Estimation of the Electrical Parameters of Spinal Motoneurons Using Impedance Measurements

Abstract

Electrical parameters of spinal motoneurons were estimated by optimizing the parameters of motoneuron models to match experimentally determined impedance functions with those of the models. The model was described by soma area, somatic and dendritic membrane resistivities, and the diameter of an equivalent dendritic cable having a standard profile. The impedance functions of motoneurons and optimized models usually differed (rms error) by <2% of input resistance. Consistent estimates for most parameters were obtained from repeated impedance determinations in individual motoneurons; estimates of dendritic resistivity were most variable. The few cells that could not be fit well had reduced impedance phase lag consistent with dendritic penetrations. Most fits were improved by inclusion of a voltage-dependent conductance GV with time constant τV. A uniformly distributed GV with τV >5 ms provided a better fit for most cells. The magnitude of this conductance decreased with depolarization. Impedance functions of other cells were adequately fit by a passive model or by a model with a somatic GV and τV <5 ms. Most of these neurons (7/8) had resting potentials positive to −60 mV. The electrotonic parameters ρ, τ, and L, estimated from model parameters, were consistent with published distributions. Most motoneuron parameters obtained in somatic shunt and sigmoidal models were well correlated, and parameters were moderately affected by changes in dendritic profile. These results demonstrate the utility and limitations of impedance measurements for estimating motoneuron parameters and suggest that voltage-dependent conductances are a substantial component of resting electrical properties.