Limits...
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.


Related in: MedlinePlus

Optimal average spine volume  and conditional probability of spine formation P for different distributions of spine sizes.Panels (A) and (B) refer to “wire volume minimization”, whereas panels (C) and (D) correspond to “spine economical maximization”. (A) Non-monotonic dependence of spine volume  and (B) conditional probability P on r for wire fractional volume minimization (γ1 = 0). (C) Spine volume  and (D) conditional probability P decrease monotonically with increasing the exponent γ2. For all panels the same labels for curves corresponding to a given distribution were used, and they are identical to the labels used in Fig 5A and 5C. The curves for Log-logistic and Log-normal correspond to different values of the parameters, respectively, β and σ that yield the minimal ED for a given r or γ2. For all panels θ = 0.321 μm3.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4593638&req=5

pcbi.1004532.g007: Optimal average spine volume and conditional probability of spine formation P for different distributions of spine sizes.Panels (A) and (B) refer to “wire volume minimization”, whereas panels (C) and (D) correspond to “spine economical maximization”. (A) Non-monotonic dependence of spine volume and (B) conditional probability P on r for wire fractional volume minimization (γ1 = 0). (C) Spine volume and (D) conditional probability P decrease monotonically with increasing the exponent γ2. For all panels the same labels for curves corresponding to a given distribution were used, and they are identical to the labels used in Fig 5A and 5C. The curves for Log-logistic and Log-normal correspond to different values of the parameters, respectively, β and σ that yield the minimal ED for a given r or γ2. For all panels θ = 0.321 μm3.

Mentions: As was previously noted, for wire minimization principle (f = 1 in Eq 1) with γ1 > 0, we obtain , and consequently P = 1, both of which are unrealistic. For wire minimization with γ1 = 0 (wire volume minimization), both and P depend non-monotonically on the parameter r (Fig 7A and 7B). For short-range distributions of spine size, and P are positively correlated, whereas for the distributions with heavy-tails these two quantities are anti-correlated. Thus for wire minimization there is no clear one-to-one correspondence between average spine size and conditional probability of spine formation. Among all the distributions, for the optimal value of r (r ≈ 0.95), the heavy-tailed Log-normal produces the most realistic spine volume , i.e. the closest to the empirical values (0.2–0.4 μm3 for human and macaque monkey [41, 42]), regardless of the value of threshold θ (Table 2; Fig 7A). For short-tail distributions the values of are strongly threshold θ-dependent (Table 2).


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

Karbowski J - PLoS Comput. Biol. (2015)

Optimal average spine volume  and conditional probability of spine formation P for different distributions of spine sizes.Panels (A) and (B) refer to “wire volume minimization”, whereas panels (C) and (D) correspond to “spine economical maximization”. (A) Non-monotonic dependence of spine volume  and (B) conditional probability P on r for wire fractional volume minimization (γ1 = 0). (C) Spine volume  and (D) conditional probability P decrease monotonically with increasing the exponent γ2. For all panels the same labels for curves corresponding to a given distribution were used, and they are identical to the labels used in Fig 5A and 5C. The curves for Log-logistic and Log-normal correspond to different values of the parameters, respectively, β and σ that yield the minimal ED for a given r or γ2. For all panels θ = 0.321 μm3.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004532.g007: Optimal average spine volume and conditional probability of spine formation P for different distributions of spine sizes.Panels (A) and (B) refer to “wire volume minimization”, whereas panels (C) and (D) correspond to “spine economical maximization”. (A) Non-monotonic dependence of spine volume and (B) conditional probability P on r for wire fractional volume minimization (γ1 = 0). (C) Spine volume and (D) conditional probability P decrease monotonically with increasing the exponent γ2. For all panels the same labels for curves corresponding to a given distribution were used, and they are identical to the labels used in Fig 5A and 5C. The curves for Log-logistic and Log-normal correspond to different values of the parameters, respectively, β and σ that yield the minimal ED for a given r or γ2. For all panels θ = 0.321 μm3.
Mentions: As was previously noted, for wire minimization principle (f = 1 in Eq 1) with γ1 > 0, we obtain , and consequently P = 1, both of which are unrealistic. For wire minimization with γ1 = 0 (wire volume minimization), both and P depend non-monotonically on the parameter r (Fig 7A and 7B). For short-range distributions of spine size, and P are positively correlated, whereas for the distributions with heavy-tails these two quantities are anti-correlated. Thus for wire minimization there is no clear one-to-one correspondence between average spine size and conditional probability of spine formation. Among all the distributions, for the optimal value of r (r ≈ 0.95), the heavy-tailed Log-normal produces the most realistic spine volume , i.e. the closest to the empirical values (0.2–0.4 μm3 for human and macaque monkey [41, 42]), regardless of the value of threshold θ (Table 2; Fig 7A). For short-tail distributions the values of are strongly threshold θ-dependent (Table 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.


Related in: MedlinePlus