Two adjacent stereocilia are connected by a fine elastic filament — the tip link — running from the tip of the shorter one to a mechanotransduction (MET) channel on its taller neighbour. Deflecting the pair toward the tall side shears them past each other and stretches the tip link (the "gating spring" model, Corey & Hudspeth 1983; Howard & Hudspeth 1988). This 2D view isolates one such pair and computes the real spring extension, tension and channel open probability from the actual geometry every frame.
Δl(x) = geometric tip-link stretch from pivot rotation
P_open(x) = 1 / (1 + exp(-(x - x50) / x_s))
x_s = kBT / (k_gs · d) (Boltzmann steepness, nm)
T = k_gs · (x - x50) (tip-link tension, pN, clamped ≥ 0)
d(x50)/dt = (x - x50) / τ (adaptation motor tracks x)
I_MET = P_open · g · ΔV (single-channel transduction current, pA)
- x — bundle deflection in nanometres; positive = toward the taller stereocilium (excitatory), negative = toward the shorter one.
- kgs — gating-spring stiffness; a stiffer spring converts less displacement into the same tension change, so Popen(x) becomes steeper and more switch-like.
- τ (adaptation) — a myosin-1c motor at the tip-link's upper insertion slips down the actin core under sustained tension, dragging the operating point x50 toward the new x and letting the channel partially reclose even while the stimulus is held.
- Auto step stimulus — alternates x between 0 and +90 nm so you can watch Popen spike on the step and relax back down as x50 catches up, the signature adaptation transient recorded in real hair cells.
d ≈ 4 nm is the single-channel gating swing and kBT ≈ 4.1 pN·nm at body temperature; both are fixed physiological constants. This is the same mechanism that converts sound-driven basilar-membrane motion into the receptor current every cochlear hair cell uses to signal pitch and loudness.