Deviation of NLC from the simple two-state Boltzmann model. NLC was measured in the presence of 0.5 mm salicylate. The NLC data were analyzed by the simple two-state Boltzmann model (Equation 3, A), the three-state model (Equation 4, B), and the two-state-C_sa model (Equation 5, C). Solid lines show the fitting curves. Improvements of the fits are visually obvious in the residual plots by the three-state fitting (B) and the two-state-C_sa fitting (C) compared with that by the simple two-state fitting (A). Indeed, >10¹³ times higher Akaike's weights were obtained for the three-state and the two-state-C_sa fittings over the simple two-state fitting. Akaike's weights for the three-state and two-state-C_sa were 0.19 ± 0.08 and 0.81 ± 0.08% (n = 8), respectively.

Summary of the salicylate-dependent NLC measurements. The salicylate-dependent NLC recording exemplified in Fig. 2 was performed on 15 OHCs. The NLC parameters determined by the three-state and the two-state-C_sa models are summarized. All bars indicate the S.D. A, shown is a reaction scheme of chloride/salicylate binding to prestin according to the competitive inhibition model. P stands for prestin. Sal, salicylate. The fraction of functional prestin that remains after application of salicylate is calculated by the displayed equation. B, inhibition of prestin-dependent charge movement by 1.5 mm salicylate is shown. The broken line indicates the prestin activity that is expected to remain (25%, see “Results”). C, shown is a summary of the basal linear capacitance increment induced by salicylate. pF, picofarads. D and E, a summary of salicylate-induced V_pk shift is shown. F, a summary of salicylate-induced change in α is shown.

Relation of charge movement and OHC displacement. A and B, simultaneous measurement of NLC and motility in the presence of salicylate is shown. In the same experimental configuration as in Fig. 2, NLC and OHC motility were simultaneously measured in the presence of salicylate. NLC and motility were simultaneously recorded with one cycle of 2-Hz, 100-mV amplitude sinusoidal voltage stimulus superimposed with two higher frequency stimuli (390.6 and 781.2 Hz, 10-mV amplitude) at time points indicated by the solid triangles, while the membrane capacitance at 0 mV was constantly monitored during the measurements (A, inset). pF, picofarads. Accompanied by the reduction of the prestin-dependent charge movement, OHC displacement decreased. The same colors were used to show matching simultaneous NLC motility recordings. For determining prestin-dependent charge movement (q), C_lin and C_sa were first determined by the three-state and two-state-Csa Boltzmann models. Subsequently the area between NLC curves and the C_lin (or C_sa) was calculated. OHC displacement (d) was determined by the maximum displacement observed. C and D, shown is a summary of the q-d relation. The measurements shown in A and B were performed on different OHCs (n = 8). The d values were plotted against the q values determined by three-state model (C) or the two-state-Csa model (D) for each OHC. Different colors represent different OHCs. The solid lines are Deming's regression lines. Average r² values from eight OHCs with S.D. are shown in each figure. E, computer simulations of NLC motility responses in the presence and absence of salicylate explain how positive d intercepts can be seen at q = 0 if m₁/m₂ < 1. The following values were used: α₁ = α₂ = 0.04 mV⁻¹ (with and without salicylate), V_pk1 = −75 mV, V_pk2 = −70 mV (without salicylate), V_pk1 = −150 mV, V_pk2 = 0 mV (with salicylate), m₁/m₂ = 0.55. F, using the d-q data shown in C and Equations 8, 9, and 10, m₂ values were determined for each OHC (n = 8). The same colors are used for matching. G, the two-step electromechanical coupling mechanism of prestin is shown. z₁ and z₂ are apparent valences calculated from α₁ and α₂, determined by the three-state model (Fig. 4F). The positive signs are assigned for the rightward transitions. K₁₂ and K₂₃ are voltage-dependent equilibrium constants defined in the text, which increase with depolarizing voltage stimuli, and vice versa.

Salicylate-dependent change of NLC parameters determined by the three-state model (A∼E) and the two-state-C_sa model (F∼J). A and F, NLC was repetitively measured on an isolated OHC before and after applying 1.5 mm salicylate in the bath solution. Different colors represent different NLC recordings at different time points shown in the inset of A. The solid lines are fitting curves by the three-state model (Equation 4, A) or the two-state-C_sa model (Equation 5, F). A and F are the same NLC data set but with different data analyses. The six NLC parameters, N, C_lin, V_pk1/V_pk2, and α₁/α₂, for the three-state model (B∼E) and the five NLC parameters, Q_max, ΔC/C₀, V_pk, and α, for the two-state-C_sa model (G∼J) were determined for each NLC curve and were plotted against the recording time. The bars indicate the S.E. of fitting. The insets of B and G show the numbers of functional prestin molecules before application of salicylate, which are plotted against C_lin or C₀. Variation of the NLC parameters obtained from the three-state model before application of salicylate was large in some recordings. For this reason, 3 of 15 data sets were not included in the analysis for the three-state model (therefore, n = 12 for the three-state model analyses).

Simultaneous measurement of NLC and motility. NLC (A) and OHC displacement (B) were measured simultaneously as described under “Experimental Procedures” and in supplemental Fig. S1. The data were analyzed using the two-state Boltzmann model-based equations (Equations 3 and 6) shown under “Results.” The solid lines are the fitting curves derived from the equations. The simultaneous NLC and motility measurements were performed on 36 different OHCs, and α values (C) and V_pk values (D) were compared against each other for testing their identity. The error bars represent the S.E. of the curve-fitting analyses. The diagonal broken lines indicate exact match (y = x). Deming linear regression analyses (solid lines) followed by t tests were performed for quantitatively testing identity (see “Experimental Procedures”). The p values for the y intercept and the slope were 0.83 and 0.62 (C) and 0.33 and 0.39 (D), none of which disagreed with the null hypothesis of identity, i.e. a = 0, b = 1. E, Q_max and D_max were estimated from the curve fitting analyses shown in A and B. D_max values are plotted against the corresponding Q_max (n = 36). The error bars represent S.E. of the curve-fitting analyses. Alternatively, the observed maximum OHC displacement (d) is plotted against the observed prestin-dependent charge movement (q) that is determined by the area between NLC curves and the C_lin (E, inset). The Deming linear regression analysis was performed with the y intercept fixed at zero (y = ax). r² values for Q_max-D_max and q-d were 0.036 and 0.41, respectively. The NLC motility data (n = 36) were also analyzed by the three-state model, and the α₁ and α₂ values (F) and the V_pk1 and V_pk2 values (G) were compared against each other. Because the three-state fitting on NLC/motility data recorded in the absence of salicylate usually finds larger S.E., only data sets whose S.E. found in V_pk1/V_pk2 were less than 100 mV are shown, with bold symbols error bars, whereas others are shown with smaller pale symbols without error bars. The p values determined by Deming linear regression analyses (solid lines) followed by t tests for the y intercept (=0) and the slope (=1) were less than 0.05 for α₁, α₂, V_pk1, and V_pk2 comparisons, suggesting that α₁, α₂, V_pk1, and V_pk2 values are different between NLC and motility. H, shown are computer simulations of m₁/m₂-dependent OHC displacements using Equation 7. The parameters used were 0.0252 mV⁻¹, 0.0239 mV⁻¹, −85.7 mV, and −52.6 mV for α₁, α₂, V_pk1, and V_pk2, all of which were derived from the NLC measurements (F and G). The generated displacement data were analyzed by Equation 7 in which m₁/m₂ was fix at unity, and the resultant fitting parameters were plotted against m₁/m₂ for α₁ and α₂ (I) and V_pk1 and V_pk2 (J). The broken lines indicate the α and V_pk values used for generating the displacement data. K and L, NLC and OHC displacement were measured simultaneously as in A and B in the presence of 0.1∼1 mm salicylate. The NLC motility data (n = 15) were analyzed by the three-state model, and the α₁ and α₂ values (K) and the V_pk1 and V_pk2 values (L) were compared against each other. The p values determined by Deming linear regression analyses (solid lines) followed by t tests for the y intercept (=0) and the slope (=1) were all greater than 0.05 for α₁, α₂, V_pk1, and V_pk2 comparisons, suggesting that the NLC and motility are coupled in terms of α₁–α₂ and V_pk1–V_pk2.