E.5 Prestin and the cochlear amplifier

Detection alone is not enough: at the faintest audible sounds, viscous drag would damp the basilar-membrane vibration away before it could be sensed. The cochlea answers by pumping energy back into the vibration on every cycle, using a molecular motor that converts voltage into length change faster than any muscle. That motor is prestin, and the loop it drives is the cochlear amplifier.

Piezoelectricity, biological and otherwise

A piezoelectric material couples mechanical strain to electric polarisation linearly: squeeze it and it develops a voltage; apply a voltage and it changes length. The coupled constitutive relations are

\sigma_\text{stress} \;=\; c\,\varepsilon_\text{strain} \;-\; e\,E, \qquad D \;=\; e\,\varepsilon_\text{strain} \;+\; \epsilon\,E,

where

$\sigma_\text{stress}$: mechanical stress Pa
$\varepsilon_\text{strain}$: mechanical strain —
$E$: electric field V/m
$D$: electric displacement C/m²
$e$: piezoelectric coupling coefficient C/m²

with the cross-coefficient $e$ tying strain to charge. Quartz and certain ceramics are passive piezoelectrics, the basis of ultrasonic transducers and precision oscillators.

Prestin: a voltage-driven motor

The outer hair cells of the mammalian cochlea perform the same trick with a protein. Their membranes are packed with prestin — of order $10^7$ copies per cell — and each molecule changes conformation, and hence area, in response to the membrane voltage. The receptor potential set up by transduction drives the whole cell to shorten and elongate, cycle by cycle, at frequencies up to $\sim 80\,\text{kHz}$ — far faster than any actin–myosin muscle, because the drive is direct electromechanical coupling rather than a chemical cycle.

Membrane potential V_m = -60 mV

Prestin is the membrane protein of outer hair cells responsible for *electromotility* — voltage-driven length change. Each cell carries ~10⁷ prestin molecules, each undergoing a conformational change when the membrane voltage shifts. The collective response is a sigmoidal length-vs-voltage curve, with the cell shortening at depolarised V_m and lengthening at hyperpolarised V_m. Total length change is up to ~4% of the cell length, at frequencies up to 80 kHz. This is the active *cochlear amplifier*: prestin pumps energy into the basilar-membrane motion, undoing viscous damping. See [Hearing Ch 4.5](/hearing/cochlea/amplifier).

Closing the loop

Timed correctly, this length change pushes on the basilar membrane in phase with its motion, feeding energy back into the travelling wave and cancelling the viscous loss that would otherwise dissipate it. The result is the cochlear amplifier: a local, active, per-cycle boost that sharpens the mechanical tuning and lifts the faintest sounds above the noise, developed in full in the cochlear amplifier lesson. It is the closest thing biology has built to a fast piezoelectric actuator, and it is what makes the ear’s sensitivity and frequency selectivity possible.

⏳ The history — From Nernst to Hodgkin–Huxley to prestin

Walther Nernst derived the equilibrium membrane-potential formula in 1888 from thermodynamics, long before the molecular structure of membranes was known. Julius Bernstein applied it to nerves in 1902, proposing correctly that the resting potential originates in the potassium gradient.

The multi-ion extension — the GHK equation — was derived by David Goldman in 1943 and by Alan Hodgkin and Bernard Katz in 1949. Hodgkin and Andrew Huxley then built the dynamical theory of voltage-gated channels on the squid giant axon through the 1950s, winning the 1963 Nobel Prize; the Hodgkin–Huxley model remains the canonical framework for excitable membranes.

The cochlear story is more recent. The endocochlear potential was measured by Hallowell Davis and colleagues in 1958, and the stria vascularis identified as its source over the following decades. Prestin, the electromotile motor of outer hair cells, was identified molecularly by Peter Dallos’s group in 2000 — the discovery that gave the cochlear amplifier its mechanism.