The pinwheel density is π

In this day and age when everything is dumbed down to a sound byte or an elevator pitch, the structure of organisms is distilled to the false conundrum of nature versus nurture. Alas, reality is much more complex. Although a cone in your retina has a matching DNA strand in its nucleus to the one in a cell in your armpit, the two cells are quite different.

The first lesson we learn is that what counts are not just the genes themselves, but which ones are expressed. For example, the genes encoding the peak spectral sensitivity for the L (red) and M (green) cones do easily get transposed, with the effect that the peak sensitivity moves. Yet, we cannot look at the DNA to determine if an observer has deficient color vision. What counts for the actual peak sensitivities are which genes are transcribed by the messenger RNA (mRNA). This can only be determined by looking a the actual opsin, there cannot be a genetic test for color deficiency because it is unethical to rip out somebody's retina. Fortunately, tests like the Ishihara Color Test and the Farnsworth-Munsell 100 Hue test do a good enough job that this is not an issue.

Another insight is epigenetics (C. H. Waddington, 1942). Today, the study of the environmental influence on our genome is a hot topic.

When we look at the brain, it appears that there is a skeleton that is present at birth. During the first period of life, the neurons grow and connect in response to stimuli, both real and virtual. This is for example why hospitals correct strabismus immediately after birth, because otherwise one eye never gets wired up to the visual system.

An interesting question is whether there are constraints on how neuronal preferences can develop. This is a problem that Fred Wolf of the Max-Planck-Institute for Dynamics and Self-Organization, at the Göttingen University has studied.

From the work of Hubel and Wiesel we know that in the visual cortex of carnivores and primates, neurons selective for the orientation of visual edges are organized in orientation columns, which are vertical arrays of neurons that prefer the same orientation.

In the figure, the column at the left is the legend for the color encoding of orientations. As shown in the inset, orientation columns are arranged around numerous singularities, called pinwheel centers. The mean number of pinwheels per orientation-hypercolumn area is called pinwheel density. The self-organization of orientation columns dominated by long-range interactions would explain a common design.

It can be shown mathematically, that for large interaction ranges, the mean pinwheel density predicted by the universal pinwheel statistics rapidly approaches an asymptotic constant equal to π.

Matthias Kaschube and his coworkers have performed a very rigorous experiment to measure the pinwheel statistics, which is described in a detailed 74 page paper Universality in the Evolution of Orientation Columns in the Visual Cortex.

They have studied the visual cortex of the tree shrew (Tupaia belangeri), galago (Otolemur crassicaudatus), and ferret (Mustela putorius) and measured the pinwheel density. The map labeled "original" in the above figure shows the orientation map from a galago visual cortex.

They also analyzed properties of orientation maps in ferrets reared in darkness beginning about 1 week before eye opening and the emergence of orientation maps, because dark-rearing alters the spatiotemporal pattern of activity in the afferent visual pathway, induces abnormal receptive field properties in the lateral geniculate nucleus and visual cortex, but does not prevent the formation of orientation maps.

Finally, they have compared the pinwheel density with randomly generated orientation maps (right map in the figure) obtained by randomizing the phases of the original measurements in the Fourier domain and then subjecting the randomized maps to the same preprocessing and analyses as the original data.

Only in the original maps the mean pinwheel density approaches an asymptotic constant equal to π.

Their empirical results and theoretical analyses suggest that the precise spatial organization of pinwheels in the visual cortex reflects cortical network self-organization rather than genetic prespecification or environmental instruction of neuronal circuit development. Their theory reveals that dynamic network self-organization can robustly constrain the spatial organization of cortical circuitry to a specific design.

Already in 1942, Waddington suggested that robustness of developmental processes may play an adaptive role in evolution, protecting developing organisms from both genetic and environmental perturbations by canalizing the physiological and anatomical organization of organisms into a much narrower range than might be expected from their genetic diversity.

If Kaschube's explanation of the common design is correct, its evolution represents a genuine example of such canalization through an emergent property of complex cortical networks expressed in long-separated mammalian lineages. Kaschube et al. conclude that wherever such complex biological systems unfold, especially in the mammalian brain where they are likely to abound, the principles of dynamic network self-organization may design and constrain system behavior as powerfully as an organism's genetic endowment or early life experiences.

Science 19 November 2010: Vol. 330 no. 6007 pp. 1113-1116 DOI: 10.1126/science.1194869