The Journal of Neurophysiology Vol. 78 No. 6 December 1997, pp. 3371-3385
Copyright ©1997 The American Physiological Society

Compartmental Model of Vertebrate Motoneurons for Ca²⁺-Dependent Spiking and Plateau Potentials Under Pharmacological Treatment

Victoria Booth¹, John Rinzel¹, and Ole Kiehn²

¹ Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health 9190, Bethesda, Maryland 20814; and ² Section of Neurophysiology, Department of Physiology, The Panum Institute, DK-2200 Copenhagen, Denmark

Booth, Victoria, John Rinzel, and Ole Kiehn. Compartmental model of vertebrate motoneurons for Ca²⁺-dependent spiking and plateau potentials under pharmacological treatment. J. Neurophysiol. 78: 3371-3385, 1997. In contrast to the limited response properties observed under normal experimental conditions, spinal motoneurons generate complex firing patterns, such as Ca²⁺-dependent regenerative spiking and plateaus, in the presence of certain neurotransmitters and ion-channel blockers. We have developed a quantitative motoneuron model, based on turtle motoneuron data, toinvestigate the roles of specific ionic currents and the effects of their soma and dendritic distribution in generating these complex firing patterns. In addition, the model is used to explore the effects of multiple ion channel blockers and neurotransmitters that are known to modulate motoneuron firing patterns. To represent the distribution of ionic currents across the soma and dendrites, the model contains two compartments. The soma compartment, representing the soma and proximal dendrites, contains Hodgkin-Huxley-like sodium (I_Na) and delayed rectifier K⁺ (I_Kdr) currents, an N-like Ca²⁺ current (I_CaN), and a calcium-dependent K⁺ current [I_K(Ca)]. The dendritic compartment, representing the lumped distal dendrites, contains, in addition to I_CaN and I_K(Ca) as in the soma, a persistent L-like calcium current (I_CaL). We determined kinetic parameters for I_Na, I_Kdr, I_CaN, and I_K(Ca) in order to reproduce normal action-potential firing observed in turtle spinal motoneurons, including fast and slow afterhyperpolarizations (AHPs) and a linear steady-state frequency-current relation. With this parameter set as default, a sequence of pharmacological manipulations were systematically simulated. A small reduction of I_Kdr [mimicking the experimental effect of tetraethylammonium (TEA) in low concentration] enhanced the slow AHP and caused calcium spiking (mediated by I_CaN) when I_Na was blocked. Firing patterns observed experimentally in high TEA [and tetrodotoxin (TTX)], namely calcium spikes riding on a calcium plateau, were reproduced only when both I_Kdr and I_K(Ca) were reduced. Dendritic plateau potentials, mediated by I_CaL, were reliably unmasked when I_K(Ca) was reduced, mimicking the experimental effect of the bee venom apamin. The effect of 5-HT, which experimentally induces the ability to generate calcium-dependent plateau potentials but not calcium spiking, was reproduced in the model by reducing I_K(Ca) alone. The plateau threshold current level, however, was reduced substantially if a simultaneous increase in I_CaL was simulated, suggesting that serotonin (5-HT) induces plateau potentials by regulating more than one conductance. The onset of the plateau potential showed significant delays in response to near-threshold, depolarizing current steps. In addition, the delay times were sensitive to the current step amplitude. The delay and its sensitivity were explained by examining the model's behavior near the threshold for plateau onset. This modeling study thus accurately accounts for the basic firing behavior of vertebrate motoneurons as well as a range of complex firing patterns invoked by ion-channel blockers and 5-HT. In addition, our computational results support the hypothesis that the electroresponsiveness of motoneurons depends on a nonuniform distribution of ionic conductances, and they predict modulatory effects of 5-HT and properties of plateau activation that have yet to be tested experimentally.

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