Figure 1.6. Operations performed, by virtue of their geometry, by callosal axons that interconnect areas 17 and 18 of the cat. Part A illustrates mapping and differential weighting. A point in one hemisphere, corresponding to the location of the cell body, is mapped into clusters of boutons (terminal columns) that are distributed in the contralateral cortex along the border between areas 17 and 18 (open triangles). Notice that the terminal columns contain different numbers of boutons, suggesting that the axon does not drive all the terminal columns with equal strength. Part B illustrates temporal transformations performed by axonal geometry. The top axon activates terminal columns simultaneously; the bottom axon with a delay due to axonal conduction within its terminal arbor; the activation of the intermediate axon is retarded in comparison to the others, owing to its smaller diameter. The active part of the axon is in solid black; the inactive part is interrupted.

Corticotopic mapping Callosal connections between areas of the two hemispheres have so far been considered to be orderly and point-to-point. This view, however, is no longer accurate. First, the tangential distribution of the terminal arbor of a single callosal axon often greatly exceeds the territory occupied by the cell body of the parent neuron, its dendrites included (Figures 1.5 and 1.7). Therefore, many individual callosal axons diverge to their site of termination. Furthermore, since the tangential extent of the callosal efferent zone (the volume containing callosally projecting neurons in one area) is wider than that of the callosal terminal territory (the volume containing the terminals of callosal axons), this implies convergence of callosal axons as well. Indeed,

Figure 1.7. Examples of three-dimensionally reconstructed callosal axons from primary visual areas 17 and 18 of the cat to the extrastriate areas 21a, 19, lateral suprasylvian (LS), as well as to 19 and LS. In each case, upper and lower boundaries of the gray matter in representative sections are also shown. The age of the animal is indicated in each case.

Figure 1.7. Examples of three-dimensionally reconstructed callosal axons from primary visual areas 17 and 18 of the cat to the extrastriate areas 21a, 19, lateral suprasylvian (LS), as well as to 19 and LS. In each case, upper and lower boundaries of the gray matter in representative sections are also shown. The age of the animal is indicated in each case.

individual callosal axons have been seen to converge, at least partially onto the same target sites (Houzel et al., 1994; Bressoud and Innocenti, 1999). For the time being, only the values of divergence of callosal axons originating near the 17/18 border are known, to some extent. In the 17/18 region of the cat, individual axons can span tangentially between 100 mm2 and several thousand mm2 (Houzel et al., 1994), with the greatest values of divergence in area 18. The degree of axonal divergence also varies among the callosal axons to the extrastriate visual areas. The highest divergence was found for axons to the lateral suprasylvian areas (probably equivalent to area MT in the monkey), and the smallest was found for those to area 21a (Bressoud and Innocenti, 1999) (see Figure 1.7). The degree of divergence of callosal axons might be related to the magnification factor of the retinotopic maps and to the size of individual receptive fields in the different areas. Given the large receptive fields found in area 18 and in the suprasylvian area, the divergence of callosal axons does not necessarily imply a mismatch between the retinal location of the receptive field of callosal axons and that of its target neurons.

The corticotopic mapping implemented by callosal axons in the primary visual areas might be the substrate for coarse stereopsis along the vertical meridian (dis cussed in Innocenti, 1986). In addition, it might correct for retinotopic mismatches in the callosal connections among visual areas (Olavarria, 1996).

Higher-order mapping Diverging callosal axons also implement mapping rules at levels of cortical organization beyond those considered above. Individual axons to the primary visual areas, to area 19, and to the visual areas in the suprasylvian sulcus of the cat often terminate with multiple clusters of boutons 300-600 mm across and separated by spaces 120-2770 mm wide (Houzel et al., 1994; Bressoud and Innocenti, 1999). The volumes containing the callosal boutons are called terminal columns. The visual areas, like most cortical areas, are organized in "columns" of neurons with similar functional properties. Callosal axons appear to respect, in their terminal distribution, this columnar organization. Indeed, it was demonstrated electrophysiologically that neurons in the primary visual areas have the same orientation specificity in the callosally as well as in the geniculocortically activated part of their receptive fields (Berlucchi and Rizzolatti, 1968). This suggests that, as intra-areal axons and axons from area 17 to area 18 of the same hemisphere (Gilbert and Wiesel, 1989), callo-sal axons interconnect cortical columns that recognize identical orientations of the visual stimulus. Further studies of the specific column-to-column connectivity in the different areas might clarify the previously discussed discrepancies among different studies, concerning the existence of segregated columns of callosally projecting neurons in cortical areas (Innocenti, 1986). Blurred columns of callosally projecting neurons were seen with retrograde transport in these areas (Boyd and Matsu-bara, 1994), while the identification of callosal terminal columns required the analysis of single axons.

Presumably, callosal axons implement still higher levels of topographical mapping. In several instances the diameter of the terminal clusters of callosal axons is inferior to what would be expected if the boutons were to occupy entirely one orientation column. Thus, only part of a column might receive callosal axons. Furthermore, callosal axons usually do not distribute to all layers in their site of termination, although in some cases they do. Most frequently, only the supragranular and in-fragranular layers receive boutons, not layer IV. This points to some complementarity between callosal axons and other afferents specific for layer IV, for example, thalamocortical axons or the recurrent projections from layer VI. It also points to levels of organization of cortical organization, which ought to be elucidated in the future.

Finally, it is not known whether the callosal axons synapse specifically on a given cell type. However, they might be selective for certain dendritic subdomains, since they appear to selectively contact dendritic spines rather than shafts (reviewed in Innocenti, 1986).

Weighting Individual callosal axons do not contribute the same number of boutons to different terminal columns. They also contribute different numbers of boutons to the different layers and can distribute to different layers in different columns. This applies to callosal axons to areas 17 and 18, as well as to those to extrastriate visual areas (Houzel et al., 1994; Bressoud and Innocenti, 1999). Usually, one or two of the columns receive many more boutons than the others. The maximal difference in the number of boutons found thus far across columns is about 1—50. Ratios of 1 — 10 or 1—20 are frequent (Houzel et al., 1994). The number of boutons per column is presumably determining the strength of the excitatory drive of the axon, the so-called synaptic weight of the axon in a given ''terminal column." Therefore, the action potentials transmitted by a callosal axon might be differentially weighted at its sites of termination by the number of contacts. Unfortunately, nothing is known about the size of the callosal terminal boutons, their vesicular content, synaptic protein composition, quantal properties of transmitter release, and so on. All of these could also contribute to the synaptic weight of the axon at its different sites of termination.

Temporal Transformations Several lines of evidence point to temporal parameters as a fundamental aspect of neural processing. Thus, neuronal subsystems characterized by the different conduction velocities of their axons exist in both the sensory and motor systems and implement different functions. In the visual system, faster-conducting axons appear to be involved in motion analysis, slower axons in form discrimination (Livingstone and Hubel, 1987). Furthermore, temporal transformations within the arbors of individual axons or between arbors belonging to different axons seem to be relevant for neural function. In the auditory system of birds, axons to the nucleus laminaris implement delay lines by distributing their action potentials to different targets with nonzero time lags (Carr and Konishi, 1990). Elsewhere, the different conduction length seems to be compensated by changes in axon diameter. This is true in systems as different as the motor neurons controlling the electric organ offish (Bennett, 1968), the climbing fiber projection from the inferior olive to the cerebellar Purkinje cell (Sugihara, Lang and Llinas, 1993), and the intraretinal part of ganglion cell axons (Stanford, 1987). The degree of temporal precision necessary for neural operations has been a matter of debate, particularly for cerebral cortex. The issue is whether cortical neurons can use temporal resolutions in the millisecond range (Softky and Koch, 1993; Softky, 1994). In the auditory system of birds and in the neural structures that process or generate electrical signals in fish, temporal resolutions on the order of microseconds are used (reviewed in Carr, 1993).

Attention to the possibility that callosal axons might be involved in temporal transformation was raised by the observation that the geometry callosal axons seems occasionally uneconomical in terms of axoplasmic production and maintenance (Innocenti, Lehmann, and Houzel, 1994). In particular, callosal axons often possess branches that run in parallel to their targets for several millimeters or exchange branches between terminal columns several hundred microns apart (Houzel et al., 1994; Innocenti et al., 1994) (see Figure 1.5). In an attempt to clarify the possible functional consequences of the above-mentioned geometry, we ran simulations of action potential propagation along serially reconstructed visual callosal axons, based on the well-established relationship between conduction velocity and axon diameter (Innocenti et al., 1994). The simulation software (MAXSIM; Tettoni et al., 1996) allows generation of frequency histograms of the activation time of the individual boutons contributed by one axon to one or more sites of termination. The precision of the simulation is limited by a number of factors, including the accuracy of axon diameter measurements and the possibility that delays or accelerations of action potential propagation occur at the sites of axonal bifurcation, as is discussed elsewhere (Innocenti et al., 1994; Tettoni et al., 1996). Those intractable uncertainties aside, for visual callosal axons of the cat, the simulation returned interhemi-spheric conduction delays in the range of those measured electrophysiologically.

In the callosal axons analyzed to this date, we found a tendency for the geometry of the axon to maximize synchronous activation of spatially separate terminal columns with precision within 1 ms. The apparently wasteful geometry mentioned above is instrumental in generating such a synchronization. However, in terms of axoplasm production and maintenance, they do not represent the most parsimonious way of achieving synchronization. This suggests that other factors, in particular developmental constraints, influence the geometry of the axons (Innocenti, 1994). Callosal axons of the kind described above might participate in the synchronization of the activity of neuronal pools within and across the hemispheres demonstrated by single-unit analysis in animals (Engel et al., 1991; Nowak et al., 1995) and by EEG analysis in animals and the human (Kiper et al., 1999, Knyazeva et al., 1999). Accordingly, the interruption of callosal axons abolishes the synchronization.

Such a synchronization may be necessary for perceptual binding and figure/background segregation (Singer, 1995).

Although current research emphasizes the importance of synchronous activation of neuronal assemblies, the opposite—the desynchronization of neuronal assemblies—may play an equally important role in neural function. Indeed, a few axons with geometry appropriate for generating activation delays were also found. These axons run tangentially in the cortex contributing boutons serially to several terminal columns. An axon of this kind could activate separate cortical columns with a delay of up to 2 ms (Innocenti et al., 1994). Furthermore, callosal axons interconnecting the primary visual areas were found to vary in their diameter between about 0.5 and 2 mm. Axonal size might correlate with differences in the receptive field properties and connectivity of the parent cell bodies. McCourt, Thalluri and Henry (1990) found the fastest interhemispheric conducting axons for neurons of the S (simple) type. Axons with different diameter were found to converge on the same cortical sites. The simulations predicted that in a case of this kind, action potentials simultaneously initiated in the parent cell bodies would reach their target sites with important temporal delays (on the order of 2.5 ms) (Innocenti et al., 1994). The delays that are theoretically generated by conduction within the same axon or across axons are large in comparison to the average interhemispheric conduction delay in the cat (2.0-2.9 ms; Innocenti, 1995).

In conclusion, the analysis of individual callosal axons has focused attention on the morphological substrate of temporal transformations of interhemispheric interaction. The importance of these transformations for brain function can hardly be overemphasized. This is highlighted by the recent suggestion that increased inter-hemispheric delays caused by increased brain size may be a cause of hemispheric specialization in humans (Ringo et al., 1994). However, this provocative and stimulating hypothesis is not supported by the available electrophysiological data (reviewed in Innocenti, 1995). In fact, comparable mean interhemispheric conduction delays, on the order of 7-8 ms, were reported in the visual cortex of the rhesus monkey and the mouse in spite of the considerable difference in brain size. Cats and ferrets, whose brain size ranges between those of monkey and mouse, seem to be similar in their inter-hemispheric conduction delays, but these are definitely shorter than those in the other two species (about 2.9 ms). Curiously, the longest interhemispheric conduction delays were measured in rabbits (17 ms). Apparently, evolution managed to maintain comparable interhemi-spheric conduction delays, in spite of manifold increases in brain size. This was probably obtained by scaling the diameter of callosal axons to brain size, as preliminary evidence suggests (Innocenti, Aggoun-Zouaoui, and Lehmann, 1995). However certain species—in particular, the carnivores—might have faster interhemispheric conduction, possibly faster conduction in all the corti-cocortical pathways.

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