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 des cribes 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 perm eability 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 t o 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 t han those required to simulate short-lasting action potentials. Sensor y 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 d omain of low discharge rates, so as to span the entire physiological r ange (from 2 to 700 sec(-1)). (ii) The relation between firing rate an d receptor potential was roughly linear over the full range of firing. (iii) Following a step increase of stimulus, the firing rate showed a daptation 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 dyna mic peak, (vi) Following a step decrease of stimulus, the receptor pot ential displayed a post-release undershoot and recovery with a time co nstant of approximately 100 msec. (vii) With sinusoidal stimuli the re ceptor 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. Th us the present equations adequately describe a range of known properti es of muscle spindle primary endings. Based on minimal modification an d extension of the Frankenhaeuser-Huxley model of action potential gen eration in myelinated fibres, they constitute a theory of sensory enco ding. This theory is further corroborated by the experimental evidence of the presence of calcium-activated potassium channels in numerous s ensory-including primary spindle-endings.