The properties of the spike encoder inferred from EPSP and spike rates at the cito-neural junction of the frog labyrinth

The cytoneural junction of the frog semicircular canals is a suitable model of synapse to study cell firing mechanisms. The electrical activity recorded from the afferent terminals at rest, and in response to acceleration of the cupula-endolymph system originates from both pre- and postsynaptic processes: the EPSP frequency is a function of neurotransmitter released from receptor cells whereas the spike rate is the result of postsynaptic membrane mechanisms. Since the EPSP and spike ratio represent the physiological input and output, respectively, of the spike "encoder' and can be recorded simultaneously in the tracings, we have made use of both these parameters to attempt an analysis of the mechanism by which the fluctuating signal generated by the summation of randomly occurring EPSPs is translated into a modulated spíke frequency. As a general rule spike frequency should be determined by the probability that the fluctuating postsynaptic potential reaches the threshold for spike generation. In the frog labyrinth, this probability doesn't increase linearly with the EPSP rate. In effect a marked rectification (silencing for negative acceleration) has been consistently observed in the spike rate but not in the EPSP rate (Rossi et al., 1989, J. Gen. Physiol.,94, 303-327). Therefore the relationship is expected to be nonlinear. In response to sustained excitatory stimuli (positive acceleration), the recovery of the spike rate toward the initial value (Rossi et al, 1989) is faster than EPSP rate. This suggests that some dynamic distorsions are present in the input-output relation, probably due to voltage and time dependent ionic conductance triggered by postsynaptic depolarization. In order to define the encoder input-output relationships, the encoder was considered like the series of two-elements: the first exhibiting static characterintics and a nonlinear gain, and the second (a linear gain filter) responsible of the dynamic features. Experiments were then performed by stimulating the labyrinth with rotational velocity steps, i.e. acceleration impulses approximating delta functions, the time course of EPSP rate, r(t), was assessed by noise analysis (Rossi et al., 1989), and the spikes were counted directly to yield the spike rate as a function of time s(t). After linearization the transfer function of the encoder, H(f) was computed by the power spectral and cross-spectral relations: Sss(f) = (H(f))2 • Srr(f) Sre(f) = H(f) • Srr(f) where S stands for power spectra, or cross spectral density function. A least square-error analytical form was calculated for the transfer function by means of the autoregressive analysis on autocovariance function of the encoder impulse reaponse, h(t). Preliminary results show that a low pass LRC (inductance-resistance-capacitance) filter is in general adequate to account for the encoder transfer function. This suggents that in the encoder are present processes that respond to the membrane potential and the encoder previous activity. In other words the probability of spike diacharge is related to the value of membrane potential, as well as, to its integral and its derivative. This is in accord with results obtained in nervous cell with galvanic stimulations, and would be reasonably expected if some of the ionic conductances described for typical spike encoders were present at the afferent terminal. Natural frequency and damping ratios of the fitted LRC-models were calculated for different cytoneural junctions at rest and with impulses of different amplitude and polarity. The results suggest that the properties of the spike frequency modulation process (encoder) are individual features of each cytoneural junction. The experimental and theoretical approaches employed in this analysis appear particularly suitable to elucidate the biophysical mechanisms of the encoding processes.