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Axonal trees and corticalarchitecture Graeme Mitchison 6raeme Mitchison is at the Physiological Laboratory, CambridgeCB23E6, UK.
In modern computer design considerable care is taken to arrange the components in such a way that wiring is kept to a minimum. Certain features of cortical structure - the mappings, stripes and blobs within areas, and areasthemselves- are somewhat reminiscentof the layout of computer components, and suggest that the cortex may also be organized so as to economize on neuronal 'wiring'. One important difference between the brain and a computer is that the wiring in the brain takes the form of elaborate branchedstructures, namely axonal trees. In this article, it is argued that an assessmentof the efficiency of cortical wiring must take account of the branchingrules of these trees.
would be to examine different spatial arrangements of neurons in the cortex that keep all the connections of each neuron unchanged (rearranging and stretching the axons if necessary). This would show whether the present configuration comes close to achieving the lowest possible wiring volume. However, this is an impossible program because so many configurations could be obtained in this way but at least it is possible to ask how altering certain key features of cortical anatomy affects the wiring volume. A large part of the mammalian brain is 'wiring'. In Scrambling the maps 8 within areas9-11 would the mouse cortex, about 30% of the volume of grey clearly be very deleterious. Even if this was done matter is taken up by axons, and dendrites occupy only within areas, the effect of shuffling connections an approximately equal volume~; similar propor- randomly, so that they would have to extend over tions are found in cat visual cortex 2. It would be an entire area rather than being grouped in a reasonable to expect that the cortex has been neighbourhood of a few hundred microns, would organized so as to keep this wiring to a minimum 3-7, clearly greatly increase the wiring volume. It is more since a wasteful arrangement of neural processes rewarding to ask what would happen if the order could significantly increase the volume of the cortex, within areas was preserved but the areas were and hence of the whole brain, and this would merged into one structure. As we shall see, this presumably carry a considerable selective penalty. suggests some guiding principles for wiring design. Both axons and dendrites could be regarded as It may also be more closely related to the process 'wiring', but axons are much longer and thinner whereby new cortical areas evolve. than dendrites and have more elaborate patterns of connectivity. It seems reasonable, therefore, to think Cortical areas of them as the basic wiring of the cortex. Dendrites, Suppose that two cortical areas9-11, assumed for which are densely studded with synapses, can be simplicity to be the same size, were merged into a regarded for the present purposes as extensions of single composite area. The cells from the two areas the cell body, designed to receive as many synapses could be interleaved, as far as possible without as possible without occupying too much volume. destroying their original order, in such a way as to How can it be decided whether the cortex is produce a sheet of the same thickness as the original efficiently wired up by its axons? One approach areas (Fig. 1). The intermixing of the two types of © 1992,ElsevierSciencePublishersLtd,(Ul II
Fig. 2. (A) Diagrammatic surface view of cortex showing the axon of a neuron ramifying in two areas (square outlines labelled I and II), the two arbors being connected by an association fibre. In (B) the two areas are merged (1+11) in such a way as to preserve topographic order. The two arbors can be combined (the arbor originally from area II is shown dotted), and the association fibre dispensed with. Two ways of combining the arbors are shown in (C): by superposition, and by a more finely divided tree.
calculation shows that, using this rule, the result of combining 100 areas would be to increase the volume by a factor of about six instead of ten. This is still comfortably in excess of the factor of two that results from including the volume of white matter. It is clear, however, that axon diameters do not remain constant, but decrease at branches. In the case of the dendrites of pyramidal cells the cross-
A 4B 4C
Stripes and blobs
Fig. 3. (A) An axon entering the visual cortex. Many of its branches run approximately parallel and make synapses in overlapping or neighbouring regions. This might seem uneconomical, because a single axon could supply the same region. However, with conservation of cross-sectional area the volume of the two axons depicted in (B) would be approximately equal to that of the single axon in (C), which replaced them. Numbers refer to cortical layers. Abbreviation: W/vl, white matter. [Part (A) taken from Ref. 18.] 124
sectional area appears to be conserved at branches; that is, the sum of the areas of the two daughter branches equals that of the parent axon TM. It is not easy to determine if the same law applies to pyramidal cell axons, because they are so much thinner than dendrites. There is the suggestive observation 17 that the number of microtubules in an axon is conserved at a branch, though this does not necessarily imply that the total area is conserved. Suppose the assumption is made that the number of synapses made by an axon increases in some fashion as the cross-sectional area of that axon increases. Although there is little direct evidence for this, it is consistent with the general behaviour of axons; for example, the larger magnocellular axons from the geniculate make many more synapses than the thin parvocellular ones TM. If it is also assumed that area is preserved at axon branches, the hypothesis can be proposed that the number of synapses supported by an axon is proportional to its crosssectional area. If correct, this hypothesis would imply that the commonly observed tendency for groups of axons to run nearly parallel over some distance (Fig. 3A) is not so neglectful of wiring economy as it might at first appear to be. Suppose two axons make synapses in the same region (Fig. 3B). If they are replaced by a single axon that makes all their connections (Fig. 3C), the cross-sectional area of this axon would be the sum of the areas of the two original axons, which implies that its volume would roughly equal that of the two original axons. This argument can be extended to show that, given our hypothesis, superposing arbors is an efficient way of constructing a combined arbor, provided that the original arbors are themselves efficiently constructed. In this case, therefore, the assumptions made in the preceding section can be justified. Within certain cortical areas there is a finer level of structure - the stripes 8'19-21, blobs 22'23 and other kinds of patches. In the primary visual cortex, neurons often make clustered connections 2 4 '2 5 (see Fig. 4A), where the distance between the clusters is approximately the period of ocular dominance stripes (Fig. 4B). This suggests that neurons make connections predominantly to others of the same ocular dominance type. A similar phenomenon is observed with blobs 26. Therefore, the stripe or blob systems have some of the properties of areas; namely, they allow neurons to form more localized connections at the cost of making a few long connections, which, in the case of stripes and blobs, are the long axons connecting the clusters. The wiring volume of stripes or blobs can be analysed by the same method used for areas. However, there is a significant difference, because the long connections between stripes run through the grey matter rather than occupying the white matter (as in the case of the association fibres). If the long fibres share the same space as the arbors of other neurons, they spread these arbors apart, thereby increasing their wiring volume. How large this effect is depends on the way axonal size changes at branches. If axon diameter is TINS, VoL 15, No. 4, 1992
fairly constant, it can be shown that, even when the axons mix with the arbors, a stripe pattern gives a lower wiring volume than a uniform mixture of neuron types. In fact, there is an optimum width to the stripes, which would lead to each neuron having four or five clusters on average 7. However, if crosssectional area is conserved, so that the long axons are thick relative to the clusters they supply, then the decrease in volume achieved by making more compact arbors within stripes is almost exactly cancelled by the volume of the long axons7. This would not be true if the long axons were segregated from the arbors, within, for example, a separate layer of the grey matter. The stria of Gennari, which give the striate cortex its name, consist in part of myelinated axons running long distances 27, and may provide an example of the kind of structure that can exploit the wiring advantages of a patchy organization. Given such a structure, the volume gains for making stripes would be the same as for an equivalent number of areas. In the striate cortex, two types of ocular dominance stripe and four types of orientation patch might be distinguished, which would give a gain equivalent to eight areas; that is, a factor of about 1.9 in volume.
need to make specific patterns of connections, like the serial synapses made by basket cell axons along apical dendrites 28, or the 'corkscrew' formations of chandelier cells29. As pointed out earlier, it is not necessarily inefficient for axons to run parallel over some distance, since a single axon replacing them might have to be proportionately thicker to support the larger number of connections it makes. However, there is no denying the wastefulness of some of the tricks axons get up to, like the backtracking seen in Fig. 3A. This does not mean that the idea of wiring economy should be abandoned, but rather that we should only look for robust gains and losses. If tidying up the axonal tree could halve its volume, then (assuming as usual that 30% of the cortex comprises axons) the gain in volume for the whole cortex would be about 16%. Against this, the gain in making 100 cortical areas is a factor of ten in total volume, and the gain in making a system of stripes could amount to a factor of two or so. In essence, the idea proposed here is that a patchy cortical organization allows an axon to make localized clusters of short connections, and thereby
Concluding remarks There seems little doubt that subdividing the cortex into areas confers a considerable advantage in wiring economy, at least when contrasted with the somewhat hypothetical alternative scheme where areas are merged into larger structures with as little possible destruction of their topographic order. It is less clear that the next level of patchiness, the stripes and blobs within areas, offers significant advantages in wiring economy. Much depends on the way the thickness of axons changes at branches. If the higher order branches are much thicker- in particular if the cross-sectional area is preserved at branches, as happens with some pyramidal cell dendrites 16 - then the axons that link localized arbors in different stripes may have a large enough volume to cancel the gains from making more compact arbors. A further question arises here: do the linking axons occupy the same region of grey matter as the axonal arbors of the same, or other, neurons? This is pertinent because fibres not only occupy volume but also fill out the space that must be traversed by other axons in order to reach their targets. It is this 'filling out' that eventually weighs against the merging of areas and makes it more efficient to segregate the association fibres in the white matter. We can rephrase our question, therefore, and ask whether there is a substructure within the grey matter that serves as a kind of 'white matter' for linking stripes and blobs within areas. The stria of Gennari in primary visual cortex may furnish an example of this. If economy of wiring is important for the cortex it would be reasonable to expect to see evidence of efficient design in individual axonal trees. In fact, axonal branches often reach their targets in a very roundabout way. This may be due in part to the TINS, Vol. 15, No. 4, 1992
5B 4B 4A 3 5A
Fig. 4. (A) A neuron in the visual cortex, the axon of which shows a very marked set of clusters at a spacing that is approximately that of ocular dominance stripes. (B) A representation of ocular dominance stripes, in a surface view of the cortex, showing how the clusters may relate to the stripe system. Numbers refer to cortical layers. Abbreviation: WM, white matter. [Part (A) taken from Ref. 25.] 125
Acknowledgements I thank A. 5ch/Jzand P. 5omogyi for helpful suggestions.
economizes on wiring. It is not difficult to think of other reasons why a patchy structure might be advantageous, although some of these can be discounted readily enough. For example, the gain in the propagation time of spikes obtained by having shorter connections is probably insignificant (a few hundred microseconds 3°, with the most favourable geometry). A more attractive possibility is that patchiness might improve the efficiency of the search for synaptic targets by a growing axon, supposing that the patches contain a higher concentration of appropriate cell types. This cannot be dismissed lightly, especially as the existence of circuitous paths taken by many axons hints that making the correct connections may be a difficult task. However, the criteria arrived at in this article should help to distinguish this goal from economy of wiring, and this in turn may give some insight into the engineering problems that have constrained cortical evolution.
Selected references 1 Braitenberg, V. and SchiJz, A. (1991) Anatomy of the Cortex, Springer-Verlag 2 Foh, E., Haug, H., K6nig, M. and Rast, A. (1973) Mlicrosc. Acta 75, 148-168 3 Cowey, A. (1979) Q. J. Exp. PsychoL 341, 1-17 4 Mitchison, G. J. and Durbin, R. M. (1986) 51A/Vl (5oc. Ind. AppL /Math.) J. AIg. Discuss./Methods 7, 571-582 5 Durbin, R. M. and Mitchison, G. J. (1990) Nature 343, 644-647 6 Nelson, M. E. and Bower, J. M. (1990) Trends Neurosci. 13, 403-408 7 Mitchison, G. J. (1991) Proc. R. Soc. London Ser. B 245, 151-158 8 Hubel, D. H. and Wiesel, T. N. (1977) Proc. R. Soc. London Ser. B 198, 1-59 9 Brodman, K. (1909) Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des
Leipzig, Barth 10 Zeki, S. M. (1978) Nature 274, 423-428 11 Van Essen,D. C. (1985) in Cerebral Cortex (Vol. 3) (Peters,A. and Jones, E. G., eds), pp. 259--329, Plenum Press 12 Crick, F. and Asanuma, C. (1987) in Parallel Distributed Processing (Vol. 2) (McClelland, J. L. and Rumelhart, D. E., eds), pp. 333-371, MIT Press 13 Braitenberg, V. (1978) in Architectonics of Cerebral Cortex (Brazier, M. A. B. and Petsche, H., eds), pp. 443-465, Raven Press 14 Caviness,V. S. (1975) J. Comp. Neurol. 164, 247-264 15 Felleman, D. J. and Van Essen,D. C. (1991) Cereb. Cortex 1, 1-47 16 Hillman, D. E. (1979) in The Neurosciences: Fourth Study Program (Schmitt, F. O. and Worden, F. G., eds), pp. 477-498, MIT Press 17 Weiss, P. A. and Mayr, R. (1971) Acta Neuropathologica (Suppl. 5), 198-206 18 Freund, T. F., Martin, K. A. C., Soltesz, I., Somogyi, P. and Whitteridge, D. (1989) J. Comp. NeuroL 289, 315-336 19 Livingstone, M. S. and Hubel, D. H. (1982) Proc. NatlAcad. 5ci. USA 79, 6098-6101 20 Tootell, R. B. H., Silverman, M. S., DeValois, R. L. and Jacobs, G. H. (1983) Science 220, 737-739 21 Blasdel, G. G. and Salama, G. (1986) Nature 321,579-585 22 Humphrey, A. L. and Hendrickson, A. E. (1980) 5oc. Neurosci. Abstr. 6, 315 23 Horton, J. C. and Hubet, D. H. (1981) Nature 292,762-764 24 Gilbert, C. D. and Wiesel, T. N. (1983) J. Neurosci. 3, 1116--1133 25 Martin, K. A. C. and Whitteridge, D. (1984) J. Physiol. 353, 463-504 26 Livingstone, M. S. and Hubel, D. H. (1984) J. Neurosci. 4, 2830-2835 27 Valverde, F. (1985) in Cerebral Cortex (Vol. 3) (Peters,A. and Jones, E. G., eds), pp. 207-257, Plenum Press 28 Kisv&rday, Z. F., Martin, K. A. C., Friedlander, M. J. and Somogyi, P. (1987) J. Comp. Neurol. 260, 1-19 29 Somogyi, P. (1979) J. Physiol. 296, 18-19 30 Waxman, S. G. and Bennett, M. V. U (1972) Nature 238, 217-219
to the editor Steady-state Ca 2+ influx and electrical activity in endocrine cells The recent TINS review by Cook, Satin and Hopkins ~ on the generation of action potentials in pancreatic B cells discusses the hypothesis that a persistent Ca 2+ conductance may underlie burst formation not only in molluscan neurons 2'3 but also in pancreatic B cells. The bursting electrical activity of pancreatic B cells is known to correlate with insulin secretion and has been suggested to be obligatory for providing Ca 2+ for the exocytosis of insulin (for review, see Ref. 4). Although similarly advocated for the association between basal Ca 2÷ influx and basal hormone release in other endocrine cells s, some caution is warranted. For example, it has been known for some time that in excitable endocrine cells in which Ca 2+ influx is of prime importance for hormone release,
Zellenbaues (Principles of comparative localization in the cerebral cortex presented as the basis of cytoarchitecture),
Ca 2+ influx may occur even in the absence of action potentials (for review, see Refs 6 and 7). Recently, this basal Ca 2+ entry was shown to be due to a steady-state conductance of voltage-dependent Ca 2÷ channels at the resting potential of - 6 0 m V to - 4 0 mV 7's. Similar to the situation that exists in smooth muscle cells9, voltage-dependent Ca 2÷ channels of various endocrine cells have a finite open probability, even at constant membrane potentials. The list of endocrine cells in which we have observed steady-state Ca 2÷ channel currents includes parafollicular cells of the thyroid (C cells) s, pituitary cells 7, chromaffin cells, enterochromaffin cells and pancreatic B cells (Scheriibl, H. and Hescheler, J., unpublished observations). The persistent Ca 2÷ conductance in B cells appears to contribute to the well-known extracellular Ca 2÷ sensitivity of hormone release from these cells. In support of the hypothesis of
Cook, Satin and Hopkins 1, modulation of the steady-state Ca 2+ conductance is known to affect the electrical activity of excitable endocrine cells such as pancreatic B cells. In particular, the Ca 2÷ channel activator Bay K 8644 or small increases in the extracellular Ca 2+ concentration induce or increase the frequency of action potentials, while Ca 2÷ channel blockers suppress the spiking 7's'1°. Thus, in excitable endocrine cells the 'spontaneous' electrical activity as well as basal, Ca 2÷dependent hormone secretion appears to depend on steadystate Ca 2÷ influx through voltagedependent Ca 2+ channels. As for the physiological role of action potentials in endocrine cells, the synchronization and possibly augmentation of the secretory activity has been suggested 1~.
Hans $cheriJbl JiJrgen Hescheler Pharmakolo#isches Institut der Freien UniversitJt Berlin, Thidallee69-73, D-tO00 Berlin 33,
FRO. TINS, VoL 15, No. 4, 1992