FIGURE 5.

Responses of the virtual hair cell. A total of 32 step forces were applied ranging from −50 to 600 pN. Each case was simulated for 2 ms. Of those 32 simulations, three time responses were selected in A and B—force magnitudes of 20, 60, and 140 pN. (A) Tip displacement along time: Solid lines are the response of active hair cells, and dashed lines are from passive hair cells with no channel activity. (B) Channel activations along time: The hair cell activation level, I, was defined as the number of open channels at the time divided by the total number of channels. For small forces, fewer channels opened and all of them were closed again. As the force stimulus increased, more channels opened and more channels remained unclosed. (C) F-X curve: For the active response with channel gating, the force-displacement curve undulates between 0 ∼ 25 nm (•). The active curve was obtained at peak response. When the channels were held in their closed state (passive response, dashed line), the F-X curve behaved smoothly. The curve fit of active response was from gating spring theory using Eq. 3a. At F = 50 nm, the active F-X curve shifts to the right by 8 nm from the passive curve, which is about the magnitude of the largest twitch. (D) Activation curves were obtained from a series of simulations. The tip deflection X was obtained when the bundle was deformed most (•) and at 2 ms after the fast adaptation finishes (○). The second order Boltzmann relations were used to fit the data points (solid lines). The best fit for peak response (•) is obtained with α₁ = 362 nm⁻¹, α₂ = 31 nm⁻¹, X₁ = 9 nm, and X₂ = 36 nm. The best fit for post-fast-adaptation (○) is obtained with α₁ = 76 nm⁻¹, α₂ = 20 nm⁻¹, X₁ = 38 nm, and X₂ = 79 nm. (E) The dashed line indicates the passive stiffness of the bundle. Solid lines are the active K-X curve obtained from the active F-X curve. The stiffness was 2.0 and 2.6 pN/nm at X = − 25 and 100 nm, respectively, and the minimum active (dynamic) stiffness was 8.0 pN/nm at X = 8 nm.