Computation of long-distance propagation of impulses elicited by Poisson-process stimulation

Abstract

1. The purpose of this work was to determine whether computed temporally coded axonal information generated by Poisson process stimulation were modified during long-distance propagation, as originally suggested by S. A. George. Propagated impulses were computed with the use of the Hodgkin-Huxley equations and cable theory to simulate excitation and current spread in 100-microns-diam unmyelinated axons, whose total length was 8.1 cm (25 lambda) or 101.4 cm (312.5 lambda). Differential equations were solved numerically, with the use of trapezoidal integration over small, constant electrotonic and temporal steps (0.125 lambda and 1.0 microsecond, respectively). 2. Using dual-pulse stimulation, we confirmed that for interstimulus intervals between 5 and 11 ms, the conduction velocity of the second of a short-interval pair of impulses was slower than that of the first impulse. Further, with sufficiently long propagation distance, the second impulse's conduction velocity increased steadily and eventually approached that of the first impulse. This effect caused a spatially varying interspike interval: as propagation proceeded, the interspike interval increased and eventually approached stabilization. 3. With Poisson stimulation, the peak amplitude of propagating action potentials varied with interspike interval durations between 5 and 11 ms. Such amplitude attenuation was caused by the incomplete relaxation of parameters n (macroscopic K-conductance activation) and h (macroscopic Na-conductance inactivation) during the interspike period. 4. The stochastic properties of the impulse train became less Poisson-like with propagation distance. In cases of propagation over 99.4 cm, the impulse trains developed marked periodicities in Interevent Interval Distribution and Expectation Density function because of the axially modulated transformation of interspike intervals. 5. Despite these changes in impulse train parameters, the arithmetic value of the mean interspike interval did not change as a function of propagation distance. This work showed that in theory, whereas the pattern of Poisson-like impulse codes was modified during long-distance propagation, their mean rate was conserved.

Ionic mechanisms underlying history-dependence of conduction delay in an unmyelinated axon

“…Poisson trains have been used before in Hodgkin-Huxley model axons to characterize spike delay and velocity (George, 1977; Moradmand and Goldfinger, 1995), but not commonly in model axons with more complex excitability. We therefore examined the history-dependence of conduction delay in the PD neuron model axon by stimulating one end of the axon and measuring conduction delay between two positions along its length (Figure 1).…”

“…It is unclear, however, how well those descriptions apply to complex excitability changes during highly repetitive activity. Additionally, theoretical investigations of the history-dependence of conduction delay have considered only minimal sets of ionic currents (Miller and Rinzel, 1981; Kepler and Marder, 1993; Moradmand and Goldfinger, 1995; Faisal and Laughlin, 2007). …”

Axonal Noise as a Source of Synaptic Variability

“…The AP upstroke becomes steeper as the AP travels away from the AP initiation site and approaches its steady-state shape after several length constants (after about 1 mm in a 0.2 µm diameter axon). The change in the average AP waveform of the stochastic simulation matches the AP waveform change of the corresponding deterministic simulated axon [31]. This is because close to the proximal stimulation site, the AP shape is determined by the stimulus driving a fully resting axon, and the response speed is limited by the resting membrane's time constant.…”

“…Changes in the width of APs, whether due to a depolarized soma [65] or application of glutamate [27], have been shown to influence post-synaptic potentials (PSPs). Moradmand et al [31] studied the deterministic transformation of propagating AP waveforms in a paired-pulse framework and showed that the second AP waveform in the pair becomes increasingly stereotyped due to refractory interaction with the first AP. Thus, even in bursts, only the first spike would be the likely candidate to carry stimulus information in the waveform over long distances.…”

Rallian "Equivalent" Cylinders Reconsidered: Comparisons With Literal Compartments

“…No predictor/corrector techniques were applied. The use of very small temporal (25 nanosec, 1.72 · 10 −5 τ m ) integration steps enhanced solution resolution and stability [93,65]. The adequacy of the integration spatial (∆x) and temporal (∆t) steps was demonstrated by a variety of tests (see below Sec.…”