For a hair-cell transduction channel

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Hearing: from air pressure to a gated channel

Problem

For a hair-cell transduction channel, the open probability is Po(x)=11+e−z(x−x0)/kBT,P_o(x) = \frac{1}{1+e^{-z(x-x_0)/k_BT}}, where xx is bundle displacement and zz is the gating force. A wild-type bundle at body temperature (kBT=4.28 pN nmk_BT = 4.28\,\mathrm{pN\,nm}) has gating force z=0.30 pNz = 0.30\,\mathrm{pN}. ((a)) Find the displacement range over which PoP_o rises from 0.10.1 to 0.90.9. ((b)) A tip-link mutation halves the effective gating force to z′=0.15 pNz' = 0.15\,\mathrm{pN} without changing anything else. Predict the new 1010-to-9090-per-cent displacement range.

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