Compartmental models of mammalian motoneurons of types S, FR and FF and their computer simulation

Mathematical models of motoneurons (MNs) of types S, FR and FF were developed based on cat MN data. Each of the three models has an initial segment, a soma and a dendritic tree. The initial segment and the soma include models of several types of ionic currents, including a calcium-dependent slow potassium current. The dendritic tree is modeled as a series association of several electrically passive cylinders. Afterhyperpolarization parameters, current to frequency relation and the responses to input current steps, ramps and sinusoids were used for model validation. The effects of sinusoidally varying synaptic inputs at different levels of the dendritic tree were studied by computer simulation. The corresponding frequency response functions resulted of lowpass type with cutoff frequencies from 10 to 40 Hz, for synapses occurring more distally or more proximally, respectively. The nonlinear effects caused by two sinusoidally varying synaptic conductances (at 7 and 11 Hz), acting at different dendritic segments, were quantified by spectral analysis of the current reaching the soma. The simulations pointed to two main nonlinear effects: (i) harmonics of the two input frequencies (e.g., 14 Hz) and (ii) intermodulation terms (e.g., 4 Hz). When the two synaptic inputs occurred on more distal dendritic compartments the nonlinear effects were more pronounced.