Nonlinear input-output behavior of the repetitive firing mechanism in crayfish tonic stretch receptor cells was studied using white-noise analysis; the latter technique allows estimation of Wiener kernel functions which provide a complete description of the system input-output behavior, at least for the conditions under which the experiment is performed. 200ms-long steps of Gaussian-distributed current levels were injected through a microelectrode as the input. Nerve impulse (spike) frequency was used as the output variable. Analysis was restricted to signal frequency components less than or equal to the cell's firing frequency. For this frequency range, the Wiener kernels can be related directly to previously known physiological properties of neurons, such as pacemaker sensitivities, thresholds, and adaptation. Different measures of "spike frequency" (instantaneous frequency, average frequency, and convolution of the spike train with a Sinc function) were tested and gave approximately the same results, with the major differences being at high frequencies. At normal carrier frequencies (approx. 10Hz) and small modulation depths (cell never shut off for long periods), the stretch receptor behaved very linearly; the first kernel had a peak at the origin followed by a negative decaying undershoot, as would be expected for a neuron with "refractory" (spike-dependent) adaptation ; higher kernels made negligible contributions. In this range, the first kernel peak corresponded approximately to the cell's pacemaker sensitivity, as would be expected.
When a high modulation depth was employed, the cell was silent for appreciable periods, indicating nonlinear behavior (half-wave rectification). The first kernels were qualitatively unchanged, but second kernels now made a significant contribution.