Highly Efficient Propagation of Random Impulse Trains Across Unmyelinated Axonal Branch Points

Probability Distributions of Markovian Sodium Channel States During Propagating Axonal Impulses With or Without Recovery Supernormality

“…It has been shown previously that this PC scheme (as modified; see Methods section) did not include a supernormal period during recovery in propagated axonal action potentials [27]. The present results revealed that modification of the speed of transitions in the PC scheme's closed loop kinetics influenced the occurrence and magnitude of supernormality.…”

“…As previously described [27], the kinetic scheme used in the present study differed from Vandenberg and Bezanilla's original scheme [10,77]: (a) the original rate constants between first and second reaction files (i.e., I 4 C 4 and O I) were replaced by rate constants e/f in order to fulfill the required constraint of symmetrical rate constant products within a kinetic loop [34,57,78]; (2) the values of c and f were doubled a to achieve a best fit to single Hodgkin-Huxley (hereafter: HH, [36]) isopotential and propagating action potentials without the inclusion of periaxonal K + accumulation [10,27].…”

“…Following a conditioning action potential, a second successive action potential can be initiated at the test site with a smaller minimal stimulus than is needed to initiate a second impulse at an infinite time after the conditioning action potential. Supernormality is a property of the recovery cycle in some axons [24,32,43,73] and is a property of the unmodified the HH formalism [27]. It has been used as a criterion for axonal classification [18,24], and has been recently applied in clinical tests for peripheral neuropathies [8,33,45,81].…”

“…In their studies of NaCh in squid axon membrane, Vandenberg and Bezanilla [76,77] obtained data from recording microscopic and macroscopic Na currents from individual and groups of NaCh together with associated gating currents; the relationships between these entities were addressed concurrently in an analysis designed to reveal a best-fit representation of the several channel transitions. The resultant kinetic scheme (hereafter: "PC" scheme, [27]) included the partial coupling between open and inactivated states within the six ranks and two files of explicit transitions, where C, O, and I refer to the closed, open, and inactivated states, as follows:…”

Antidromic propagation of action potentials in branched axons: implications for the mechanisms of action of deep brain stimulation

“…A study of rat paraventricular nucleus and supraoptic nucleus neurons concluded that activity-dependent accumulation of extracellular potassium due to repetitive antidromic axonal firing can reduce axonal excitability leading to slowed conduction and eventual conduction failure (Pittman 1983). In a modeling study of orthodromic propagation through branching myelinated axons, branches with periaxonal K + accumulation experienced prolonged recovery cycles after action potential propagation and did not support shorter interspike intervals that were supported by branches with no periaxonal K + accumulation (Goldfinger 2005). A similar study found that trains of orthodromic impulses were attenuated to a greater degree at 400 Hz with extracellular K + accumulation than without (Zhou and Chiu 2001).…”