An active motor model for adaptation by vertebrate hair cells.

Bullfrog saccular hair cells adapt to maintained displacements of their stereociliary bundles by shifting their sensitive range, suggesting an adjustment in the tension felt by the transduction channels. It has been suggested that steady-state tension is regulated by the balance of two calcium-sensitive processes: passive "slipping" and active "tensioning." Here we propose a mathematical model for an adaptation motor that regulates tension, and describe some quantitative tests of the model. Slipping and tensioning rates were determined at membrane potentials of -80 and +80 mV. With these, the model predicts that the I(X) curve (relating bundle displacement and channel open probability) should shift negatively by 124 nm when the cell is depolarized, with an exponential time course that is slower on depolarization from -80 to +80 mV than on repolarization. This was observed: on depolarization, the I(X) curve shifted by an average of 139 nm, and displayed the expected difference in rates at the two potentials. Because the negative shift of the I(X) curve on depolarization represents an increase in the tension on transduction channels, the model also predicts this tension should cause an unrestrained bundle to pivot negatively by 99 nm on depolarization. Such movement was observed using high-resolution video microscopy; its amplitude was variable but ranged up to about 100 nm, and its time course was asymmetric in the same way as that of the I(X) curve shift. In additional comparisons, the active bundle movements and I(X) curve shift exhibited a similar steady-state voltage dependence, and were both reversibly abolished by reduced bath Ca2+ or by the transduction channel blocker streptomycin. Lastly, among different cells, the amplitude of the movement increased with the size of the transduction current. Thus, a quantitative mechanical model for adaptation also accounts for the observed mechanical behavior of the bundle, suggesting that the same mechanism is responsible for both, and that adaptation is mediated by an active, force-producing mechanism.