A MODEL STUDY ON THE INFLUENCE OF A SLOWLY ACTIVATING POTASSIUM CONDUCTANCE ON REPETITIVE FIRING PATTERNS OF MUSCLE-SPINDLE PRIMARY ENDINGS

The general mathematical model of Frankenhaeuser and Huxley, which describes the generation of action potentials in myelinated nerve fibres, has been used as a kernel for a model of a sensory nerve ending. Two types of modifications were implemented. First, the four original permeability constants (those of potassium, sodium, non-specific and leak) were changed simultaneously (using an automated tuning algorithm), in order to introduce few-frequency repetitive firing capability (down to 15 Hz), keeping the deviations from the original values as small as possible. Second, a slow potassium conductance was added, in order to model slow processes (like accommodation) with time constants longer than those required to simulate short-lasting action potentials. Sensory stimuli were simulated as changes in passive conductance. The model displayed the following properties, which are typical of many sensory endings in general and of muscle spindle primary endings in particular: (i) The range of sustained repetitive firing was extended into the domain of low discharge rates, so as to span the entire physiological range (from 2 to 700 sec(-1)). (ii) The relation between firing rate and receptor potential was roughly linear over the full range of firing. (iii) Following a step increase of stimulus, the firing rate showed adaptation with a time constant of about 70 msec. (iv) Sudden reduction of the stimulus was followed by post-release silence. (v) Following a step increase of stimulus, the receptor potential showed a short dynamic peak, (vi) Following a step decrease of stimulus, the receptor potential displayed a post-release undershoot and recovery with a time constant of approximately 100 msec. (vii) With sinusoidal stimuli the receptor potential showed band-pass filter properties with phase advance below and phase lag above 12 Hz and a peak in gain at about 20 Hz. Thus the present equations adequately describe a range of known properties of muscle spindle primary endings. Based on minimal modification and extension of the Frankenhaeuser-Huxley model of action potential generation in myelinated fibres, they constitute a theory of sensory encoding. This theory is further corroborated by the experimental evidence of the presence of calcium-activated potassium channels in numerous sensory-including primary spindle-endings.