Estimation of the Electrical Parameters of Spinal Motoneurons Using Impedance Measurements

Characteristics and organization of discharge properties in rat hindlimb motoneurons

The discharge properties of hindlimb motoneurons in ketamine-xylazine anesthetized rats were measured to assess contributions of persistent intrinsic currents to these characteristics and to determine their distribution in motoneuron pools. Most motoneurons (30/37) responded to ramp current injections with adapting patterns of discharge and the frequency-current (f-I) relations of nearly all motoneurons included a steep subprimary range of discharge. Despite the prevalence of adapting f-I relations, responses included indications that persistent inward currents (PICs) were activated, including increased membrane noise and prepotentials before discharge, as well as counterclockwise hysteresis and secondary ranges in f-I relations. Examination of spike thresholds and afterhyperpolarization (AHP) trajectories during repetitive discharge revealed systematic changes in threshold and trajectory within the subprimary, primary, and secondary f-I ranges. These changes in the primary and secondary ranges were qualitatively similar to those described previously for cat motoneurons. Within the subprimary range, AHP trajectories often included shallow approaches to threshold following recruitment and slope of the AHP ramp consistently increased until the subprimary range was reached. We suggest that PICs activated near recruitment contributed to these slope changes and formation of the subprimary range. Discharge characteristics were strongly correlated with motoneuron size, using input conductance as an indicator of size. Discharge adaptation, recruitment current, and frequency increased with input conductance, whereas both subprimary and primary f-I gains decreased. These results are discussed with respect to potential mechanisms and their functional implications.

Estimates of the location of L-type Ca2+ channels in motoneurons of different sizes: a computational study

In the presence of monoamines, L-type Ca(2+) channels on the dendrites of motoneurons contribute to persistent inward currents (PICs) that can amplify synaptic inputs two- to sixfold. However, the exact location of the L-type Ca(2+) channels is controversial, and the importance of the location as a means of regulating the input-output properties of motoneurons is unknown. In this study, we used a computational strategy developed previously to estimate the dendritic location of the L-type Ca(2+) channels and test the hypothesis that the location of L-type Ca(2+) channels varies as a function of motoneuron size. Compartmental models were constructed based on dendritic trees of five motoneurons that ranged in size from small to large. These models were constrained by known differences in PIC activation reported for low- and high-conductance motoneurons and the relationship between somatic PIC threshold and the presence or absence of tonic excitatory or inhibitory synaptic activity. Our simulations suggest that L-type Ca(2+) channels are concentrated in hotspots whose distance from the soma increases with the size of the dendritic tree. Moving the hotspots away from these sites (e.g., using the hotspot locations from large motoneurons on intermediate-sized motoneurons) fails to replicate the shifts in PIC threshold that occur experimentally during tonic excitatory or inhibitory synaptic activity. In models equipped with a size-dependent distribution of L-type Ca(2+) channels, the amplification of synaptic current by PICs depends on motoneuron size and the location of the synaptic input on the dendritic tree.

Rallian "equivalent" cylinders reconsidered: comparisons with literal compartments

In Rall's "equivalent" cylinder morphological-to-electrical transformation, neuronal arborizations are reduced to single unbranched core-conductors. The conventional assumption that such an "equivalent" reconstructs the electrical properties of the fibers it represents was tested directly; electrical properties and responses of "equivalent" cylinders were compared with those of their literal branch constituents for fibers with a single symmetrical bifurcation. The numerical solution methods were validated independently by their accurate reconstruction of the responses of an analog circuit configured with compartmental architecture to solve the cable equation for passive fibers with a symmetrical bifurcation. In passive fibers, "equivalent" cylinders misestimated the spatial distribution of voltage amplitudes and steady-state input resistance, partly due to the lack of axial current bifurcation. In active fibers with a single propagating action potential, the spatial distributions of point-to-point conduction velocity values (measured in meters/second) for a literal branch point differed significantly from those of their "equivalent" cylinders. "Equivalent" cylinders also underestimated the diameter-dependent delay in propagation through the branch point and branches, due to the larger "equivalent" diameter. Corrections to the "equivalent" cylinder did not reconcile differences between "equivalent" and literal models. However, "equivalent" and literal branch fibers had the same (a) steady-state resistance "looking into" an isolated symmetrical branch point and (b) geometry-independent point-to-point propagation velocity when measured in space constants per millisecond except within +/-1 space constant from the geometrical inhomogeneity. In summary, Rall's "equivalent" cylinders did not accurately reconstruct all passive or active electrophysiological properties and responses of their literal compartments. For the modeling of individual neurons, the requirement of single-branch resolution is discussed.

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

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.

Location and Magnitude of Conductance Changes Produced by Renshaw Recurrent Inhibition in Spinal Motoneurons

The mean location of Renshaw synapses on spinal motoneurons and their synaptic conductance were estimated from changes in impedance magnitude produced by sustained recurrent inhibition. Motoneuron impedance was determined by injecting quasi-white noise current into lumbosacral motoneurons of pentobarbital-anesthetized cats. Synaptic location and conductance were estimated by comparing observed impedance changes to simulation results obtained using standard motoneuron models and compartmental models fit to each impedance function. Estimated synaptic locations ranged from 0.10 to 0.41λ, with a mean of 0.19 or 0.24λ, depending on the estimation method. Average dendritic path length was 262 μm. Average synaptic conductance was 23 to 27 nS (range: 6.7 to 57.9 nS), corresponding to conductance changes of 78 to 88% of resting membrane conductance. Estimated accuracy was supported by consistency using different estimation methods, agreement with Fyffe's 1991 morphological data, and comparisons of observed and simulated recurrent IPSP amplitudes. Synaptic location, but not synaptic conductance, was correlated with rheobase, a measure of motoneuron excitability. Synaptic conductance did not depend on synaptic location. A regression analysis demonstrated that synaptic conductance and cell impedance were the principal factors determining recurrent IPSP amplitude. Simulations using the observed values and locations of Renshaw conductance demonstrate that recurrent inhibition can require as much as an additional 14 to 18% sustained excitatory synaptic conductance to depolarize motoneurons sufficiently to activate somatic or dendritic inward currents and recruit motoneurons or amplify excitatory synaptic currents.