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.

Contribution of Malic Enzyme, Pyruvate Kinase, Phosphoenolpyruvate Carboxylase, and the Krebs Cycle to Respiration and Biosynthesis and to Intracellular pH Regulation during Hypoxia in Maize Root Tips Observed by Nuclear Magnetic Resonance Imaging and Gas Chromatography-Mass Spectrometry1

In vivo pyruvate synthesis by malic enzyme (ME) and pyruvate kinase and in vivo malate synthesis by phosphoenolpyruvate carboxylase and the Krebs cycle were measured by 13C incorporation from [1-13C]glucose into glucose-6-phosphate, alanine, glutamate, aspartate, and malate. These metabolites were isolated from maize (Zea mays L.) root tips under aerobic and hypoxic conditions. 13C-Nuclear magnetic resonance spectroscopy and gas chromatography-mass spectrometry were used to discern the positional isotopic distribution within each metabolite. This information was applied to a simple precursor-product model that enabled calculation of specific metabolic fluxes. In respiring root tips, ME was found to contribute only approximately 3% of the pyruvate synthesized, whereas pyruvate kinase contributed the balance. The activity of ME increased greater than 6-fold early in hypoxia, and then declined coincident with depletion of cytosolic malate and aspartate. We found that in respiring root tips, anaplerotic phosphoenolpyruvate carboxylase activity was high relative to ME, and therefore did not limit synthesis of pyruvate by ME. The significance of in vivo pyruvate synthesis by ME is discussed with respect to malate and pyruvate utilization by isolated mitochondria and intracellular pH regulation under hypoxia.