Axon Surface Infolding and Axon Size Can be Quantitatively Related in Gastropod Molluscs

A quantitative estimate of infolding and of its effect on electrical characteristics in axons of different sizes is given by expressions based on the allometric equation, y = ax^β. These expressions can be used to describe the effect of stretching the axon and the size dependence of the axo-somatic conductance ratio.

The parameters in the allometric equation are determined for a range of axon sizes in three species of opisthobranchs from original and from published data. Analysis of variance for these data suggests that interaxonal variability of infolding is less for axons of an identifiable neurone from different specimens of the same species than for axons of different neurones from the same specimen. With the exception of the Aplysia R2 axon where the infolding size dependence may be less, the ratio of axon volume to surface in these neurones is given approximately by the equivalent axon diameter to the one-half power. For this relation of infolding to size (and if it is assumed that infolding in the soma varies with size in the same way as in the axon), the axo-somatic conductance ratio is inversely proportional to soma diameter to the three-fourths power.

These results suggest that conduction velocity increase with size is small, and because of the penalty in the concomitant increase in axon surface membrane with size, selection for larger axons probably does not occur to satisfy a requirement of decreased response time.