Figure 3.

Self-tuning of a hair bundle. If the Ca²⁺ concentration C within the cell is artificially high, the hair bundle is initially quiescent, but as Ca²⁺ ions are pumped from the cell, it gradually begins to oscillate with small amplitude. If C is suddenly artificially lowered, the hair bundle becomes unstable and executes high-amplitude spontaneous oscillations. Because these movements open the transduction channels, the influx J of Ca²⁺ ions increases; the consequent change in C regulates the motors and diminishes the amplitude of the oscillation until it almost disappears. In the steady state, the bundle executes self-tuned critical oscillations. For this simulation, we assumed that the probability of transduction channels opening was P_o(z) = (1 + 10 exp(−20 z/l)⁻¹, where z is the motor displacement, and that the time constant for equilibration of the Ca²⁺ concentration was τ = 1,000/α.