A model for electrical resonance and frequency tuning in saccular hair cells of the bull-frog, Rana catesbeiana

Abstract

1. Electrical resonance in solitary hair cells was examined under several experimental conditions using the tight-seal recording technique in the whole-cell current-clamp mode. 2. Resonance was characterized by the frequency and quality factor of oscillations in membrane potential evoked by depolarizing current pulses. Oscillation frequency increased with depolarization, from about 90 Hz at the resting potential to a limiting value of about 250 Hz. The quality factor of the oscillations was a bell-shaped function of membrane potential that reached a maximum of up to 12.6 at a potential slightly positive to the resting potential. 3. Pharmacological experiments were performed to assess which of three ionic currents participate in electrical resonance. Reduction of the voltage-gated Ca2+ current (ICa) and the Ca2+-activated K+ current (IK(Ca)) by lowering the extracellular Ca2+ concentration, or reduction of IK(Ca) with tetraethylammonium ion (TEA) degraded the resonance. In contrast, blockade of the transient K+ current (IA) with 4-aminopyridine (4-AP) had no significant effect. 4. To test the sufficiency of the Ca2+ and the Ca2+-activated K+ currents to account for resonance, we developed a model using mathematical descriptions of the two currents derived in the preceding paper (Hudspeth & Lewis, 1988), with additional terms for leakage conductance and membrane capacitance. The model correctly predicts the oscillatory responses to applied current pulses, including the non-linear dependences of oscillation frequency and quality factor on membrane potential. 5. Simulations of current-clamp experiments in the presence of a reduced extracellular Ca2+ concentration or of TEA were generated respectively by decreasing the model's values for the maximal Ca2+ or Ca2+-activated K+ conductances. The model's predictions of membrane-potential oscillations under these conditions agree qualitatively with experimental results, providing further support for the model as a description of the resonance mechanism. 6. To identify the factors most important in determining the hair cell's resonance properties, we systematically altered the values of selected parameters in the model. Frequency was most profoundly influenced by increasing the magnitude and activation rate of the Ca2+-activated K+ conductance, whereas the quality factor was most sensitive to increases in the level of the Ca2+ conductance. 7. By including a term describing activation of the hair cell's mechanically sensitive transduction conductance, we used the model to predict a tuning curve for responses to mechanical inputs of various frequencies.(ABSTRACT TRUNCATED AT 400 WORDS)