A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Protein folding kinetics exhibit an Arrhenius temperature dependence when corrected for the temperature dependence of protein stability

The anomalous temperature dependence of protein folding has received considerable attention. Here we show that the temperature dependence of the folding of protein L becomes extremely simple when the effects of temperature on protein stability are corrected for; the logarithm of the folding rate is a linear function of 1/T on constant stability contours in the temperature–denaturant plane. This convincingly demonstrates that the anomalous temperature dependence of folding derives from the temperature dependence of the interactions that stabilize proteins, rather than from the super Arrhenius temperature dependence predicted for the configurational diffusion constant on a rough energy landscape. However, because of the limited temperature range accessible to experiment, the results do not rule out models with higher order temperature dependences. The significance of the slope of the stability-corrected Arrhenius plots is discussed.

Hybridization of single-stranded DNA targets to immobilized complementary DNA probes: comparison of hairpin versus linear capture probes

A microtiter-based assay system is described in which DNA hairpin probes with dangling ends and single-stranded, linear DNA probes were immobilized and compared based on their ability to capture single-strand target DNA. Hairpin probes consisted of a 16 bp duplex stem, linked by a T2-biotin·dT-T2 loop. The third base was a biotinylated uracil (UB) necessary for coupling to avidin coated microtiter wells. The capture region of the hairpin was a 3′ dangling end composed of either 16 or 32 bases. Fundamental parameters of the system, such as probe density and avidin adsorption capacity of the plates were characterized. The target DNA consisted of 65 bases whose 3′ end was complementary to the dangling end of the hairpin or to the linear probe sequence. The assay system was employed to measure the time dependence and thermodynamic stability of target hybridization with hairpin and linear probes. Target molecules were labeled with either a 5′-FITC, or radiolabeled with [γ-33P]ATP and captured by either linear or hairpin probes affixed to the solid support. Over the range of target concentrations from 10 to 640 pmol hybridization rates increased with increasing target concentration, but varied for the different probes examined. Hairpin probes displayed higher rates of hybridization and larger equilibrium amounts of captured targets than linear probes. At 25 and 45°C, rates of hybridization were better than twice as great for the hairpin compared with the linear capture probes. Hairpin–target complexes were also more thermodynamically stable. Binding free energies were evaluated from the observed equilibrium constants for complex formation. Results showed the order of stability of the probes to be: hairpins with 32 base dangling ends > hairpin probes with l6 base dangling ends > 16 base linear probes > 32 base linear probes. The physical characteristics of hairpins could offer substantial advantages as nucleic acid capture moieties in solid support based hybridization systems.