Sound-driven stereocilia deflection opens mechanotransduction channels, producing a receptor potential inside the outer hair cell (OHC). The cell membrane behaves as a resistor–capacitor (RC) circuit, so the potential is low-pass filtered before it ever reaches the prestin motors embedded in the lateral wall:
|H(f)| = 1 / sqrt(1 + (f / f_c)^2), f_c = 1 / (2πRC)
V_rp(f) = V_0 · |H(f)| (phase lag φ = arctan(f / f_c))
The motor protein prestin (SLC26A5) converts this filtered voltage into a real change in cell length — somatic electromotility — roughly linear in the receptor potential over the physiological range:
ΔL(t) ≈ k_prestin · V_rp(f) · cos(2πft − φ)
That length change pushes back on the organ of Corti in phase with the incoming vibration, injecting mechanical energy into the traveling wave near its own characteristic place — the cochlear amplifier, responsible for ~40–60 dB of sensitivity and the ear's sharp frequency tuning. Because the receptor potential is RC-filtered, the motor's driving voltage — and hence the amplification it can deliver — collapses above fc. This "RC problem" is exactly why the amplifier is most powerful at the base-to-middle turns and why extending it to the highest audible frequencies remains only partly explained by membrane biophysics alone (fast, voltage-independent components likely help).
- Tone frequency — the stimulus driving the hair cells; watch the cilia bundle and OHC row oscillate in phase with it.
- Membrane corner fc — sets the RC low-pass cutoff; push the tone frequency past it and the receptor potential (and the amplification) collapses.
- Prestin motor gain — how much length change a given receptor potential produces; scales the electromotile feedback pushed into the basilar membrane.
- Amplifier ON/OFF — compares the active, electromotility-boosted basilar-membrane vibration against the passive response it would have without the OHCs.