Spike initiation by transmembrane current: a white‐noise analysis.

Abstract

Transmembrane current features correlated with spike initiation were examined in Aplysia neurons using a Gaussian white-noise stimulus. This stimulus had the advantages that it presented numerous wave forms in random order without prejudgement as to their efficacies, and that it allowed straightforward statistical calculations. Stimulation with a repeating segment of Gaussian white-noise current revealed remarkable invariance in the firing times of the tested neurons and indicated a high degree of reliability of their response. Frequencies (< 5 Hz) involved in spike triggering propagated faithfully for up to several millimeters, justifying intrasomatic current injection to examine spike initiation at the trigger locus. Examination of current wave forms preceding spikes indicated that a wide variety could be effective. A statistical analysis included computation of probability densities, averages, standard deviations and correlation coefficients of pairs of current values. Each statistic was displayed as a function of time before the spike. The average current trajectory preceding a spike was multiphasic and depended on the presence and polarity of a DC bias. An early, relatively small inward- or outward-going phase was followed by a large outward phase before the spike. The early phase tended to oppose the polarity of the DC bias. The late outward phase of the average current trajectory reached a maximum 40-75 ms before triggering the action potential (AP) and returned to near zero values at the moment of triggering. The current peak occurring in advance of the AP was probably partly caused by a phase delay between the transmembrane current and potential. The failure of the average current trajectory to return to control values immediately following the peak argued for a positive role of the declining phase in spike triggering. Probability densities preceding spikes were Gaussian, indicating that the average was also the most probable value. Although the densities were broad, confirming that spikes were preceded by a wide variety of current wave forms, their standard deviations were reduced significantly with respect to controls, suggesting a preferred status of the average current trajectory in spike triggering. The matrix of correlation coefficients between current pairs suggested that spikes tended to be preceded by wave forms that in part kept close to the average current trajectory and in part preserved its shape. The average 1st and 2nd derivatives of spike-evoking epochs revealed that current slope and acceleration, respectively, were most crucial in the last 200 ms before spike triggering, and that these dynamic stimulus components were more important for a cell maintained under a depolarizing, rather than a hyperpolarizing bias. A simple model of the spike-triggering system, consisting of a linear filter (1st-order Wiener kernel) followed by a threshold device with ''dead-time'', was quite accurate in predicting experimentally observed spike timings. A number of stimulus parameters (polarity and amplitude, variability, slope, acceleration, temporal correlation) were relevant in spike-triggering, and for a particular stimulus (e.g., a postsynaptic potential), the absence of one feature could be compensated for by the presence of another.