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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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Spiny cell axon arbor wiring compared with minimum-length tree.(A) Example putative excitatory pyramidal cell axon arbor (coronal view) showing the location of numerous boutons (upper), its Euclidean Steiner Minimal Tree (ESMT) graph (middle), and overlay of axon arbor and graph (lower) with dotted circles (white) showing locations where axon wiring was absent in minimum-length graph taken to connect same bouton set. (Key: axon wiring  =  grey lines, graph wiring  =  red lines, axonal bouton  =  yellow dots, cell body  =  green dot; anatomical axes: D, dorsal; L, lateral; P, posterior.) (B) Example of the shortest path from axon origin (root vertex) of this neuron to a selected bouton (upper, see region of interest) for the biological arbor (middle) was, after branching from the main descending axon, fairly direct (0.85 mm path length) but for the length-minimized tree (lower) the route was more circuitous (2.63 mm path length), including a trajectory reversal (marked by blue asterisk), because the artificial arbor lacked wire present in the axon arbor (dotted blue lines). Arrows show direction of flow from axon origin to bouton. (Key: shortest path  =  thick black lines, unvisited arbor wiring  =  grey lines, axon wiring absent in graph  =  dotted blue lines.).
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pcbi-1000711-g004: Spiny cell axon arbor wiring compared with minimum-length tree.(A) Example putative excitatory pyramidal cell axon arbor (coronal view) showing the location of numerous boutons (upper), its Euclidean Steiner Minimal Tree (ESMT) graph (middle), and overlay of axon arbor and graph (lower) with dotted circles (white) showing locations where axon wiring was absent in minimum-length graph taken to connect same bouton set. (Key: axon wiring  =  grey lines, graph wiring  =  red lines, axonal bouton  =  yellow dots, cell body  =  green dot; anatomical axes: D, dorsal; L, lateral; P, posterior.) (B) Example of the shortest path from axon origin (root vertex) of this neuron to a selected bouton (upper, see region of interest) for the biological arbor (middle) was, after branching from the main descending axon, fairly direct (0.85 mm path length) but for the length-minimized tree (lower) the route was more circuitous (2.63 mm path length), including a trajectory reversal (marked by blue asterisk), because the artificial arbor lacked wire present in the axon arbor (dotted blue lines). Arrows show direction of flow from axon origin to bouton. (Key: shortest path  =  thick black lines, unvisited arbor wiring  =  grey lines, axon wiring absent in graph  =  dotted blue lines.).

Mentions: To investigate wire length economy, we contrasted the total length of intracortical axon arbors to minimum-length graphs (Figures 3–7; see Table S1). Spiny cell axon arbors were not optimized for wire length (p<0.001, Wilcoxon signed rank test, one-sided; εspiny = 0.86±0.04, mean ± sd) with on average 5.66±2.93 mm excess wire per axon or 14±4% of total wire length (Figure 3). For example, a minimum-length graph connecting the same bouton set as a layer III pyramidal (spiny) axon arbor used 6 mm less wire or 15% of total axon length (Figure 4). Basket cell axons also were suboptimal for wire length (p<0.005, Wilcoxon signed rank test, one-sided; εbasket = 0.76±0.02) and even significantly less economical than spiny cells (εspiny vs. εbasket: p<0.0005, Mann-Whitney U test, one-sided) (Figure 3) with on average 10.33±4.13 mm excess wire per axon or 24±2% total axon length. For instance, a minimum-length graph of a large layer III basket cell axon arbor used nearly 14 mm less wire or 24% of total axon length (Figure 5). In comparison, star graphs used around 40–50 times more wire than axons (εstar = 0.02±0.01 and 0.02±0.02, respectively; see Figure 3). Both wire and path length economy measures were uncorrelated with either total arbor length or bouton number (Figure 6), suggesting they are scale-invariant measures and robust to incomplete axon arbor reconstruction.


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)

Spiny cell axon arbor wiring compared with minimum-length tree.(A) Example putative excitatory pyramidal cell axon arbor (coronal view) showing the location of numerous boutons (upper), its Euclidean Steiner Minimal Tree (ESMT) graph (middle), and overlay of axon arbor and graph (lower) with dotted circles (white) showing locations where axon wiring was absent in minimum-length graph taken to connect same bouton set. (Key: axon wiring  =  grey lines, graph wiring  =  red lines, axonal bouton  =  yellow dots, cell body  =  green dot; anatomical axes: D, dorsal; L, lateral; P, posterior.) (B) Example of the shortest path from axon origin (root vertex) of this neuron to a selected bouton (upper, see region of interest) for the biological arbor (middle) was, after branching from the main descending axon, fairly direct (0.85 mm path length) but for the length-minimized tree (lower) the route was more circuitous (2.63 mm path length), including a trajectory reversal (marked by blue asterisk), because the artificial arbor lacked wire present in the axon arbor (dotted blue lines). Arrows show direction of flow from axon origin to bouton. (Key: shortest path  =  thick black lines, unvisited arbor wiring  =  grey lines, axon wiring absent in graph  =  dotted blue lines.).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000711-g004: Spiny cell axon arbor wiring compared with minimum-length tree.(A) Example putative excitatory pyramidal cell axon arbor (coronal view) showing the location of numerous boutons (upper), its Euclidean Steiner Minimal Tree (ESMT) graph (middle), and overlay of axon arbor and graph (lower) with dotted circles (white) showing locations where axon wiring was absent in minimum-length graph taken to connect same bouton set. (Key: axon wiring  =  grey lines, graph wiring  =  red lines, axonal bouton  =  yellow dots, cell body  =  green dot; anatomical axes: D, dorsal; L, lateral; P, posterior.) (B) Example of the shortest path from axon origin (root vertex) of this neuron to a selected bouton (upper, see region of interest) for the biological arbor (middle) was, after branching from the main descending axon, fairly direct (0.85 mm path length) but for the length-minimized tree (lower) the route was more circuitous (2.63 mm path length), including a trajectory reversal (marked by blue asterisk), because the artificial arbor lacked wire present in the axon arbor (dotted blue lines). Arrows show direction of flow from axon origin to bouton. (Key: shortest path  =  thick black lines, unvisited arbor wiring  =  grey lines, axon wiring absent in graph  =  dotted blue lines.).
Mentions: To investigate wire length economy, we contrasted the total length of intracortical axon arbors to minimum-length graphs (Figures 3–7; see Table S1). Spiny cell axon arbors were not optimized for wire length (p<0.001, Wilcoxon signed rank test, one-sided; εspiny = 0.86±0.04, mean ± sd) with on average 5.66±2.93 mm excess wire per axon or 14±4% of total wire length (Figure 3). For example, a minimum-length graph connecting the same bouton set as a layer III pyramidal (spiny) axon arbor used 6 mm less wire or 15% of total axon length (Figure 4). Basket cell axons also were suboptimal for wire length (p<0.005, Wilcoxon signed rank test, one-sided; εbasket = 0.76±0.02) and even significantly less economical than spiny cells (εspiny vs. εbasket: p<0.0005, Mann-Whitney U test, one-sided) (Figure 3) with on average 10.33±4.13 mm excess wire per axon or 24±2% total axon length. For instance, a minimum-length graph of a large layer III basket cell axon arbor used nearly 14 mm less wire or 24% of total axon length (Figure 5). In comparison, star graphs used around 40–50 times more wire than axons (εstar = 0.02±0.01 and 0.02±0.02, respectively; see Figure 3). Both wire and path length economy measures were uncorrelated with either total arbor length or bouton number (Figure 6), suggesting they are scale-invariant measures and robust to incomplete axon arbor reconstruction.

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