Prestin-driven cochlear amplification is not limited by the outer hair cell membrane time constant

Abstract

Outer hair cells (OHCs) provide amplification in the mammalian cochlea using somatic force generation underpinned by voltage-dependent conformational changes of the motor protein prestin. However, prestin must be gated by changes in membrane potential on a cycle-by-cycle basis and the periodic component of the receptor potential may be greatly attenuated by low-pass filtering due to the OHC time constant (τ(m)), questioning the functional relevance of this mechanism. Here, we measured τ(m) from OHCs with a range of characteristic frequencies (CF) and found that, at physiological endolymphatic calcium concentrations, approximately half of the mechanotransducer (MT) channels are opened at rest, depolarizing the membrane potential to near -40 mV. The depolarized resting potential activates a voltage-dependent K+ conductance, thus minimizing τ(m) and expanding the membrane filter so there is little receptor potential attenuation at the cell's CF. These data suggest that minimal τ(m) filtering in vivo ensures optimal activation of prestin.

Figure 1

MT Currents and Receptor Potentials in Rat OHCs (A) Saturating receptor currents with hair bundles exposed to saline containing Na⁺ and 1.5 mM Ca²⁺. (B) Saturating receptor currents in a different OHC with hair bundles locally perfused with artificial endolymph containing K⁺ and 0.02 mM Ca²⁺. Note larger MT current amplitude and increased fraction on at rest compared to 1.5 mM Ca²⁺. (C) Receptor potentials, V_m, for cell in (A) with hair bundles exposed to Na⁺, 1.5 mM Ca²⁺ saline. (D) Receptor potentials for cell in (B) with hair bundles exposed K⁺, 0.02 mM Ca²⁺ endolymph. The sinusoidal stimulus (top), which applies to both receptor currents and potentials, was delivered with a fluid jet, hair bundle motion being calibrated by projection on a photodiode pair; holding potential in voltage clamp −84 mV. (E) Relation between MT current (I) and bundle displacement (X) in (A) over one cycle of the response (dashed line). (F) MT current versus bundle displacement in (B) over one cycle of the response (dashed line). I–X results fitted with single Boltzmann (continuous line): I = I_MAX/(1 + (exp((X₁ − X)/X_e)) where I_MAX = 1.51 nA, X_e = 0.017 μm, X₁ = 0.04 μm (C, perilymph); I_MAX = 2.4 nA, X_e = 0.035 μm, X₁ = 0.008 μm (D, endolymph). Apical cochlear location, P8 (A and C), P9 (B and D) rats, T = 22°C.

Figure 2

Tonotopic Variation in MT Currents with Hair Bundles Exposed to Endolymph (0.02 mM) Ca²⁺ (A) Saturating MT currents and receptor potentials in an apical gerbil OHC (CF = 0.35 kHz). (B) Saturating MT currents and receptor potentials in a gerbil middle turn OHC (CF = 2.5 kHz). In both (A) and (B), about half the maximum MT current was activated at rest and the current was abolished by addition of 0.2 mM DHS. Top traces show driving voltage to piezo. (C) MT current (mean ± SEM) versus CF for three gerbil locations (filled squares) and two rat locations (filled circles), number of measurements indicated by each point. (D) Resting open probability (P_open; mean ± SEM) of the MT channels for gerbil and rat locations (P7–P10 animals). Currents recorded at −84 mV holding potential, T = 22°C–24°C.

Figure 3

OHC Endogenous Ca²⁺ Buffer Assayed with Perforated Patch (A) MT currents recorded with an intracellular solution containing 1 mM EGTA as the Ca²⁺ buffer, in Na⁺, 1.5 mM Ca²⁺ saline (middle), and during local perfusion with K⁺, 0.02 mM Ca²⁺ endolymph (bottom). (B) MT currents under perforated-patch in Na⁺, 1.5 mM Ca²⁺ (middle) and during local perfusion with K⁺, 0.02 mM Ca²⁺ endolymph (bottom). Top traces are the bundle stimuli evoked by a piezoelectric-driven glass probe. (C) MT current, I, scaled to its maximum value I_MAX, versus hair bundle displacement for recording with EGTA. I_MAX = 0.90 nA (1.5 Ca²⁺) and 1.45 nA (0.02 Ca²⁺). (D) I/I_MAX, versus hair bundle displacement for perforated patch recording. I_MAX = 0.99 nA (1.5 Ca²⁺) and 1.38 nA (0.02 Ca²⁺) and 0.62 nA (1.5 Ca²⁺ wash). For both conditions, low Ca²⁺ endolymph increased the fraction of MT current on at rest, but this was much smaller with EGTA (0.08) than with perforated patch (0.43).

Figure 4

Resting Potentials and Membrane Time Constants (τ_m) in Gerbil OHCs (A) Voltage responses to current steps in an apical OHC with the hair bundle exposed to 1.3 mM Ca²⁺, 0.02 mM Ca²⁺, and 0.2 mM DHS + 1.3 mM Ca²⁺. Note low Ca²⁺ depolarizes the OHC and reduces τ_m. Blocking MT channels with DHS hyperpolarizes the OHC and increases τ_m. τ_m was obtained by fitting voltage onsets (dashed lines) with: V = A(1 − exp (−t/τ_m)), where τ_m = 2.3 ms (1.3 Ca²⁺), 0.6 ms (0.02 Ca²⁺), 5.3 ms (1.3 Ca²⁺ + DHS). (B) Collected resting potentials (mean ± SEM) from apical OHCs with bundles exposed to 1.3 mM Ca²⁺ (control, n = 15; wash, n = 14), 0.02 mM Ca²⁺ (n = 5), and 0.2 mM DHS + 1.3 mM or 0.02 mM Ca²⁺ (n = 9). (C) Collected corner frequencies (F_0.5 = 1/2πτ_m; mean ± SEM) calculated from τ_m measurements as in (A), numbers of measurements in each category as in (B). (D) Voltage responses to current steps with hair bundles perfused with 0.02 mM Ca²⁺ for three gerbil cochlear locations with different CFs. τ_m obtained from fits (dashed lines) and CF: 0.67 ms (0.35 kHz); 0.23 ms (0.9 kHz); 0.10 ms (2.5 kHz).

Figure 5

Voltage-Dependent K⁺ Currents in Gerbil OHCs Current records for voltage steps (left), steady-state current-voltage relationships (middle), and conductance-voltage relationships (right) in: P16–P28 animals. CF and recording temperature in (A–D) (left panels) are shown next to traces. Currents were recorded by applying hyperpolarizing and depolarizing voltage steps in 10 mV nominal increments from the holding potential of −84 mV. Holding currents, plotted as zero current, were −148 pA (0.35 kHz), −175 pA (0.9 kHz), −441 pA (2.5 kHz), and −2484 pA (12 kHz).The current-voltage and conductance-voltage relations in (C) and (D) were corrected to 36°C using Q₁₀ of 1.7. Conductance G_K determined from G_K = I/(V − E_K) where E_K is the current reversal potential, −75 mV. G_K-V relations fitted with single Boltzmann with G_K = G_{K, MAX} /(1 + exp (− (V − V_0.5)/V_S)) where G_{K, MAX}, V_0.5, V_S are (A) 30 nS, −52 mV, 9.2 mV; (B) 60 nS, −63 mV, 8.4 mV; (C) 107 nS, −67 mV, 11 mV; (D) 280 nS, −56 mV, 18 mV.

Figure 6

Predicted In Vivo OHC Resting Potentials (A) Two main ionic currents in OHCs, I_MT flowing through MT channels in the hair bundle that faces endolymph and I_K exiting through voltage-dependent K⁺ channels in the basolateral membrane facing perilymph. There is a +90 mV potential (EP) between endolymph and perilymph. (B) Equivalent electrical circuit for the OHC containing MT conductance, G_MT(X), modulated by bundle displacement X and in series with battery E_MT, the reversal potential for the MT channels (0 mV); and G_K(V) gated by membrane potential V in series with battery E_K, the reversal potential for the K⁺ channels (−75 mV). G_OC is a parallel organ of Corti conductance, large compared to OHC membrane conductances. The capacitances of the apical (C_A) and basolateral (C_B) membranes are also indicated. (C) Predicted resting potential, V_R (mean ± SEM), versus CF calculated by inserting into circuit measured values of G_MT and G_K, corrected to T = 36°C. Dashed line, mean of all values = −40 mV. (D) K⁺ conductance (G_K,r) at OHC resting potential (mean ± SEM) versus CF. Number of measurements indicated beside each point.

Figure 7

Predicted In Vivo Membrane Time Constant and Corner Frequency (A) Linear OHC membrane capacitance, C_m, (mean ± SEM) versus CF for gerbils (filled squares) and rats (filled circles); (B) τ_m (mean ± SEM) versus CF for gerbils (open squares from Figure 4; filled squares, predicted) and rats (filled circles, predicted); (C) corner frequency, F_0.5 (= 1/2πτ_m) versus CF; continuous line is the fit to the data and the dashed line has slope of 1, where CF equals F_0.5.

Figure 8

Membrane Currents, Resting Potentials, and τ_m in Gerbil IHCs (A and B) Saturating MT currents in apical-coil gerbil IHCs exposed to 1.3 mM Ca²⁺ (A) and endolymphatic Ca²⁺ (0.02 mM) (B). Note the larger MT current amplitude and increased P_OPEN at rest compared to 1.3 mM Ca²⁺. In 0.02 mM Ca²⁺ ∼20% of the maximum MT current was activated at rest and this was abolished by 0.2 mM DHS, T = 24°C. (C–E) Voltage-dependent K⁺ currents in apical gerbil IHCs. Current records for voltage steps in 10 mV nominal increments (C), steady-state current-voltage (D), and conductance-voltage relationships (E) in a P18 IHC, T = 36°C. Conductance G_K was determined as described for OHCs (Figure 5) and the conductance-voltage relation was fitted with a single Boltzmann where G_K, MAX, V_0.5, V_S are: 580 nS, −26 mV, 11 mV. (F) Voltage responses to current steps in apical IHCs with hair bundle exposed to 1.3 mM Ca²⁺, 0.02 mM Ca²⁺, and 0.2 mM DHS + 0.02 mM Ca²⁺. τ_m from fitting voltage onsets (dashed lines): 1.0 ms (1.3 Ca²⁺), 0.8 ms (0.02 Ca²⁺), 1.0 ms (0.02 Ca²⁺ + DHS). (G) IHC resting potential (mean ± SEM; n = 4) for the three conditions in (F). (H) Time constant τ_m (mean ± SEM) from recordings as in (F).