The circuitry of the brain is too complex to be completely specified by genetic information – at least not down to the level of each connection. There are hundreds of billions of neurons in your brain, each making an average of 1,000 connections to other cells. There are simply not enough genes in the genome to specify all of these connections.

What the genetic program can achieve is a very good wiring diagram of initial projections between neurons in different brain areas (or layers or between particular cell types). This circuitry is then refined and elaborated at the cellular level by processes of activity-dependent development, under the principle that “cells that fire together, wire together”. The circuitry of the brain is thus a self-organising system, which assembles under the influence of local interactions, mediated first by molecular interactions and second by patterns of electrical activity.

A new study highlights an important additional factor that allows global patterns of nerve projections, or “neural maps”, to emerge from these local interactions. Neural maps are systematic representations of sensory information across the surface of the brain. A study of the structures of visual maps across a range of quite distantly related species reveals a universal pattern and argues strongly that it cannot be explained by either genetic or environmental instructions but instead arises due to self-organising principles. Remarkably, mathematical descriptions of these principles fit the observed structures extremely well and reveal that one important structural parameter is constant across all species and equal to the mathematical constant π.

Obtaining such a robust mathematical result in any biological system is a rare event and reinforces the view that it reflects a fundamental principle of self-organising systems. To understand the significance of this result, we need to examine the organisation of the visual system in more detail. Starting in the retina, the visual system is built up in a hierarchical series of relays. At each level, the system is wired to combine and compare inputs from neighbouring cells in the preceding level. In this way, more and more complex and global patterns of visual objects can be extracted (starting with dots, then lines, then parts of shapes, simple geometrical shapes and eventually complex objects).

Photons of light are initially detected by photoreceptors in the retina. Each single photoreceptor at any given moment registers light coming into the retina from a particular point of visual space. These cells relay information through a series of layers to the retinal ganglion cells, which are the output cells of the retina. Importantly, each ganglion cell integrates information from multiple, neighbouring photoreceptors. These connections can be either excitatory or inhibitory. A single ganglion cell is usually most strongly activated when a central photoreceptor is active but its neighbours are not. This means that ganglion cells are particularly sensitive to areas of visual space with high contrast – where there is an edge of an object, for example. (If the light across the visual field is uniform then the ganglion cells are less active).

Retinal ganglion cells project in turn to the visual thalamus, which relays this information to the primary visual cortex (area V1). Cells in V1 integrate information from multiple retinal ganglion cells, extracting more high-level features of the visual information. In particular, many cells in V1 respond best to short lines – you can imagine how such a response can be achieved by integrating inputs from neighbouring retinal ganglion cells, each responding to high contrast in a central domain (a line in visual space would then maximally excite these cells, compared to a solid block for example).

Depending on the layout of the ganglion cells whose inputs are integrated, each cell in V1 will be most sensitive to lines of a particular orientation (vertical, horizontal, diagonal). This sensitivity can be directly observed by using electrodes to record the responses of cells in V1 when an animal is shown various visual stimuli. The ground-breaking work of Hubel and Wiesel first revealed the remarkable preferences of individual cells for lines of different orientation. It also revealed another important principle, which is that the organisation of these cells with respect to each other is highly structured.

This structure is apparent at two levels: first, cells with similar orientation selectivity form small clusters, called columns (because the selectivity actually extends in a column across the six layers of the cortex). Second, clusters are laid out across the surface of V1 in a non-random pattern characterised by a “pinwheel” structure, where the direction of orientation selectivity varies smoothly across neighbouring columns, which are arranged in a spiral fashion around the pinwheel centre. (The diagram represents the layout of columns with different orientation selectivities, denoted by the colour code).

Not all species show these properties. Cells in visual cortex of rodents, for example, are selective for particular orientations of stimuli but they are not clustered – individual cells are effectively scattered across V1. But wherever clustering is observed, the pinwheel organisation is also observed. This is true across multiple species where it must have evolved independently. This result is not trivial – there are many other ways that these maps could theoretically be structured (stripes, lattices, etc.). So why do they emerge in this particular pattern?

To investigate this, Matthias Kaschube, Fred Wolf and colleagues analysed the orientation maps in three distantly related species: ferrets, tree shrews and galagos. Tree shrews, despite their name, are not rodents but a sister group of primates. Ferrets are on the carnivore branch and galagos, also known as bush-babies, are primates. Importantly, these three species have quite different habits and ecological habitats, arguing against any commonalities in environmental experience as driving similarities in the organisation of visual maps.

All three species show orientation columns and all show the pinwheel organisation. However, the sizes of individual columns vary considerably across these species and even across individuals within each species. To determine whether there was really any universality in the organisation of these maps, the authors painstakingly measured a range of parameters across many individuals. These parameters include the average column size, the average distance between columns of the same orientation preference and the density of pinwheel centres. They found that the pinwheel density, in relation to the other parameters, was constant across all species.

Not fairly constant or kind of constant – really constant (or as close as one could ever expect in a biological system). And not only was it constant in the sense that it was consistent – the value was equal to a mathematical constant: π (pi, the ratio of a circle’s circumference to its diameter). This had been predicted from mathematical models of the underlying processes, which I wish I understood better. Even though they are all Greek to me, the fact that the value is not just some arbitrary number indicates that it reflects a fundamental mathematical constraint on the self-organisation of this system.

The authors show that this constraint is most likely imposed by the pattern of long-range connections, which link columns of similar orientation selectivity. These horizontal connections, which are formed in an activity-dependent manner, impose a more global structure on the layout of columns and constrain the possible organisation of the map as a whole.

The results of this study argue strongly that neither genetic nor environmental instruction is sufficient to generate the observed pattern. Instead, given a set of initial conditions and biochemical algorithms instructing changes in connectivity based on local interactions, global patterns will emerge based on very general mathematical principles of self-organising systems.

Kaschube M, Schnabel M, Löwel S, Coppola DM, White LE, & Wolf F (2010). Universality in the evolution of orientation columns in the visual cortex. Science (New York, N.Y.), 330 (6007), 1113-6 PMID: 21051599