Further Evidence for Tuning Mechanisms of High Dynamic Order in Lower Vertebrates

Abstract

In recent years, data from individual hair cells have suggested that frequency selectivity in lower vertebrates is accomplished by the amplitude tuning peaks of underdamped electrical resonances (Crawford and Fettiplace, 1981; Lewis and Hudspeth, 1983; Pitchford and Ashmore, 1987). In the present study we have used the reverse-correlation (REVCOR) method (Evans, 1989; Eggermont et al, 1983; de Boer and Kuyper, 1968; de Boer and de Jongh, 1977) to study linear tuning responses from primary afferent axons of the three inner-ear organs in which these resonances were first reported -- the turtle basilar papilla and the frog sacculus and amphibian papilla. The characteristic signature of a single (undcrdamped) resonance comprises the following features: (I) impulse response in the fonn of a sinusoid with exponentially declining amplitude, (2) sinusoidal steady-state phase shift limited to one-half cycle, (3) convexity of the gain (amplitude) tuning curve limited to the highest three decibels (where the tuning curve is plotted on the conventional log-log coordinates), and (4) absolute values of the limiting slopes of the gain tuning curve which sum to two (decades per decade). If the outputs of resonances were added (not subtracted) in parallel, producing a tuning structure of high dynamic order, the characteristic signature of that structure would comprise features (2) and (4) from the previous list, plus (5) global concavity of the gain tuning curve (convexity only within approximately 3 dB of the tuning peaks). Among 155 axons included in this study, all displayed the following properties: (I) impulse responses that are more complex than exponentially decaying sinusoids, (2) sinusoidal steady-state phase shifts ranging over one or more cycles, (3) gain tuning curves exhibiting global convexity (with occasional, local concavity) and, (4) limiting gain-tuning-curve slopes whose absolute values sum to numbers considerably greater than two. We conclude that frequency selectivity in these axons is not accomplished by underdamped resonance peaks acting alone or in parallel combination (through positive addition), but rather by the asymptotic slopes of amplitude tuning curves, made steep by high dynamic order.