Electrotonic architecture of type-identified α-motoneurons in the cat spinal cord

1. Measurements of input resistance (R(N)), time constant (τ₀), and electrotonic length (L(peel)) were derived from intracellular voltage changes produced by injection of current pulses in six type-identified triceps surae α-motoneurons. The motoneurons were labeled with horseradish peroxidase and subsequently reconstructed and measured from serial sections. These quantitative morphological and physiological data were incorporated into detailed computer models of the motoneurons. 2. Steady-state and dynamic models were used to determine values for specific membrane resistivity (R(m)) that matched the experimental estimates of R(N), τ₀, and L(peel) for each motoneuron. The models were based on the following assumptions 1) the membrane was electrically passive, 2) cytoplasmic resistivity (R(i)) was 70 Ω-cm, and 3) 'sealed-end' boundary conditions were present at dendritic terminations. We also considered the nature and magnitude of possible errors introduced by using linear (passive) computer models to match responses from motoneurons with nonlinear (i.e., voltage-dependent) conductances. 3. If we assume that the experimental measurements of R(N) and τ₀ were correct, uniform R(m) values that reproduced the experimentally measured R(N) required widely varying values of C(m) (1.4-8.6 μF/cm²) to match the experimental τ₀. Furthermore, the electronic distance to dendritic terminals was generally much greater than expected from physiological estimates of L(peel). However, if we assumed that the R(N) measurements could have been underestimated by as much as 30% and that C(m) = 1.0 μF/cm², it was possible to choose spatially uniform R(m) that matched the observed τ₀ in three of six cases. 4. Relaxing the assumption of spatially uniform membrane resistivity permitted us to reconcile the anatomical and physiological characteristics of all six motoneurons. Two qualitatively different models of R(m) nonuniformity gave equally good fits to the experimental results 1) a step-wise increase in R(m) from a low value at the soma to a much higher but uniform value over the entire dendritic tree, and 2) a monotonic increase in R(m) from soma to distal dendrites as a sigmoidal function of path distance along the dendrites. The step and sigmoidal models of the spatial distribution of R(m) generated different electronic architectures in motoneuron dendritic trees, but both gave essentially identical elctrical responses at the soma. 5. The complex electrotonic structure of the dendrites precluded the use of equivalent cylinder models. Instead, using the approach of Rall (47), we constructed equivalent cable models with varying diameter that were based on the actual dendritic morphology. These models were useful in predicting the system time constant, τ₀, of neurons with nonuniform R(m) and markedly unequal electrotonic path lengths but did not accurately reproduce the transient response obtained in the models that embodied the full branching structure. 6. We conclude that the effective membrane resistivity of α-motoneurons is probably lower at and, perhaps, near the soma, and that the dendritic trees of these cells are electrotonically compact (overall L values ~ 1.5). Possibilities for the genesis of nonuniform membrane resistivity are discussed. The results are consistent with the suggestion that the effective, spatially weighted average membrane resistivity of α-motoneurons varies systematically with motor-unit type in the sequence: type FF < type FR < type S.