortical axons.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000711-g010: Excess axonal wire originates from nature of bouton distribution, ‘bouton-free’ internodal length, and branching complexity.(A) Whole arbor wire economy was negatively correlated with the proportion of boutons on first- and second-order branches (Spearman rank correlation, rs = −0.84, p<10−6, one-sided; linear regression (solid grey line), slope  = −109.21, intercept  = 183.35). (B) Whole arbor wire economy was strongly negatively correlated with the proportion of internodal wire length due to ‘bouton-free’ axonal sections (Spearman rank correlation, rs = −0.94, p<10−6, one-sided; linear regression, slope  = −1.93, intercept  = 1.75). (C) Average wire economy of axonal subtrees decreased with parent branch order towards whole arbor economy levels suggesting basket axon poorer wire economy was associated with their greater degree of branching complexity. (D) Percentage excess wire grew with branch order towards whole arbor levels implying each level of branching costs excess wire length in neocortical axons.
Mentions: When examining how different wire-related arbor properties varied with branch order, we discovered that while the proportion of total axon length and bouton number, and bouton density all decreased with branch order, conversely, the proportion of internodal bouton-free axon length increased (see Figure 9). For example, first- and second-order branches accounted for the vast majority of boutons (spiny, 88.9±7.2% & basket, 97.1±2.1%; c.f. grouped 92±5% [43]) and axonal wire (spiny, 80.6±6.5% & basket, 76.1±3.7%; c.f. length uncorrected & grouped 82±6% [43]) (see Figure 9AB). In addition, mean bouton density (bouton-laden sections only) fell as branch order increased with, for example, basket cell first- and second-order branches having a greater density than spiny cells axons (e.g. at first-order: spiny, 0.07±0.01 & basket, 0.18±0.03 boutons per micron, or interbouton interval (ibi) 14.1 & 5.7 microns per bouton, respectively; c.f. grouped ibi 3–11 microns per bouton [43]), though thereafter bouton density declined similarly to zero by fifth-order (see Figure 9C). Importantly, we found whole arbor wire length economy was negatively correlated with the proportion of total boutons per arbor located on first- and second-order branches (Spearman rank correlation, rs = −0.84, p<10−6, one-sided; linear regression, slope  = −109.21, intercept  = 183.35; see Figure 10A) suggesting wire length economy improved when boutons were more evenly spread over an arbor.

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