Cochlear outer hair cells are a class of mechano-sensory cells in the ear that convert sound-induced mechanical vibration into electrical signal. These cells also act as a fast motor capable of responding at auditory frequencies. The sensitivity and the sharp frequency discrimination of the mammalian ear is achieved by outer hair cells' activity in pumping energy into mechanical resonance of the basilar membrane. We have previously established that the hair cell motor uses electrical energy based on piezoelectricity. This is achieved by the coupling of electric charge transfer across the membrane with membrane area changes. Specifically, this motility can be reasonably explained by a simple two state model in which two states differ in charge and membrane area but not in the mechanical compliance. The area difference is determined by tension dependence of the motor activity. The model leads to a biphasic dependence of the axial stiffness analogous of gating compliance. However, the experimentally observed axial compliance monotonically increases with depolarization. Such observation appears to be explained by assuming that a large compliance of the state with smaller membrane area. However, such an assumption leads to incorrect tension dependence of the motor. It is found that this inconsistency is associated with the condition that increased membrane tension reverses the size of membrane areas of the two states. To avoid this paradox, the compliance of the state with smaller membrane area must decrease rapidly as membrane tension increases. That means that the axial compliance that is monotonic with respect to voltage can be predicted only if turgor pressure is less than 0.1 kPa, somewhat less than reported estimates.
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