Determination of the Location and Magnitude of Synaptic Conductance Changes in Spinal Motoneurons by Impedance Measurements

Abstract

The relation between impedance change and the location and magnitude of a tonic synaptic conductance was examined in compartmental motoneuron models based on previously published data. The dependency of motoneuron impedance on system time constant (τ), electrotonic length (L), and dendritic-to-somatic conductance ratio (ρ) was examined, showing that the relation between impedance phase and ρ differed markedly between models with uniform and nonuniform membrane resistivity. Dendritic synaptic conductances decreased impedance magnitude at low frequencies; at higher frequencies, impedance magnitude increased. The frequency at which the change in impedance magnitude reversed from a decrease to an increase—the reversal frequency, Fr—was a good estimator of electrotonic synaptic location. A measure of the average normalized impedance change at frequencies less than Fr, cuΔZ, estimated relative synaptic conductance. Fr and cuΔZ provided useful estimates of synaptic location and conductance in models with nonuniform (step, sigmoidal) and uniform membrane resistivity. Fr also provided good estimates of spatial synaptic location on the equivalent cable in both step and sigmoidal models. Variability in relations between Fr, cuΔZ, and conductance location and magnitude between neurons was reduced by normalization with ρ and τ. The effects on Fr and cuΔZ of noise in experimental recordings, different synaptic distributions, and voltage-dependent conductances were also assessed. This study indicates that location and conductance of tonic dendritic conductances can be estimated from Fr, cuΔZ, and basic electrotonic motoneuron parameters with the exercise of suitable precautions.