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SUPPLEMENTARY MATERIAL: There are now animated illustrations for the spatiotemporal patterns.

A book by
William H. Calvin
Thinking a Thought in the Mosaics of the Mind
MIT Press
copyright ©1996 by William H. Calvin

Cloning in Cerebral Cortex

All scribes, however careful, are bound to make a few errors, and some are not above a little willful "improvement." If they all copied from a single master original, meaning would not be greatly perverted. But let copies be made from other copies, which in their turn were made from other copies, and errors will start to become cumulative and serious. We tend to regard erratic copying as a bad thing, and in the case of human documents it is hard to think of examples where errors can be described as improvements. I suppose the scholars of the Septuagint could at least be said to have started something big when they mistranslated the Hebrew word for "young woman" into the Greek word for "virgin," coming up with the prophecy: "Behold a virgin shall conceive and bear a son. . . ." Anyway, as we shall see, erratic copying in biological replicators can in a real sense give rise to improvement, and it was essential for the progressive evolution of life that some errors were made.
    Richard Dawkins, The Selfish Gene, 1976

This is the hardest chapter in the whole book. In it, I have to delve into the neuroanatomy and neurophysiology of cortical neurons, importing lessons from such seemingly unrelated subjects as synchronously flashing fireflies. By the end of this chapter, I will have shown how copying could arise in neocortex. By the end of the sixth chapter, the cortical equivalents of all the darwinian essentials and all the accelerating factors will have been examined. But it gets easier, not harder, starting with the fourth chapter.


    Neurophysiologists distinguish between cell properties and circuit properties, much as biologists distinguish between genotype and phenotype. Some phenomena are clearly due to the circuit rather than the cells involved, to the wiring rather than the components -- a new property "emerges" from the particular combination. You won't find it in any one neuron. The classical example of an emergent property involves lateral inhibition and it is the reason that Keffer Hartline got a Nobel Prize in 1967.

    Thanks to local activity contributing to a ring of depression in surrounding neurons, lateral inhibition sharpens up fuzzy boundaries. Compound eyes, the many narrow-angle photoreceptors of which provide an extreme case of fuzzy optics, have a series of inhibitory interconnections that are capable of recreating a light-dark boundary in the environment, restoring much of what was lost.

    But lateral inhibition also has a tendency to produce features where none exist, illusions such as the Mach bands that you see if looking through a narrow slit between your fingers. Georg von Békésy, whose studies of such sideways interactions in the cochlea were the subject of his 1961 Nobel Prize, also produced illusions from skin surfaces, to illustrate the generality of the lateral inhibition principles. Antagonistic surrounds ("Mexican hats") are common in all the first half-dozen stages of the analysis of a visual image, though they become somewhat elongated and asymmetric ("Australian bush hats") in primary visual cortex. Because of the many axon collaterals that branch laterally in neocortex, lateral inhibition extends several millimeters.

    Both the sharpening of fuzzy boundaries and the illusions are emergent properties of a laterally inhibiting neural network. What might be the emergent consequences of lateral excitation?

There is good reason to worry about recurrent excitation. It is potentially regenerative, in the same sense as a string of firecrackers. It is also the most prominent wiring principle of mammalian neocortex.

    A few words about cerebral cortex, the icing on the brain's cake: in this cake, it's the frosting that has the appearance of layering! Six layers are usually identified on the basis of cell size or axon packing density, though we sometimes subdivide it further (in primary visual cortex, one talks about layers 4a, 4b, 4c , and 4c ). At other times, we lump layers together: when I mention the "superficial layers," I'm combining layers 1, 2, and 3.

    Furthermore, there are three functional groupings that have become apparent: on the analogy to the mail boxes stacked on many a desk, layer 4 could be said to be the IN box of neocortex, because most of the inputs from the thalamus terminate there. The deep layers could be called the OUT box, as pyramidal neurons of layers 5 and 6 send axons outside the cortex, back to thalamus or down to the spinal cord, and so forth. The neurons of the superficial layers seem to constitute the INTERNAL mailbox of the neocortex, specializing in the interoffice memos. Interactions among the superficial pyramidal neurons are what this book is mostly about, as these neurons seem capable of implementing a darwinian copying competition, one that can shape up quality from humble beginnings.

    The axons of the superficial pyramidal cells are prominent in the corpus callosum and other long corticocortical paths, but also in the intrinsic horizontal connections: those axon branches that never leave the superficial layers because they run sideways. They preferentially terminate on other superficial pyramidal neurons -- and in a patterned manner, too. Some axon branches go to near neighbors, but the ones that go further ignore a whole series of intermediate neurons before communicating with those about 0.5 mm distant.

    Those sparsely populated gaps are something like the Sherlock Holmes story about the dog that didn't bark in the night. It took a long time before anyone noticed this fact. In 1975 came the first hint of these gap patterns. In 1982, when Jennifer Lund and Kathleen Rockland first studied the gaps in the superficial layers' intrinsic horizontal connections, it was in the visual cortex of the tree shrew. Though the gap distance varies, we now know that it is a common arrangement for many areas of neocortex, and for many animal species. Thanks to the detailed reconstructions of several HRP-injected superficial pyramidal neurons by Barbara McGuire and her colleagues, we also know that these synaptic connections are likely to be excitatory, probably using glutamate as their neurotransmitter, and that their predominant targets are other superficial pyramidal neurons.

    Their axons have dozens of branches, going sideways in many radial directions, fanning out eventually into thousands of axon terminals. Although no single superficial pyramidal neuron has enough terminals to fill in a doughnut, we might expect a small minicolumn group of such neurons to produce a ring of excitation, as well as the central spot of excitation from the branches to immediate neighbors. Point-to-area is the more common arrangement for axon projections, such as those of the pyramidal neurons of the deep layers. Recurrent inhibition is also seen, but only the recurrent excitation of the superficial layers of neocortex has this Sherlock-Holmes feature of prominent silent gaps.

    Optical imaging techniques that look down on the brain's surface are now capable of resolving a spread of activity in cortex. Stimulation of a restricted area of retina, of a type that classically would be expected to concentrate cortical activity in only one area of the exposed cortical surface, is now seen to contribute to multiple hot spots of activity at macrocolumnar separations, much as predicted.

    The neocortical versions of long-term potentiation (LTP) are also concentrated in the superficial layers. We know that N-methyl-d-aspartate (NMDA) types of postsynaptic receptors, which have the unusual characteristic of augmenting their strength when inputs arrive in clusters (such as quasi-synchronously from different sources), are especially common in the superficial layers.

    All of this raises the possibility of self-reexciting loops, not unlike the reverberating circuits postulated for the spinal cord by Rafael Lorente de Nó in 1938, in the very first volume of the Journal of Neurophysiology. If the synaptic strengths are high enough, and the paths long enough to escape the refractory periods that would otherwise limit re-excitation, closed loops of activity ought to be possible, impulses chasing their tails. Moshe Abeles, whose Jerusalem lab often observes more than a dozen cortical neurons at a time, has seen some precise impulse timing of one neuron, relative to another, in premotor and prefrontal cortex neuron ensembles. It is unknown whether or not these firing patterns represent reverberation, in Lorente's original sense of recirculating loops. These long, precisely-timed firing patterns are important for the notion of spatiotemporal patterns that I will later develop.

Emergent synchrony is well known as a commonplace consequence of recurrent excitation, one that ought to be seen with even weak connection strengths and short paths. In 1665, the Dutch physicist Christiaan Huygens noticed that two pendulum clocks hanging from a common support were synchronized. When he disturbed the synchrony, it returned within a half hour. Harmonic oscillators are slower to entrain than nonlinear relaxation oscillators, which can take just a few cycles.

    The most famous example of entrainment is probably menstrual cycles in women's dormitories. More dramatic in appearance is a whole tree filled with little lights, flashing in unison. No, I don't mean a Christmas tree wired up, under the control of a single flasher -- there's a natural, wireless example based on hundreds of independent oscillators. The little lights are hundreds of fireflies, and they have no leader to set the pace.

Imagine a tree thirty-five to forty feet high, apparently with a firefly on every leaf, and all the fireflies flashing in perfect unison at a rate of about three times in two seconds, the tree being in complete darkness between flashes. Imagine a tenth of a mile of river front with an unbroken line of mangrove trees with fireflies on every leaf flashing in synchronization, the insects on the trees at the ends of the line acting in perfect unison with those between. Then, if one's imagination is sufficiently vivid, he may form some conception of this amazing spectacle.

    It doesn't require any elaborate notions of mimicry to account for the firefly entrainment; even small tendencies to advance to the next flash when stimulated with light will suffice to create a "rush hour." Furthermore, you usually do not see waves propagating through such a population, except perhaps when the flashing is just beginning or ending. Even in cortical simulations with propagation delays, near-synchrony is seen, in much the way (anomalous dispersion) that some velocities can exceed the speed of light.

    Weak mutual re-excitation (a few percent of threshold) is quite sufficient to entrain; one need not postulate strong connection strengths in the manner needed for Lorente's recirculating chains. So long as the neurons (or fireflies) already have enough input to fire repeatedly, there will be an entrainment tendency if they mutually re-excite one another. And that is exactly what superficial pyramidal neurons, 0.5 mm apart, seem so likely to do. The triple combination -- mutual re-excitation, silent gaps that focus it, and the resulting entrainment tendencies -- is what gives the superficial layers of neocortex the potential of being a Darwin Machine.

SUPPLEMENTARY MATERIAL: There are now animated illustrations for the spatiotemporal patterns.

Looking down from on high at the superficial layers of neocortex, in what the neuroanatomists call "tangential slices," is like looking down on a forest from a balloon. Any one neuron is seen in a top-down perspective, orthogonal to that seen from the side in the usual surface-to-depth slice. Like the branches of any one tree, any one neuron has a dendritic tree, but also an axon tree, much as the forest's tree has branching roots below ground.

    The axon of a single superficial pyramidal neuron will be seen to spread in many directions. Though sensory neurons and motor neurons may vary, the average interneuron sends out as many synapses as it receives, usually between 2,000 and 10,000. Not enough radial plots have yet been done to know how symmetric the horizontal spread is, but it seems clear that the axon branches travel in many directions from the cell.

    The distance from the cell body to the center of the axon terminal cluster, studied mostly in the side views, is not the same in all cortical areas. That "0.5 mm" mentioned earlier is really as small as 0.4 mm (in primary visual cortex of monkeys) or as large as 0.85 mm (in sensorimotor cortex). It scales with the width of the basal dendritic tree. I'll use 0.5 mm as my standard example of this local metric; it corresponds to a basal dendritic tree of about 0.25 mm spread, which is also about the spread of one cluster of axon terminals and the extent of one silent gap.

    If two superficial pyramidal neurons, about 0.5 mm apart, are interested in the same features because of similar inputs and thresholds, their spike trains ought to start exhibiting occasional spike synchrony. It need not be all the spikes from each neuron for the following analysis to be relevant; only some of their spikes need synchronize via the recurrent excitation.
    There should also be some minor tendency for two such cells, already firing repeatedly, to recruit another cell 0.5 mm away that is almost active. If that third superficial pyramidal neuron becomes active, we should see three often-synchronized neurons forming an equilateral triangle. But that is not the end of it: there is a second site receiving synchronous input from the parent pair (this is exactly like that elementary exercise in plane geometry where a compass is used to bisect a line or drop a perpendicular). So a fourth neuron might join the chorus.

    And because the third and fourth cells provide new annuli of excitation, either can combine with one of the first pair to bring a fifth point into synchrony. What we have, it is apparent, is a mechanism for forming up a triangular array of some size, nodes of synchronized activity 0.5 mm from corresponding cells of this chorus. It could work either by synchronizing preexisting activity or by recruiting otherwise subthreshold neurons at the nodes. Once a potential node is surrounded by a few synchronous nodes exciting it, there ought to be a hot spot, an unusually effective convergence of simultaneous inputs.

    This triangular array annexation tendency is not unlimited. (Regions with insufficiently excited neurons, as I discuss in the latter part of chapter 6, provide barriers to any further empire-building.) And the triangular array is surely ephemeral, here now and gone in seconds. When it is shut down by enough inhibition (or reduction of excitation), it will be as if a blackboard had been erased.

    Traces will linger, however, in much the way that blackboards retain ghostly images of former patterns. The synaptic strengths should remain changed for a while; indeed, the synchrony-sensitive long-term potentiation of the superficial neocortical layers suggests that synaptic strength can remain augmented for many minutes. This will make it easier to recreate the active form of the triangular array -- perhaps not all of its spatial extent, but part of it.

The lattice connectivity seen in the anatomy, it should be said, does not fall into neat triangular arrays, measured by distance in the tangential plane of section. Though the neuroanatomists speak of "polka-dot" patterns and "lattices" for the axon terminal clusters in the superficial layers, the spacing of the clusters is only roughly triangular. Of course, adjusting conduction velocity or synaptic delay during a tune-up period could make a triangular array, when replotted as "driving time" rather than distance.

    But not even an equal conduction time, for converging simultaneously on a potential recruit, is actually required for the present theory. Though exact synchrony has been convenient for introducing the principles, all that triangular arrays require in the long run is a prenatal tune-up period that results in a good-enough self-organization, so that most of the six surrounding nodes produce axon clusters that mutually overlap in a manner that aids entrainment. It may not matter to this self-organizing principle what an external observer would find "regular." I'll stick to triangular array terminology for the theory, but don't expect to find exact triangles in either the anatomy or physiology, only good-enough approximations.

From a pair of like-minded cells, we see the possibility of a large chorus, all singing in synchrony. Furthermore, it's a chorus that can recruit additional members out on its edges. Like a choir standing on risers, these singers tend to space themselves so that each is standing in between two singers on the row below. The choir isn't as perfect a triangular array as the fruit displays at your corner grocery, but it's a good enough approximation to the familiar packing principle.

    So far, this choir only chants in unison. It's monomaniacal, perhaps only interested in one feature of the stimulus. It's surely not the true Hebbian cell-assembly. The choir corresponding to a concept representation would surely sing in parts, just as sopranos carry one melody and the altos another, each group having different interests. We will need polyphony for harmonious categories, not just chants.

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