Effects of extracellular Ca2+ concentration on hair-bundle stiffness and gating-spring integrity in hair cells

When a hair cell is stimulated by positive deflection of its hair bundle, increased tension in gating springs opens transduction channels, permitting cations to enter stereocilia and depolarize the cell. Ca2+ is thought to be required in mechanoelectrical transduction, for exposure of hair bundles to Ca2+ chelators eliminates responsiveness by disrupting tip links, filamentous interstereociliary connections that probably are the gating springs. Ca2+ also participates in adaptation to stimuli by controlling the activity of a molecular motor that sets gating-spring tension. Using a flexible glass fiber to measure hair-bundle stiffness, we investigated the effect of Ca2+ concentration on stiffness before and after the disruption of gating springs. The stiffness of intact hair bundles depended nonmonotonically on the extracellular Ca2+ concentration; the maximal stiffness of ≈1200 μN⋅m−1 occurred when bundles were bathed in solutions containing 250 μM Ca2+, approximately the concentration found in frog endolymph. For cells exposed to solutions with sufficient chelator capacity to reduce the Ca2+ concentration below ≈100 nM, hair-bundle stiffness fell to ≈200 μN⋅m−1 and no longer exhibited Ca2+-dependent changes. Because cells so treated lost mechanoelectrical transduction, we attribute the reduction in bundle stiffness to tip-link disruption. The results indicate that gating springs are not linearly elastic; instead, they stiffen with increased strain, which rises with adaptation-motor activity at the physiological extracellular Ca2+ concentration.

Torsional directed walks, entropic elasticity, and DNA twist stiffness

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the “torsional directed walk.” Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835–1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.