Yair Manor, Christof Koch and Idan Segev

Multiple successive geometrical irregularities, such as extensive arborization and terminal varicosities, are usual characteristics of axons. Near such regions the velocity of the action potential (AP) changes. This study uses AXONTREE, a modeling tool developed in the companion paper for two purposes: (a) to gain insights into the consequence of these irregularities for the propagation delay along axons, and (b) to simulate the propagation of APs along a reconstructed axon from a cortical cell, taking into account information concerning the distribution of boutons (release sites) along such axons to estimate the distribution of arrival times of APs to the axon release sites. We used Hodgkin-Huxley (1952) like membrane properties at 20 C. Focusing on the propagation delay which results from geometrical changes along the axon (and not from the actual diameters or length of the axon), the main results are: (a) the propagation delay at a region of a single geometrical change (a step change in axon diameter or a branch point) is in the order of a few tenths of a millisecond. This delay critically depends on the kinetics and the density of the excitable channels; (b) as a general rule, the lag imposed on the AP propagation at a region with a geometrical ratio GR > 1 is larger than the lead obtained at a region with a reciprocal of that GR value; (c) when the electrotonic distance between two successive geometrical changes (Xdis) is small, the delay is not the sum of the individual delays at each geometrical change, when isolated. When both geometric al changes are with GR > 1 or both with GR < 1, this delay is supralinear (larger than the sum of individual delays). The two other combinations yield a sublinear delay; and (d) in a varicose axon, where the diameter changes frequently from thin to thick and back to thin, the propagation velocity may be slower than the velocity along a uniform axon with the thin diameter. Finally, we computed propagation delays along a morphologically characterized axon from layer V of thesomatosensory cortex of the cat (Fig. 5 b; Schwark and Jones, 1990. Brain Res. 78: 501-513). This axon projects mainly to area 4 but also sends collaterals to areas 3b and 3a. The model predicts that, for this axon, areas 3a, 3b and the proximal part of area 4 are activated ~ 2 ms before the activation of the distal part of area 4.