Limits...
Communication and wiring in the cortical connectome.

Budd JM, Kisvárday ZF - Front Neuroanat (2012)

Bottom Line: We report three main conclusions.To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description.We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.

View Article: PubMed Central - PubMed

Affiliation: Department of Informatics, University of Sussex Falmer, East Sussex, UK.

ABSTRACT
In cerebral cortex, the huge mass of axonal wiring that carries information between near and distant neurons is thought to provide the neural substrate for cognitive and perceptual function. The goal of mapping the connectivity of cortical axons at different spatial scales, the cortical connectome, is to trace the paths of information flow in cerebral cortex. To appreciate the relationship between the connectome and cortical function, we need to discover the nature and purpose of the wiring principles underlying cortical connectivity. A popular explanation has been that axonal length is strictly minimized both within and between cortical regions. In contrast, we have hypothesized the existence of a multi-scale principle of cortical wiring where to optimize communication there is a trade-off between spatial (construction) and temporal (routing) costs. Here, using recent evidence concerning cortical spatial networks we critically evaluate this hypothesis at neuron, local circuit, and pathway scales. We report three main conclusions. First, the axonal and dendritic arbor morphology of single neocortical neurons may be governed by a similar wiring principle, one that balances the conservation of cellular material and conduction delay. Second, the same principle may be observed for fiber tracts connecting cortical regions. Third, the absence of sufficient local circuit data currently prohibits any meaningful assessment of the hypothesis at this scale of cortical organization. To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description. In addition, structural analyses of temporal cost for cortical circuits should take account of both axonal conduction and neuronal integration delays, which appear mostly of the same order of magnitude. We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.

No MeSH data available.


Related in: MedlinePlus

Spatial and temporal cost trade-off alters arbor morphology. An example network consists of 80 labeled vertices (small yellow filled circles) plus a root vertex (large green filled circle). Here, total wiring cost = spatial cost + (β × temporal cost), where the parameter β, which varies between 0 and 1, is used to trade-off spatial construction cost against temporal routing cost. (A) Artificial arbor structures optimized for different values of a cost trade-off parameter, β = 0.0 (spatial cost optimization, left), 0.8 (mixed cost optimization, middle), and 1.0 (temporal cost optimization, right). (B) Relative communication costs vary as a function of the trade-off parameter. Relative spatial cost (wire length) increases with β rapidly when β > 0.8, while relative temporal cost (path length) steadily decreases with β. Costs at equilibrium around β = 0.8. Artificial arbors were generated using Gastner and Newman (2006) algorithm.
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Figure 2: Spatial and temporal cost trade-off alters arbor morphology. An example network consists of 80 labeled vertices (small yellow filled circles) plus a root vertex (large green filled circle). Here, total wiring cost = spatial cost + (β × temporal cost), where the parameter β, which varies between 0 and 1, is used to trade-off spatial construction cost against temporal routing cost. (A) Artificial arbor structures optimized for different values of a cost trade-off parameter, β = 0.0 (spatial cost optimization, left), 0.8 (mixed cost optimization, middle), and 1.0 (temporal cost optimization, right). (B) Relative communication costs vary as a function of the trade-off parameter. Relative spatial cost (wire length) increases with β rapidly when β > 0.8, while relative temporal cost (path length) steadily decreases with β. Costs at equilibrium around β = 0.8. Artificial arbors were generated using Gastner and Newman (2006) algorithm.

Mentions: In network design, simultaneously minimizing both construction and routing costs is considered an intractable (NP-hard) optimization problem because these are conflicting objective functions (Hu, 1974; Alpert et al., 1995; Khuller et al., 1995; Wu et al., 2002; Gastner and Newman, 2006). Figure 2 illustrates how a trade-off between these conflicting objective functions affects the structure of a spatial network. Here, optimizing total weight (construction cost) only leads to a minimum spanning tree (Figure 2A, left) or, if additional vertices are inserted, a Steiner minimal tree design (Garey and Johnson, 1979). In contrast, optimizing average/total path length only (routing cost) generates a star tree (Figure 2A, right), where there is direct connection from a central hub to each remaining vertex to create a hub-and-spoke design. Instead, a suboptimal minimization of construction cost permits a low routing cost (Figure 2A, middle). Figure 2B shows the relative change in communication costs in this spatial network for different values of β, a parameter that trade-offs spatial construction cost against temporal routing cost. When β = 0 then spatial cost is minimized and temporal cost maximized. Whereas when β = 1, the situation is reversed. Between these extremes, temporal cost decreases monotonically with increasing β while simultaneously spatial cost increases slowly until after the equilibrium point (β = 0.79) when it increases rapidly.


Communication and wiring in the cortical connectome.

Budd JM, Kisvárday ZF - Front Neuroanat (2012)

Spatial and temporal cost trade-off alters arbor morphology. An example network consists of 80 labeled vertices (small yellow filled circles) plus a root vertex (large green filled circle). Here, total wiring cost = spatial cost + (β × temporal cost), where the parameter β, which varies between 0 and 1, is used to trade-off spatial construction cost against temporal routing cost. (A) Artificial arbor structures optimized for different values of a cost trade-off parameter, β = 0.0 (spatial cost optimization, left), 0.8 (mixed cost optimization, middle), and 1.0 (temporal cost optimization, right). (B) Relative communication costs vary as a function of the trade-off parameter. Relative spatial cost (wire length) increases with β rapidly when β > 0.8, while relative temporal cost (path length) steadily decreases with β. Costs at equilibrium around β = 0.8. Artificial arbors were generated using Gastner and Newman (2006) algorithm.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3472565&req=5

Figure 2: Spatial and temporal cost trade-off alters arbor morphology. An example network consists of 80 labeled vertices (small yellow filled circles) plus a root vertex (large green filled circle). Here, total wiring cost = spatial cost + (β × temporal cost), where the parameter β, which varies between 0 and 1, is used to trade-off spatial construction cost against temporal routing cost. (A) Artificial arbor structures optimized for different values of a cost trade-off parameter, β = 0.0 (spatial cost optimization, left), 0.8 (mixed cost optimization, middle), and 1.0 (temporal cost optimization, right). (B) Relative communication costs vary as a function of the trade-off parameter. Relative spatial cost (wire length) increases with β rapidly when β > 0.8, while relative temporal cost (path length) steadily decreases with β. Costs at equilibrium around β = 0.8. Artificial arbors were generated using Gastner and Newman (2006) algorithm.
Mentions: In network design, simultaneously minimizing both construction and routing costs is considered an intractable (NP-hard) optimization problem because these are conflicting objective functions (Hu, 1974; Alpert et al., 1995; Khuller et al., 1995; Wu et al., 2002; Gastner and Newman, 2006). Figure 2 illustrates how a trade-off between these conflicting objective functions affects the structure of a spatial network. Here, optimizing total weight (construction cost) only leads to a minimum spanning tree (Figure 2A, left) or, if additional vertices are inserted, a Steiner minimal tree design (Garey and Johnson, 1979). In contrast, optimizing average/total path length only (routing cost) generates a star tree (Figure 2A, right), where there is direct connection from a central hub to each remaining vertex to create a hub-and-spoke design. Instead, a suboptimal minimization of construction cost permits a low routing cost (Figure 2A, middle). Figure 2B shows the relative change in communication costs in this spatial network for different values of β, a parameter that trade-offs spatial construction cost against temporal routing cost. When β = 0 then spatial cost is minimized and temporal cost maximized. Whereas when β = 1, the situation is reversed. Between these extremes, temporal cost decreases monotonically with increasing β while simultaneously spatial cost increases slowly until after the equilibrium point (β = 0.79) when it increases rapidly.

Bottom Line: We report three main conclusions.To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description.We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.

View Article: PubMed Central - PubMed

Affiliation: Department of Informatics, University of Sussex Falmer, East Sussex, UK.

ABSTRACT
In cerebral cortex, the huge mass of axonal wiring that carries information between near and distant neurons is thought to provide the neural substrate for cognitive and perceptual function. The goal of mapping the connectivity of cortical axons at different spatial scales, the cortical connectome, is to trace the paths of information flow in cerebral cortex. To appreciate the relationship between the connectome and cortical function, we need to discover the nature and purpose of the wiring principles underlying cortical connectivity. A popular explanation has been that axonal length is strictly minimized both within and between cortical regions. In contrast, we have hypothesized the existence of a multi-scale principle of cortical wiring where to optimize communication there is a trade-off between spatial (construction) and temporal (routing) costs. Here, using recent evidence concerning cortical spatial networks we critically evaluate this hypothesis at neuron, local circuit, and pathway scales. We report three main conclusions. First, the axonal and dendritic arbor morphology of single neocortical neurons may be governed by a similar wiring principle, one that balances the conservation of cellular material and conduction delay. Second, the same principle may be observed for fiber tracts connecting cortical regions. Third, the absence of sufficient local circuit data currently prohibits any meaningful assessment of the hypothesis at this scale of cortical organization. To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description. In addition, structural analyses of temporal cost for cortical circuits should take account of both axonal conduction and neuronal integration delays, which appear mostly of the same order of magnitude. We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.

No MeSH data available.


Related in: MedlinePlus