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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

Shortest path for the same problem can be different depending on the type of network representation used. An example network consists of four labeled vertices A, B, C, and D. The aim is to find shortest path between vertex A to vertex D. (A) Unweighted network representation. The topology of undirected (left) and directed versions (right) is shown graphically (top) with their corresponding adjacency (connectivity) matrices below (bottom). Brown lines show shortest paths. Red cross indicates a counter-directional edge, which creates an invalid path from vertex A to vertex D. (B) Weighted network representation. Graphical representation (top) of an undirected weighted graph with values of weights (distance) shown next to edges and recorded in the cost or weight matrix below (bottom). Note in the cost or weight matrix the absence of an edge is recorded as an infinite cost (“inf”) while in adjacency matrix it is recorded as zero. (C) Summary table for path length results corresponding to each type of network. Shortest paths are shown in bold brown text.
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Figure 1: Shortest path for the same problem can be different depending on the type of network representation used. An example network consists of four labeled vertices A, B, C, and D. The aim is to find shortest path between vertex A to vertex D. (A) Unweighted network representation. The topology of undirected (left) and directed versions (right) is shown graphically (top) with their corresponding adjacency (connectivity) matrices below (bottom). Brown lines show shortest paths. Red cross indicates a counter-directional edge, which creates an invalid path from vertex A to vertex D. (B) Weighted network representation. Graphical representation (top) of an undirected weighted graph with values of weights (distance) shown next to edges and recorded in the cost or weight matrix below (bottom). Note in the cost or weight matrix the absence of an edge is recorded as an infinite cost (“inf”) while in adjacency matrix it is recorded as zero. (C) Summary table for path length results corresponding to each type of network. Shortest paths are shown in bold brown text.

Mentions: How a system is represented graphically influences what can be inferred about its communication or processing characteristics. Figure 1 illustrates this point by comparing the shortest path length in unweighted (Figure 1A) and weighted network representations (Figure 1B) for the same toy problem. Recall that path length is measured differently between weighted and unweighted networks (see Box 1). In the unweighted representation, the use of directional edges removes one of two possible paths connecting vertex A to vertex D (Figure 1C). So if the directions of information flow were known for the system but not incorporated in the network model, inferences concerning the directness of communication would be distorted; the undirected network would allow information to flow along paths that were impossible in the real system. Similarly, the shortest length path in the unweighted network representation (Figure 1A, left) is the one with the fewest hops whereas in the weighted network representation of the same system (Figure 1B) it is the path with the lowest total cost (see Figure 1C). This means that the choice of graphical representation can for the same system identify different shortest paths, though this choice may be dictated by available data.


Communication and wiring in the cortical connectome.

Budd JM, Kisvárday ZF - Front Neuroanat (2012)

Shortest path for the same problem can be different depending on the type of network representation used. An example network consists of four labeled vertices A, B, C, and D. The aim is to find shortest path between vertex A to vertex D. (A) Unweighted network representation. The topology of undirected (left) and directed versions (right) is shown graphically (top) with their corresponding adjacency (connectivity) matrices below (bottom). Brown lines show shortest paths. Red cross indicates a counter-directional edge, which creates an invalid path from vertex A to vertex D. (B) Weighted network representation. Graphical representation (top) of an undirected weighted graph with values of weights (distance) shown next to edges and recorded in the cost or weight matrix below (bottom). Note in the cost or weight matrix the absence of an edge is recorded as an infinite cost (“inf”) while in adjacency matrix it is recorded as zero. (C) Summary table for path length results corresponding to each type of network. Shortest paths are shown in bold brown text.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Shortest path for the same problem can be different depending on the type of network representation used. An example network consists of four labeled vertices A, B, C, and D. The aim is to find shortest path between vertex A to vertex D. (A) Unweighted network representation. The topology of undirected (left) and directed versions (right) is shown graphically (top) with their corresponding adjacency (connectivity) matrices below (bottom). Brown lines show shortest paths. Red cross indicates a counter-directional edge, which creates an invalid path from vertex A to vertex D. (B) Weighted network representation. Graphical representation (top) of an undirected weighted graph with values of weights (distance) shown next to edges and recorded in the cost or weight matrix below (bottom). Note in the cost or weight matrix the absence of an edge is recorded as an infinite cost (“inf”) while in adjacency matrix it is recorded as zero. (C) Summary table for path length results corresponding to each type of network. Shortest paths are shown in bold brown text.
Mentions: How a system is represented graphically influences what can be inferred about its communication or processing characteristics. Figure 1 illustrates this point by comparing the shortest path length in unweighted (Figure 1A) and weighted network representations (Figure 1B) for the same toy problem. Recall that path length is measured differently between weighted and unweighted networks (see Box 1). In the unweighted representation, the use of directional edges removes one of two possible paths connecting vertex A to vertex D (Figure 1C). So if the directions of information flow were known for the system but not incorporated in the network model, inferences concerning the directness of communication would be distorted; the undirected network would allow information to flow along paths that were impossible in the real system. Similarly, the shortest length path in the unweighted network representation (Figure 1A, left) is the one with the fewest hops whereas in the weighted network representation of the same system (Figure 1B) it is the path with the lowest total cost (see Figure 1C). This means that the choice of graphical representation can for the same system identify different shortest paths, though this choice may be dictated by available data.

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