Active hair-bundle movements can amplify a hair cell’s response to oscillatory mechanical stimuli

To enhance their mechanical sensitivity and frequency selectivity, hair cells amplify the mechanical stimuli to which they respond. Although cell-body contractions of outer hair cells are thought to mediate the active process in the mammalian cochlea, vertebrates without outer hair cells display highly sensitive, sharply tuned hearing and spontaneous otoacoustic emissions. In these animals the amplifier must reside elsewhere. We report physiological evidence that amplification can stem from active movement of the hair bundle, the hair cell’s mechanosensitive organelle. We performed experiments on hair cells from the sacculus of the bullfrog. Using a two-compartment recording chamber that permits exposure of the hair cell’s apical and basolateral surfaces to different solutions, we examined active hair-bundle motion in circumstances similar to those in vivo. When the apical surface was bathed in artificial endolymph, many hair bundles exhibited spontaneous oscillations of amplitudes as great as 50 nm and frequencies in the range 5 to 40 Hz. We stimulated hair bundles with a flexible glass probe and recorded their mechanical responses with a photometric system. When the stimulus frequency lay within a band enclosing a hair cell’s frequency of spontaneous oscillation, mechanical stimuli as small as ±5 nm entrained the hair-bundle oscillations. For small stimuli, the bundle movement was larger than the stimulus. Because the energy dissipated by viscous drag exceeded the work provided by the stimulus probe, the hair bundles powered their motion and therefore amplified it.

Dressed polyions, counterion condensation, and adsorption excess in polyelectrolyte solutions.

The phenomenon of Manning-Oosawa counterion condensation is given an explicit statistical mechanical and qualitative basis via a dressed polyelectrolyte formalism in connection with the topology of the electrostatic free-energy surface and is derived explicitly in terms of the adsorption excess of ions about the polyion via the nonlinear Poisson-Boltzmann equation. The approach is closely analogous to the theory of ion binding in micelles. Our results not only elucidate a Poisson-Boltzmann analysis, which shows that a fraction of the counterions lie within a finite volume around the polyion even if the volume of the system tends towards infinity, but also provide a direct link between Manning's theta-the number of condensed counterions for each polyion site-and a statistical thermodynamic quantity, namely, the adsorption excess per monomer.