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Cortical Composition Hierarchy Driven by Spine Proportion Economical Maximization or Wire Volume Minimization.

Karbowski J - PLoS Comput. Biol. (2015)

Bottom Line: As an alternative, a new principle called "spine economy maximization" is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results.Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates.In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland.

ABSTRACT
The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites take each about 1/3 of cortical space, spines and glia/astrocytes occupy each about (1/3)(2), and capillaries around (1/3)(4). Moreover, data analysis across species reveals that these fractions are roughly brain size independent, which suggests that they could be in some sense optimal and thus important for brain function. Is there any principle that sets them in this invariant way? This study first builds a model of local circuit in which neural wire, spines, astrocytes, and capillaries are mutually coupled elements and are treated within a single mathematical framework. Next, various forms of wire minimization rule (wire length, surface area, volume, or conduction delays) are analyzed, of which, only minimization of wire volume provides realistic results that are very close to the empirical cortical fractions. As an alternative, a new principle called "spine economy maximization" is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results. Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates. However, such a combined meta-principle yields much better results than the constraints related solely to minimization of wire length, wire surface area, and conduction delays. Interestingly, the type of spine size distribution also plays a role, and better agreement with the data is achieved for distributions with long tails. In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

No MeSH data available.


Hierarchical organization of the five major components in the gray matter of cerebral cortex.Empirical data points for each component are denoted by blue diamonds and correspond to different mammals (see Table 1). Solid black lines represent integer powers of the fraction 1/3. In particular, these fractions are: (1/3)4 for capillaries, (1/3)2 for glia and spines, and 1/3 for dendrites and axons. Note, that on average empirical fractional volumes across species approximately conform to this simple rule.
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pcbi.1004532.g001: Hierarchical organization of the five major components in the gray matter of cerebral cortex.Empirical data points for each component are denoted by blue diamonds and correspond to different mammals (see Table 1). Solid black lines represent integer powers of the fraction 1/3. In particular, these fractions are: (1/3)4 for capillaries, (1/3)2 for glia and spines, and 1/3 for dendrites and axons. Note, that on average empirical fractional volumes across species approximately conform to this simple rule.

Mentions: Existing experimental data on fractional volumes of cortical gray matter components were analyzed (see the Methods), and it is found that these fractions exhibit a certain hierarchy, since they can be approximated by integer powers of 1/3 (Table 1; Fig 1). Specifically, axons and dendrites occupy each about 1/3 of cortical space, dendritic spines and glia/astrocytes constitute each roughly (1/3)2 of the cortex, and capillaries take an extremely small volume fraction around (1/3)4 (Table 1; Fig 1). This regularity is called here the rule of “powers of 1/3”. Moreover, an allometric analysis reveals that the fractions of all examined cortical components are species- and brain size independent, i.e. they do not correlate significantly with cortical size and scale with exponents close to zero (Table 1; Fig 2). Typical values for axons: exponent = −0.036, R2 = 0.083, p = 0.713; for dendrites: exponent = −0.002, R2 = 0.037, p = 0.717; for spines: exponent = −0.013, R2 = 0.008, p = 0.885; for glia/astrocytes: exponent = 0.031, R2 = 0.180, p = 0.477; and for capillaries: exponent = 0.064, R2 = 0.243, p = 0.399 (Fig 2).


Cortical Composition Hierarchy Driven by Spine Proportion Economical Maximization or Wire Volume Minimization.

Karbowski J - PLoS Comput. Biol. (2015)

Hierarchical organization of the five major components in the gray matter of cerebral cortex.Empirical data points for each component are denoted by blue diamonds and correspond to different mammals (see Table 1). Solid black lines represent integer powers of the fraction 1/3. In particular, these fractions are: (1/3)4 for capillaries, (1/3)2 for glia and spines, and 1/3 for dendrites and axons. Note, that on average empirical fractional volumes across species approximately conform to this simple rule.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4593638&req=5

pcbi.1004532.g001: Hierarchical organization of the five major components in the gray matter of cerebral cortex.Empirical data points for each component are denoted by blue diamonds and correspond to different mammals (see Table 1). Solid black lines represent integer powers of the fraction 1/3. In particular, these fractions are: (1/3)4 for capillaries, (1/3)2 for glia and spines, and 1/3 for dendrites and axons. Note, that on average empirical fractional volumes across species approximately conform to this simple rule.
Mentions: Existing experimental data on fractional volumes of cortical gray matter components were analyzed (see the Methods), and it is found that these fractions exhibit a certain hierarchy, since they can be approximated by integer powers of 1/3 (Table 1; Fig 1). Specifically, axons and dendrites occupy each about 1/3 of cortical space, dendritic spines and glia/astrocytes constitute each roughly (1/3)2 of the cortex, and capillaries take an extremely small volume fraction around (1/3)4 (Table 1; Fig 1). This regularity is called here the rule of “powers of 1/3”. Moreover, an allometric analysis reveals that the fractions of all examined cortical components are species- and brain size independent, i.e. they do not correlate significantly with cortical size and scale with exponents close to zero (Table 1; Fig 2). Typical values for axons: exponent = −0.036, R2 = 0.083, p = 0.713; for dendrites: exponent = −0.002, R2 = 0.037, p = 0.717; for spines: exponent = −0.013, R2 = 0.008, p = 0.885; for glia/astrocytes: exponent = 0.031, R2 = 0.180, p = 0.477; and for capillaries: exponent = 0.064, R2 = 0.243, p = 0.399 (Fig 2).

Bottom Line: As an alternative, a new principle called "spine economy maximization" is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results.Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates.In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland.

ABSTRACT
The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites take each about 1/3 of cortical space, spines and glia/astrocytes occupy each about (1/3)(2), and capillaries around (1/3)(4). Moreover, data analysis across species reveals that these fractions are roughly brain size independent, which suggests that they could be in some sense optimal and thus important for brain function. Is there any principle that sets them in this invariant way? This study first builds a model of local circuit in which neural wire, spines, astrocytes, and capillaries are mutually coupled elements and are treated within a single mathematical framework. Next, various forms of wire minimization rule (wire length, surface area, volume, or conduction delays) are analyzed, of which, only minimization of wire volume provides realistic results that are very close to the empirical cortical fractions. As an alternative, a new principle called "spine economy maximization" is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results. Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates. However, such a combined meta-principle yields much better results than the constraints related solely to minimization of wire length, wire surface area, and conduction delays. Interestingly, the type of spine size distribution also plays a role, and better agreement with the data is achieved for distributions with long tails. In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

No MeSH data available.