The Bullfrog Sacculus

from the Outside

Part 2

Inferences about saccular signal processing and its underlying mechanisms

Now that we have compared the general signal-processing properties of the bullfrog sacculus to those of the other three acoustic sensors in the bullfrog ear, we shall move on to the sacculus itself, in more detail. Before we do that, here is one more comparison between the sacculus and its spectral neighbor, the bullfrog amphibian papilla (AP).

As we saw in Part I, the ac response component in the bullfrog amphibian papilla is accompanied by a negative dc adaptation component, with the ac component growing linearly with stimulus amplitude, the dc component growing as the square of the stimulus envelope. Here, on the left we see the impact of that combination on a representative series of cycle histograms taken under steady-state conditions (the sinusoidal stimulus was applied for several seconds before the data were collected). For low-level auditory stimuli, the peak ac response was relatively strong and grew with increasing stimulus amplitude. For higher-level stimuli, the negative dc response began to overwhelm the ac response, although the phase of the peak of the latter remained fixed. For stimuli equal to or greater than 0.7 Pa, no steady-state response at all could be observed in this unit. There remained, however, a brief (transient) response when the stimulus was first applied.

Bullfrog saccular units showed no such dc response. The ac response continued to grow (linearly, as we shall soon see), but the phase of the peak steady-state response shifted leftward as the stimulus amplitude increased.

These effects are modeled in the following two figures.

Imagine that the blue line is the generator potential at the spike trigger of the unit being observed, and that the generator potential comprises an inherent (resting) dc level (rst bias) combined with the ac and dc responses to the stimulus. The total resulting dc level (rsp bias) thus is the sum of the resting bias and the dc response. Between the upper and lower thresholds (thr) in this model is the region of continuous spike-rate modulation, As long as the generator potential falls in this region, it produces continuous modulation of instantaneous spike rate. When it moves below the lower threshold, the instantaneous spike rate is zero; when it moves above the upper threshold, the instantaneous spike rate is at its maximum level. For the stimulus frequencies employed in the cycle histograms of the previous figure, the unit produced at most one spike per cycle (owing to refractoriness). Thus the dynamics of the spike trigger play an important role in the actual timing of the spikes. The model does not explicitly include that role.

Apply the same assumptions to this model. Here, however, the dc bias remains fixed at its inherent level. As the amplitude of the generator potential sweeps beyond the upper and lower thresholds, spike trigger dynamics guarantee that spike occurrences will be limited to the rising phase of the generator potential, as it passes through the region of continuous modulation. As the duration of that phase is shortened, spike occurrences will be confined to a shorter time interval, leading to a higher peak instantaneous spike rate. This model accounts for the leftward shift in the peak as well as its continuing to increase with increasing stimulus amplitude— even with very high-level stimuli (see next figure).

The figure caption here was taken from Lewis et al., 2001. According to the model, when the peak (instantaneous) spike rate response exceeds the mean spike rate, the spikes are confined to the rising phase of the generator potential as it sweeps through the region of continuous modulation. Truly linear response (through all phases of the sinusoidal generator potential) occurs when the peak response is well below the mean spike rate. The ordinates of the circles were computed by taking the discrete Fourier transform of the cycle histogram and computing the peak amplitude of the fundamental (50 Hz in this case). The ordinates of the squares were computed by observing the peak spike rate directly in the cycle histogram, and subtracting from it the mean spike rate of the unit at rest (unstimulated).

Xiaolong Yu combined noise with the Hodgkin-Huxley model to demonstrate how dithering of a spike trigger might produce a region of continuous modulation of instantaneous spike rate. French and Stein had done the same thing twenty years earlier with simpler triggers (e.g., integrate-and-fire models). We chose to extend their studies to the Hodgkin-Huxley model because that model includes both refractory mechanisms (whereby threshold is increased temporarily following a spike) and accommodative mechanisms (whereby threshold tends to move away from a slowly increasing generator potential). We were interested in how these phenomena, together, would shape the cycle histograms. We also were interested in the biophysical feasibility of the noise amplitude required for effective dithering.

This figure illustrates the effects of dithering noise at very low levels. Without noise added, the Hodgkin-Huxley model responds to a continuously-increasing stimulus current by jumping suddenly from 0 spikes/sec to near maximum spike rate. Dithering noise eliminates that jump and provides a broad region of continuous spike-rate modulation. The following two figures compare responses of a saccular unit to four levels of sinusoidal stimulus amplitude to the responses from the dithered Hodgkin-Huxley model (HHN model) to four levels of sinusoidal generator-current amplitude. It seems that here we have a reasonable biophysical basis for the two graphical models with their continuous spike-rate modulation regions.

Here are linear gains taken from our early work on the seismic sense of the bullfrog sacculus.

These gains were computed for saccular units by discrete Fourier transform of responses to low-amplitude vibrational sinusoids. Note that at the threshold of the previous champs (snakes and cockroaches), which is 0.02 cm/sec², units with gains in the 1000-3000 bracket would produce peak responses of 20 to 60 spikes per sec. In many cases, that would be beyond the linear operating ranges of the units.

And here are best (band-center) tuning frequencies.

These data were taken by Ellen Leverenz, Hironori Koyama, Richard Baird, and me in the early 1980s. The distribution of best frequencies conforms well to what we have observed in the years since that time. It is useful to note that the frequencies of the electrical resonances observed in bullfrog saccular hairs cells ranged from about 90 Hz to about 250 Hz—mostly well beyond the range of saccular sensitivity.

To test for involvement of electrical resonances in bullfrog saccular units, David Egert examined the temperature sensitivity of tuning. Electrical resonances in hair cells are strongly dependent on temperature. David found virtually no variation in the frequencies of tuning peaks and troughs as the temperature was altered. This result strongly implies that the resonances, observed in isolated hair cells, are not involved significantly in the tuning of saccular sensitivity. Aside from the deep, persistent notches, the ragged nature of these tuning curves is a consequence of short sampling times used in the triggered-correlations.

The following figure shows results of similar experiments (by Pim van Dijk) on the bullfrog amphibian papilla.

In that organ, tuning peaks of lower-frequency units units shift markedly with temperature changes, implying strong involvement of electrical resonances.

Bullfrog saccular units respond to airborne sound (presented to the tympanum) as well as to substrate vibration. Xiaolong Yu found that there frequently were conspicuous differences between the auditory and vibrational tuning curves of bullfrog saccular units. The latter often exhibited deep anti-resonant notches (for which David Egert subsequently found no temperature dependence). This implies that auditory and vibrational stimuli take different routes to reach saccular hair cells.

Here are the two traditionally-cited pathways for acoustic stimuli to reach the sacculus. Both paths converge at the oval window. The anti-resonance notches were present in some saccular units, absent in others— in any given bullfrog. Furthermore, where they occurred, their frequencies varied from unit to unit in any given bullfrog. Therefore, their source did not lie in a common signal path from the periphery. This suggests profound differences in the sources of auditory and vibrational sensitivities in the bullfrog sacculus.

The investment in the bullfrog saccular otoconial mass, shown here in a dry state, is huge. When one opens the otic capsule of the frog, the saccular otoconial mass is by far the largest visible structure. One supposes that it must participate importantly in saccular vibratory sensitivity—perhaps as a sensing mass that tends to stay put as the rest of the ear is subjected to vibration, allowing the sacculus to function as an accelerometer. The otoconial mass actually is a viscous slurry of otoconia (calcium carbonate crystals) in a gel-like medium, surrounded by an inextensible but flexible membrane. It is connected through a gelatinous pad to individual hair bundles. It is easy to imagine variations in tuning properties, including the occurrences of anti-resonances, from place to place over that pad. On the other hand, it is not clear why those anti-resonances would not come into play for acoustic stimuli propagating from the tympanum, through the oval window to the sacculus. It is interesting to contemplate the micromechanical differences between otoconial motion that would be induced by whole-body acceleration and those that would be induced by differential motion of the oval window alone.

This takes us to the inside of the bullfrog ear—beyond the scope of this presentation. Our goal, in the research presented here, was to examine the bullfrog ear with minimal disturbance to its internal mechanical milieu. Of course our interest in the bullfrog saccule extended both inward-- into that milieu, and outward—to the role of vibration in frog behavior.

We studied micro-morphology in the amphibian ear.

We identified correspondences between micro-morphological structures and function.

We examined the morphogenesis of the frog sacculus and its hair bundles.

We discovered how amazingly sensitive the frog saccule was to vibrational stimuli .

And, together with Peter Narins, we found evidence that frogs can use vibrational signals for communication—

a useful acoustic alternative when the airborne pathway is cluttered with noise and interference.