To assess the degree of coupling between hair cells, we measure the movements of hair bundles, with the overlying membrane left intact on top of the sensory tissue. A localized mechanical stimulus was applied with a glass fiber mounted on a piezoelectric actuator, and the induced deflections were measured at various distances from the point of contact. We find that within the physiological regime of amplitudes and frequencies, phase-locking persists across most or all of the epithelium. The sacculus presents us with a highly coupled system, with individual bundles responding to applied stimulation.
Imaging through the
To fully characterize the dynamics of hair bundle motility, we apply mechanical stimulation at various frequencies and amplitudes. A 3D plot of the phase-locked component of the response displays the Arnold Tongue shape characteristic of nonlinear systems.
Our data indicate strong effects of imposed deflections on the dynamics of the oscillation. Negative displacements enhanced and prolonged the quiescent intervals during which the bundle did not oscillate, extending by more than 5-fold the original period of oscillation. Further increases in DC offset reduced the amplitude of innate movement, eventually leading to its complete suppression. The crossing of the supercritical Andronov-Hopf bifurcation would predict the amplitude of oscillation to decay continuously to zero as the control parameter shifts towards quiescent regime. The period of oscillation, however, is expected to remain the same. We see that the period of oscillation drastically changes, with a critical slowing down accompanying a reduction in amplitude. Hence, we propose that the system can cross an infinite-period bifurcation, a supercritical Hopf, or a multi-critical point.
We explore whether self-tuning or other modulation of dynamic state can occur in response external stimulus, in isolated sensory tissue. To mimic the effects of loud sound on a single cell, we apply high-amplitude mechanical deflection, for 10-1000 cycles, and then measure the subsequent oscillations. We find that spontaneous oscillations observed in vitro can be transiently suppressed, with a subsequent recovery of native oscillation. The duration of the quiescent state depends on the intensity and length of the applied stimulus train.
Hair bundle deflection imposed via magnetic probe