Gating energies and forces of the mammalian hair cell transducer channel and related hair bundle mechanics

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Abstract
We quantified the molecular energies and forces involved in opening and closing of mechanoelectrical transducer channels in hair cells using a novel generally applicable method. It relies on a thermodynamic description of the free energy of an ion channel in terms of its open probability. The molecular gating force per channel as reflected in hair bundle mechanics is shown to equal kT/I(X)dI(X)/dX, where I is the transducer current and X the deflection of the hair bundle. We applied the method to previously measured I(X) curves in mouse outer hair cells (OHCs) and vestibular hair cells (VHCs). Contrary to current models of transduction, gating of the transducer channel was found to involve only a finite range of free energy (>10 kT), a consequence of our observation that the channel has a finite minimum open probability of ca. 1% for inhibitory bundle deflections. The maximum gating forces per channel of both cell types were found to be comparable (ca. 300–500 fN). Because of differences in passive restoring forces, gating forces result in very limited mechanical nonlinearity in OHC bundles compared to that in VHC bundles. A kinetic model of channel activation is proposed that accounts for the observed transducer currents and gating forces. It also predicts adaptation–like effects and spontaneous bundle movements ensuing from changes in state energy gaps possibly related to interactions of the channel with calcium ions.