Technical Comments

Comment on “Universality in the Evolution of Orientation Columns in the Visual Cortex”

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Science  27 Apr 2012:
Vol. 336, Issue 6080, pp. 413
DOI: 10.1126/science.1205737


Kaschube et al. (Reports, 19 November 2010, p. 1113) argue that pinwheel density in three mammalian species follows a universal constant of π as predicted by their orientation-selective suppressive long-range connectivity model. We dispute their conclusions and suggest that a simple brain size–pinwheel density scaling law suffices in predicting the self-organized and disorganized orientation maps from primates to rodents.

Kaschube et al. (1) proposed that the emergence of orientation columns in visual cortex can be explained by a common design in a self-organized network with suppressive long-range connectivity. Based largely on theoretical grounds under a set of assumptions, their model predicts that the pinwheel density, defined as the average number of pinwheels per orientation-hypercolumn area, approaches a universal constant of π. Kaschube et al. reported that the precisely measured pinwheel densities in three mammalian species were virtually identical and approached the predicted value of π. These findings, if true, would be of fundamental importance in implicating a universal law in the self-organization of orientation columns across the mammalian phylum. However, several concerns arise that cast doubts on the validity of the proposed universal constant.

The notion of a common design for orientation maps across different mammalian species fundamentally runs counter to a classic animal scaling law, which states that many behavioral and physiological attributes scale in proportion to brain sizes (2). To test whether pinwheel density also obeys this scaling law or is constant at π, it is imperative to examine species with widely different brain sizes. Unfortunately, all three species studied by Kaschube et al. (ferret, galago, and tree shrew) are of similar sizes for primary visual cortex. While emphasizing the phylogenetic and ecologic diversity of these chosen species, the authors have unwittingly limited their data to a single point on the brain size scale (Fig. 1). Could the pinwheel density depart from the proposed constant value of π for much larger or smaller species? Interestingly, extant data in the literature suggest that absolute pinwheel density (number of pinwheels per mm2) may vary widely across different species (39). As summarized in Table 1, which is modified from a previous report by the same group (3), the pinwheel densities calculated from reported data for ferret and tree shrew consistently underestimate the value of π, whereas those for much larger species, such as macaque monkey, overestimate it. These estimates from early studies are necessarily imprecise because of the limitations of such measurements. Despite this, the remarkable correlation between the estimated pinwheel densities and sizes of primary visual cortex across a wide range of species (see Fig. 1) cannot be attributed to experimental errors and data variability alone, because any systematic or random errors would equally apply to studies in all animal species. The overestimation of the value of π in macaque is particularly revealing in light of the underestimation in ferret and tree shrew. In contrast, the authors’ decidedly precise measurements of pinwheel densities in three species with similar brain sizes cannot answer this very basic question about the effect of brain size scaling. To substantiate the proposed common design for orientation maps, the onus probandi is to demonstrate that the same universal constant of π for pinwheel density holds regardless of the brain sizes of the specific species chosen.

Fig. 1

Pinwheel densities (filled squares) versus primary visual cortex (V1) areas for different species. Filled squares give the mean pinwheel densities, and gray bars show the upper and lower range of the pinwheel densities estimated from different data sources listed in Table 1. The solid circle (in red) indicates two species (ferret and tree shrew) studied by Kaschube et al., both of which prove to be of similar V1 sizes (data for the V1 size of galago not available, although its body size is similar to that of ferret and tree shrew). Dashed circles indicate species with one order of magnitude larger (macaque monkey), similar (gray squirrel), and one order of magnitude smaller (mouse) V1 areas compared with species studied by Kaschube et al. The horizontal dashed line gives the reference level of π. Pinwheel density of macaque monkey overestimates the critical value of π, whereas those of ferret and tree shrew underestimate it. Such V1 size-dependent correlation cannot be attributed to systematic or random measurement errors alone. The pinwheel densities plotted in this figure are from Table 1. The V1 sizes are from (10, 11).

Table 1

Pinwheel density in different species. [Modified from (3)]

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Whereas definitive data for pinwheel density in larger and widely studied species such as cat and monkey showing unequivocal conformance to the proposed universal constant of π remain to be seen, the most telling evidence to date that pinwheel density may scale with brain sizes rather than being fixed at π comes from much smaller species such as small rodents (rats and mice), in which the primary visual cortex is one order of magnitude smaller than those of ferret and tree shrew (10, 11). It is well known that the visual cortex of rats and mice has a random salt-and-pepper arrangement of preferred orientations (12). Hence, the layout of orientation maps, if any, is totally fractured, and pinwheel density is virtually nil in these small animals (Fig. 1). Thus, size does matter. Apparently, the size of the visual cortex is not the only factor that may influence pinwheel density, because orientation maps are also absent in some larger rodents such as gray squirrel (10) and some lagomorphs such as rabbit (13) (Fig. 1). It has been suggested that differences in intracortical circuits may explain such anomalies (11, 12), further arguing against a common design in these circuits.

Kaschube et al. draw questionable conclusions based on experimental data from a singular subset of species, with limited applicability to the prediction of pinwheel densities across the mammalian phylum. We believe that a simple scaling law for brain size–pinwheel density correlation suffices in most cases in predicting the self-organized and disorganized orientation maps from primates to rodents.

References and Notes

  1. Acknowledgments: The work of Y.M. and C.-S.P. was supported in part by research grants from NIH. The work of S.T. was partially supported by a Grant-in-Aid for Scientific Research (21500268), Japan.
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