Variability of axonal arborizations hides simple rules of construction: A topological study from HRP intracellular injections

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Abstract
Intracellular staining with horseradish peroxidase (HRP) allows the analysis of the extent and diversity of axonal field, as the Golgi techniques did for dendritic fields. In this study, we have used such HRP injections to investigate possible rules of construction that underlie the variability in the observed morphological patterns of axons. The Mauthner cell of the teleost provides a suitable material for such a work since it receives inhibitory inputs from two distinct classes of cells that can be identified physiologically prior to their intracellular staining: those that contribute to a recurrent collateral network and those that are part of the commissural vestibuloves-tibular pathway. The distribution of their terminal boutons over the M-cell surface was quantified and their axonal arborizations were analyzed topologically with the help of a centripetal method of terminal ordering. The results indicated (1) that both types of interneurons have qualitatively a similar distribution of boutons over this target, encompassing the soma, initial portions of the main dendrites, and the cap-dendrites, and (2) that furthermore, the terminals have a tendency to form clusters, the proportion of which is relatively constant regardless of the total number of boutons established by a given afferent cell. In respect to their projection on the M-cell, the two populations differ mainly in the number of established contacts, which averaged 44.1 ± 28.2 (n = 10) and 14.4 ± 11.3 (n = 43) for collateral and commissural interneurons, respectively. These differences reflect the variations in axonal arborizations. A topological analysis has revealed that (1) branching occurs mainly as bifurcations, whereas in contrast three or four segments issuing from a branch point are only occasionally observed at the level of the last segment; (2) for each cell, the distribution of boutons within orders is not random and rather follows an unimodal distribution, centered on the mean order (θ); (3) the terminals of each subset, or class, of neurons have their own pattern of distribution within orders; and finally (4) the mean order (θ) is linked to the number of terminal segments (nT) by the relation θ = 1.28 log2 nT. This parameter is of importance: it characterizes the axonal arborization and it allows one to predict the number of terminal segments of individual neurons. Similar analysis of camera lucida reconstruction of axonal arborizations of various cell types studied by other investigators suggests that this relation can be generalized. Thus, although the axons of each class of neurons can be distinguished on the basis of their ramifications (or number of boutons), their arborizations might nevertheless result from common principles of construction, for which simple mathematical expressions have been found.