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Joined 2026-09-21 Message
Incoming links: Ion-channel open probability
Past exam of the biological physics course of the University of Oxford 2015 8 iii Solution 2026-10-25
Single-molecule experiments expose distributions and ordered events that an ensemble average can hide. Several distinct biological systems make this advantage concrete.
- In titin single-molecule force spectroscopy, individual sawtooth drops reveal sequential domain unfolding and contour release. An ensemble stretching curve can smooth away that sequence and obscure variation in unfolding thresholds. Force-dependent waiting-time distributions also distinguish stochastic transitions from a single deterministic breaking strength.
- In a patch clamp recording of one ion channel, discrete open-current levels and closed intervals reveal single-channel conductance, gating dwell times, and ion-channel open probability. An ensemble current alone cannot distinguish a few frequently open channels from many rarely open ones, or reveal a brief intermediate state with the same clarity.
- In Single-molecule observation of F1 rotation, a probe on the motor shaft reports angular progression and pauses associated with the catalytic cycle. Rotation demonstrates mechanical coupling directly; individual stepping and dwell-time statistics can connect chemical turnover to angular motion, whereas bulk ATP consumption alone cannot establish the motor's trajectory.
- In DNA unwinding measured by magnetic tweezers, individual extension changes resolve the waiting time and extent of open promoter complex formation by RNA polymerase. Separate binding, opening, and later movements can otherwise merge into one population-averaged response.
These methods also have limitations: the attached probe or applied load may perturb the molecule, inactive or heterogeneous molecules may be overrepresented, and finite temporal resolution can hide fast steps. Repeated independent trajectories and appropriate controls are needed to connect a single observed event to a reproducible mechanism. The gain is access to trajectories and heterogeneity, rather than an assumption that one molecule alone represents every molecule.
The average electric current is the number of channels times their ion-channel open probability times the electric current carried by an open channel:Consequently the identifiable answer isTODO (missing input): The source does not supply or the potassium thermodynamic activities for this experiment. A unique numerical electrical conductance cannot follow from the listed electric current, count and ion-channel open probability alone. For the explicitly additional choice mV, pS. Taking mV instead gives pS: both match the measured electric current. The table in question 3 describes a skeletal-muscle resting state, and cannot silently supply the conditions of this separate recording.
Rapid permeation is possible because the hydrated pore and coordinating groups of the selectivity filter provide a favorable free-energy landscape for repeated ion transit. Several ions can occupy the filter and their interactions favor onward passage, while the channel remains open for many successive transits. Selectivity need not mean that each transported ion remains tightly trapped for a long time. This is passive downhill transport; it does not consume one ATP molecule per ion crossing.