Simulation of the accommodation phenomena in motoneuron models with passive dendrite

Leonardo Abdala Elias
Escola de Engenharia El?trica e de Computa??o - UFG

Marcus Fraga Vieira
Laborat?rio de Biomec?nica - FEF/UFG

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     Last modified: February 28, 2007

Abstract
The mechanisms involving the motoneurons accommodation are related mainly to changes in the fast sodium conductance and the potassium conductance. Long latencies are suggested in spinal, and mesencephalic cat motoneurons, assuming slow accommodations, although experimental observations show that fast accommodation can occur (Frank and Fuortes, 1960; Schlue et al., 1974a, 1974b, 1974c).
Mathematical models of motoneurons were evaluated under their accommodations when an injection of ramp current was simulated in their soma. Different accommodation rates were evaluated in the models in order to classify them as slow accommodation group or fast accommodation group, besides providing useful data to support the experimental research.
In this study, compartmental motoneuron models of different types were used (S, FR and FF), whose geometric and electronic parameters can be found in classic works of the experimental literature with lumbar-sacral motoneurons of cats, and the dendrite was passively modeled (Vieira, 2002; Vieira e Kohn, 2005).
In order to simulate slow excitatory actions, a ramp current with variable slope in order to evoke repetitive discharges was injected in the soma of the models. The time of the first action potential was registered, and also the current intensity capable to evoke these discharges. Therefore, a relationship between the current intensity and the latency was measured, and the resultant curve was named threshold latency curve (TL-curve).
The accommodation rates were calculated by the relation between the current intensity of a 1 s ramp current with a slope sufficiently able to evoke one discharge and the previously calculated reobase current (I0) of the models (Elias and Vieira, 2006a, 2006b).
It could be verified, in all the models, that the TL-curves present similar results to experimental data reported in literature, and there is a steady range with low intensity of current for low ramp slope and a linear range for high ramp slope. For the accommodation rates, values of 1.463 for type S model, 1.456 for type FR, and 1.418 for type FF were reported.
With these results, we can conclude that the models represent slow accommodation motoneurons, since the accommodation rates were always less than 1.6 (Schlue et al., 1974a, 1974b, 1974c). However, the results quite close among the models might occur by the similar modeling in the fast sodium conductance, and the potassium conductance, both responsible for accommodation mechanisms in vertebrate motoneurons.