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William H. Calvin
University of Washington
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William H. Calvin

"Cortical Columns, Modules, and Hebbian Cell Assemblies"

as it appeared in
The Handbook of Brain Theory and Neural Networks, edited by Michael A. Arbib (Bradford Books/MIT Press), pp.269-272 (1995).

copyright ©1995 by William H. Calvin and MIT Press


Our cerebral cortex sits atop the white matter like a thin layer of icing, about 2 mm thick. About 148,000 neurons lay under each square millimeter; however, it is this "icing" that is horizontally layered, not the "cake" beneath. Neurons with similar interests tend to be vertically arrayed in the cortex, forming cylinders known as cortical columns (though they are sometimes elongated curtainlike bands); minicolumns. are about 30 um in diameter while macrocolumns are 0.4-1.0 mm.

The superficial cortical layers of the primary visual cortex in primates (V1) have regions that contain neurons particularly sensitive to color; these "blobs" selectively project to color-sensitive zones in area V2 called "stripes." The "blobs" are separated by macrocolumnar distances (Bartfeld & Grinvald, 1992), with surrounding regions containing neurons more sensitive to visual form than to color; however, only 30-35 percent of blob neurons are color-sensitive and many animals with poor color vision nonetheless have blobs. Besides the color stripes of V2, there are stripes in parallel which specialize in form, others in binocular aspects (Livingstone & Hubel, 1988).

Columns, barrels, blobs, and stripes have all been called cortical modules, and the term is frequently applied to any segmentation or repeated patchiness (Purves et al, 1992). By so loose a definition, both a dried-up river bed and the fur of a "marmalade" cat are also modular. Frequently there is no evidence of either function or detailed internal circuitry, just premature talk of "repeating patterns of circuitry" and "iterated modular units." Module is also loosely used by theoreticians to mean any functional grouping in the brain, also violating the notion of repeating standardized units. Some columns may indeed be modular by the usual conventions of modular furniture and modular electronics, but a favorite candidate for a higher-order module, the "hypercolumn," has now been shown not to be modular at all (Blasdel, 1992).

Why should neurons with similar functional specializations cluster together? Why should some clusters extend vertically through most of the cortical layers? The reasons could be functional (Bullock, 1980; Shaw et al, 1982) or merely an epiphenomenon of development (Purves et al, 1992). Here the problem will be approached via clustering tendencies provided by the cortex's horizontal connections (Katz & Callaway, 1992).

1.1 Layering and its Functional Correlates

Traditionally six neocortical layers were distinguished by neuroanatomists, but this has been subject to some lumping and splitting. Layers II and III can usually be lumped together, as when one talks of the superficial pyramidal neurons. But layer IV has had to be repeatedly subdivided in the visual cortex (IVa, IVb, IVcAlpha, IVcBeta).

Layer IV neurons send most of their outputs up to II and III. Some superficial neurons send messages down to V and VI, though most connect (either laterally or via U-fibers in white matter) in their own layers. Layer VI sends messages back down to the thalamus via the white matter while V sends signals to other deep and distant neural structures, sometimes even the spinal cord. A simple path would come into IV, then up to III, down to V or VI, and then back out of the cortex to some "subcortical" structure (White, 1989). So for any column of cortex, the bottom layers are like a subcortical OUT box, the middle layer like an IN box, and the superficial layers somewhat like an INTEROFFICE box connecting the columns and different cortical areas. These are not, of course, exclusive roles, e.g., VI pyramids also have axon branches extending horizontally to terminate in IV.Schematic of cortical layers

Traditionally, the association cortex was simply terra incognita, the 90% of human cerebral cortex that isn't motor strip or a primary sensory area. However, Diamond (1979) argues that the "motor cortex" isn't restricted to the motor strip but is the fifth layer of the entire cerebral cortex. That's because V, whatever the area, contains neurons that at some stage of development send their outputs down to the spinal cord, with copies to the brain stem, basal ganglia, and hypothalamus. Diamond likewise argues that the fourth layer everywhere is the "sensory cortex" and that second and third layers everywhere are the true "association cortex." Calvin (1994) argues that the superficial layers have the right properties to implement darwinian processes on the time scale of thought and action.

1.2 Columnar Clustering

A given neuron, however, may have dendrites spanning a few layers, especially if it is a pyramidal neuron: these taproot-shaped cells are the excitatory neurons of neocortex. The other neuron types are thought to be inhibitory (exception: IV's spiny stellate neuron is excitatory). In Nissl stains that show only cell bodies of neurons, Ramon y Cajal saw narrow columns (hereafter, minicolumns) running from white matter to the cortical surface; the cell-sparse gaps are about 30 um apart in human cortex. It now appears that the gaps are vertical bundles of axons and apical dendrites. In monkeys, these minicolumns are 31 um diameter but in cats they are about twice that diameter (Peters & Yilmaz, 1993). In monkey, there are about 100 neurons in such a minicolumn (143 in V1), 39 of which are superficial pyramidal neurons.

The human cerebral cortex totals 2,200 cm2; unfolded, it would fit on four sheets of letter-sized paper. That of the apes would fit on a single sheet, that of cats and monkeys on a postcard, and that of a rat on a small postage stamp. On the basis of layering differences, there are 52 "areas" in each human hemisphere; a Brodmann area averages 21 cm2 and 250 million neurons grouped into several million minicolumns. Physiologically, there are aggregations (hereafter, macrocolumns) which would seem to contain, at most, a few hundred minicolumns; this may be secondary to an organization of the input wiring into projection macrocolumns (see Figure).

In 1957, Mountcastle and coworkers discovered a tendency for somatosensory strip neurons responsive to skin stimulation (hair, light touch) to alternate with those specializing in joint and muscle receptors about every 0.5 mm. It now appears that there is a mosaic organization of similar dimensions, the neurons within each macrocolumn (or "segregate") having a receptive field optimized for the same patch of body surface (see Favorov & Kelly, Somatosensory system). Hubel and Wiesel, recording in monkey visual cortex, saw curtainlike clusters ("ocular dominance columns") which specialized in the left eye, with an adjacent cluster about 0.4 mm away specializing in the right eye.

Orientation columns are of minicolumn dimensions, within which the neurons prefer lines and edges that are tilted about the same angle from the vertical; there are many such minicolumns specializing in various angles within an ocular dominance macrocolumn (Hubel & Wiesel, 1977). The visual cortex provides us with our best insights into cortical circuitry (see Lund et al, Visual cortex). The relationships between minicolumns and macrocolumns are best seen there (see Miller, Ocular dominance and orientation columns), though it is hazardous to generalize because ocular dominance columns themselves are less than universal, e.g., they are not a typical feature of New World monkeys.

1.3 Horizontal Organization in Neocortex

Lateral connections in an array are similar to the relaxation algorithms used for neurallike problem-solving. Recurrent inhibition is thought, in cortex as elsewhere, to provide an antagonistic organization that sharpens responsiveness to an area far smaller than would be predicted from the anatomical funneling of inputs (see Barlow, Lateral inhibition). Recurrent excitation may be especially prominent in the superficial layers of primate neocortex. The superficial pyramids send myelinated axons out of the cortical layers into the white matter; their eventual targets are typically the superficial layers of other cortical areas when of the "feedback" type; when "feedforward" they terminate in IV and deep III. Long corticocortical terminations are often organized into interdigitating macrocolumns.

But superficial pyramidal neurons also send unmyelinated collaterals to adjacent superficial pyramids: roughly 70 percent of the excitatory synapses on any superficial pyramid (but less than 1 percent of those on layer V pyramids) are derived from pyramidal neurons less than 0.3 mm away. In general, the average cortical neuron contacts fewer than 10 percent of all the neurons in that radius, so superficial pyramids may be said to have an unusually strong propensity to excite one another.

There is also an unusual patterning to such superficial connections that suggests a columnar organizing principle. The collateral axon travels a characteristic lateral distance without giving off any terminal branches; then it produces a tight terminal cluster (see Fig. 5 in Gilbert, 1993). The distance to the center of the terminal patch is about 0.43 mm in primary visual cortex, 0.65 mm in the secondary visual areas, 0.73 mm in sensory strip, and 0.85 mm in motor cortex of monkeys (Lund et al, 1993). The axon may then continue for an identical distance and then produce another cluster, and this occasionally continues for some mm.

Because of this local standard for axon length, recurrent excitation becomes probable among some cell pairs. Horizontal connections are also found among the pyramidal neurons of V and VI, but the regular spacing has been noted only for the pyramids of the superficial layers. In the absence of simultaneous recordings at appropriate spacings, we can only guess at the consequences of the mutual re-excitation. Even if the synaptic strengths were high, much longer axons would be required to give conduction times that escape refractoriness and create (even briefly) the proverbial reverberating circuit (corticocortical conduction velocities are about 0.3-0.5 mm/msec).

1.4 Synchrony-shaped Connectivity

Recurrent excitation, however, can induce synchrony: even weak coupling between relaxation oscillators is known to quickly produce entrainment (see Segundo, Stiber, & Vibert, Entrainment and synaptic coding of spike trains). Were the cells otherwise active, they would soon tend to produce some spikes at about the same time. Cells in cortical minicolumns often fire in synchrony; more widespread synchronized firing has been a recent theme in cortical neurophysiology; such synchrony occurs more frequently during difficult tasks and is the best-known correlate of perceptual binding (see Singer, Synchronization of neuronal responses as a putative binding mechanism).

Synchronized firing in the context of the superficial layers of neocortex has some important implications for synaptic enhancement. The local field potentials associated with synchronized firing have their source in the superficial layers. The long-term potentiation (LTP; it is dependent on sufficient postsynaptic depolarization by other inputs) demonstrated in motor cortex is confined to those layers, and that is where most N-methyl-d-aspartate (NMDA) receptors for glutamate are located.

In such a system, near-simultaneous arrivals may enhance the synaptic strength of the coincident inputs -- but, even more importantly, repeated coincidences should be particularly effective in NMDA-like synapses. One can imagine synchronous "test patterns" during development serving to shape up adult cortical connectivity via use dependence and selective survival. The superficial pyramid's lateral connections suggest that they could organize synchronous clusters about 0.4 mm apart in primary visual cortex -- which happens to be the approximate size of the macrocolumns of Area 17, the ocular dominance columns. It is thought that ocular dominance columns are organized by a gradual segregation of geniculate afferents into layer IV, but such selective survival might be secondary to neural activity during development and thus dependent on connectivity in the superficial layers.


2.1 Permanent and Temporary Macrocolumns

Given that both are about a half millimeter, what is the relationship between the permanent macrocolumns and the ephemeral entrained pairs, whose synchrony can be destroyed in an instant by a wave of inhibition?

Entrained cells probably form triangular mosaics on occasion, given that a superficial pyramid sends axon collaterals in many directions. Two entrained cells may send axon terminals to an equidistant point, with impulses arriving simultaneously, and so entrain it as well. This equilateral triangle forms the basis of a triangular mosaic; the spacing will be the local metric, whether 0.43 mm or 0.85 mm (hereafter, simply "0.5 mm"). Because the basis of recruitment and entrainment is conduction time, not distance per se, various distortions of the triangular mosaic might be seen if conduction velocity (typically 0.3-0.5 mm/msec within cortex) and synaptic delay are not constant.

Just from the geometry, the overall impression should be like that of wallpaper, where corresponding points in a repeating pattern can be identified -- but where the "origin" of the pattern cannot necessarily be identified. One can, however, artificially inscribe a boundary such that homologous points are approached but not included. If one does this with many neighboring points, each of which is part of a different triangular mosaic, the largest possible "unit area" without repetitions will be hexagonal in shape. The distance between parallel sides of the hexagon will be 0.5 mm as well. Like the wallpaper's unit pattern, this hexagon need not have a unique "origin" and it might be meaningless to speak of a hexagonal boundary unless underlying resonances with synaptic strengths were so organized. One could speak (Calvin & Ojemann 1994) however, of this hexagonal unit pattern being laterally copied or cloned, thanks to the triangular mosaic tendencies of recurrent excitation among superficial pyramids.

Because a pair of synchronized neurons could form a triangular mosaic that is not parallel to the others, hexagonal mosaic cloning depends, in effect, on two identical and adjacent hexagons of spatiotemporal patterning. This parent pair could be due to evoked activity in an input pathway, or the initial spatiotemporal pattern could be generated by cortical connectivity just as the gaits of locomotion are generated by spinal cord circuitry. The spatial-only connectivity patterns in cortex that generate the spatiotemporal firing patterns could themselves be contained in adjacent hexagons; were this visible to anatomical or physiological techniques, we might consider it a permanent macrocolumn. Otherwise, we would merely see transient physiological ensembles of macrocolumnar dimensions with hexagonal repeats.

2.2 Modular Aspects

It is widely expected that cerebral cortex will turn out to have circuits which, in different cortical patches, are merely repeats of a standard pattern. However, module has instead been loosely applied to a wide range of functional or anatomical collectives. A true module would be a cortical patch which, whatever the origin of its inputs or the destination of its outputs, nonetheless has an internal architecture which is the same from one instance to another, with only minor differences in local tuning. The best candidate for a true module was the "hypercolumn" (Hubel & Wiesel, 1977): two adjacent ocular dominance columns, each containing a full set of orientation columns. Adjacent hypercolumns would merely represent different patches of the visual field; inputs and outputs might differ, but internal wiring should be similar from one hypercolumn to the next.

However, newer mapping techniques have shown that ocular dominance repeats are somewhat independent of orientation column repeats (Blasdel, 1992), making adjacent hypercolumns internally nonidentical, i.e., not iterated. For this reason, "hypercolumn" now appears with scare quotes around it in the visual system literature. No current use of "cortical module" bears any relationship to the technological use of the term; cortical cluster would be a more appropriate term.

2.3 The Hebbian Cell Assembly

Representations via a pattern are familiar from the trichromatic theory of color perception and the similar aspects of taste. Evoking the memory of your grandmother's face is probably not a matter of activating a single specialized neuron; rather, it is thought to involve the activity pattern in an ensemble of cortical neurons, each of which helps to implement other memories as well. Different sensory or motor schemas might be characterized by different firing patterns in time and space, each characteristic spatiotemporal pattern serving as a code for an item from an individual's memory.

Memory recall may consist of the creation of a spatiotemporal sequence of neuron firings, probably one similar to that present at the time of the input to memory, just shorn of some of the nonessential frills that promoted it. It would be like a message board in a stadium, with lots of little lights flashing on and off, but creating a pattern. A somewhat more general version of a Hebbian cell assembly (Calvin & Ojemann 1994) would avoid anchoring the spatiotemporal pattern in particular cells, to make it more like the way the message board can scroll. The pattern continues to mean the same thing, even though it's implemented by different lights. Though we tend to focus on the lights which turn on, note that lights which remain off also contribute to the pattern.

The notion of convergence zones for associative memories raises the issue of maintaining the identity of a spatiotemporal code during long-distance corticocortical transmission, such as through the corpus callosum. Distortions of the spatiotemporal pattern by a lack of precise topographic mappings might be unimportant where the information flows in only the one direction. But because the connections between distant cortical regions are typically reciprocal, any distortions of the original spatiotemporal firing pattern during forwards transmission would need to be compensated in the reverse path in order to maintain the characteristic spatiotemporal pattern as the local code for a sensory or motor schema. In addition to inverse transforms or error-correction mechanisms, degenerate codes seem possible (as when six different RNA triplets all code for leucine).

Error correction is particularly interesting because reliable copying capabilities often provide insight into possible codes, e.g., the genetic code puzzle was solved after identifying which physical patterns could be readily duplicated. Are there physiological clones of cerebral schemas that might help us identify a cerebral code such as the relevant Hebbian cell assembly?

Spatiotemporal pattern copying was inferred from the need to reduce timing jitter during precision throwing using Law of Large Numbers averaging. The triangular mosaic of electrical activity predicted from standard-length axons has an inherent error-correction property that can maintain spatiotemporal patterns during copying, so long as they are small enough to fit inside a macrocolumn-sized hexagon of cerebral cortex. This suggests that hexagonal Hebbian cell assemblies could implement a cerebral code (Calvin, 1994).


* especially suitable for getting oriented

Bartfeld, E., and Grinvald, A., 1992, Relationships between orientation-preference pinwheels, cytochrome oxidase blobs, and ocular-dominance columns in primate striate cortex. Proc. Natl. Acad. Sci. USA 89:11905-11909.

*Blasdel, G.G., 1992, Orientation selectivity, preference, and continuity in monkey striate cortex. J. Neurosci. 12:3139-3161.

Bullock, T.H., 1980, Reassessment of neural connectivity and its specification, in Information Processing in the Nervous System, (H.M. Pinsker and W.D. Willis, Jr., Eds.), New York: Raven Press, pp.199-220.

Calvin, W.H., 1994, The emergence of intelligence. Scientific American 271(4):100-107.

Calvin, W.H., Ojemann, G.A., 1994, Conversations with Neil's Brain: The Neural Nature of Thought and Language. Reading MA: Addison-Wesley.

Diamond, I., 1979. The subdivisions of neocortex: A proposal to revise the traditional view of sensory, motor, and association areas, in Progress in Psychobiology and Physiological Psychology 8 (J.M. Sprague, A.N. Epstein, Eds.), New York: Academic Press, pp. 1-43.

Gilbert, C.D., 1993, Circuitry, architecture, and functional dynamics of visual cortex. Cerebral Cortex 3:373-386.

Goldman-Rakic, P., 1990. Parallel systems in the cerebral cortex: the topography of cognition, in Natural and Artificial Parallel Computation (M.A. Arbib, J.A. Robinson, Eds.), Cambridge: M.I.T. Press, pp.155-176.

Hubel, D.H., Wiesel, T.N., 1977, Functional architecture of macaque visual cortex. Proc. Roy. Soc. (London) 198B:1-59.

Katz, L.C., Callaway, E.M., 1992, Development of local circuits in mammalian visual cortex. Ann. Rev. Neurosci. 15:31-56.

*Livingstone, M.S., Hubel, D.H., 1988, Segregation of form, color, movement, and depth: Anatomy, physiology, and perception. Science 240:740-749.

Lund, J.S., Yoshioka, T., Levitt, J.B., 1993, Comparison of intrinsic connectivity in different areas of macaque monkey cerebral cortex. Cerebral Cortex 3:148-162.

*Mountcastle, V.B., 1979, An organizing principle for cerebral function: The unit module and the distributed system, in The Neurosciences Fourth Study Program (F.O. Schmitt and F.G. Worden, Eds.). Cambridge: MIT Press, pp.21-42.

Favorov, O.V., Kelly, D.G., 1994, Minicolumnar organization within somatosensory cortical segregates: I. Development of afferent connections. Cerebral Cortex 4:408-427.

Peters, A., Yilmaz, E., 1993, Neuronal organization in area 17 of cat visual cortex. Cerebral Cortex 3:49-68.

*Purves, D., Riddle, D.R., LaMantia, A-S., 1992. Iterated patterns of brain circuitry (or how the cortex gets its spots). Trends in the Neurosciences 15:362-368 (see letters at 16:178-181).

Shaw, G.L., Harth, E., Scheibel, A.B., 1982, Cooperativity in brain function: assemblies of approximately 30 neurons. Exp. Neurol. 77:324-358.

White, E. L., 1989. Cortical circuits Boston: Birkhauser.

The figure is NOT the exact one which appears in the handbook but an improved one which appears in W. H. Calvin, The Cerebral Code (MIT Press 1996). || Home Page || Calvin publication list || My Science Surf column || The Calvin Bookshelf || Revised 5 December 1996