Curvature screen: a statistical test for decay data

• A significant result rules out one explanation: a passive mixture of independent decays.
• It does not say what the cause is. A sequence of steps, a driven cycle, a gel that relaxes in a compressed way, and instrument effects such as a clipped window or dead time can all give the same sign.
• A result that is not significant shows nothing.
• Nothing here bears on CF treatment or on who is eligible for a CFTR modulator.

On a logarithmic scale, the middle of three equally spaced readings of any mixture of independent exponential decays with positive weights lies on or below the straight line joining the other two. A middle reading clearly above that line, by more than noise can explain, rules such a mixture out.

For lists of event durations, a second check asks the same question with every event: do the durations vary less than any mixture of memoryless processes can? If they do, by more than chance explains, a passive mixture is ruled out.

One such list is the length of each burst of a single CFTR channel. CFTR is the cystic fibrosis transmembrane conductance regulator, the protein that does not work properly in CF. A burst is a period when one channel is mostly open.

• Public experimental datasets from other laboratories: fluorescence recordings (lifetime and single-molecule), X-ray scattering, a potassium channel, a molecular motor, and a gel of purified pig stomach mucus, which is not airway mucus or CF sputum. None is a CFTR recording and none holds patient data. An appendix applies the same arithmetic to public astronomy data as an illustration only.
• Simulations of CFTR bursts under a stated two-step model. No CFTR recording and no patient data have been analyzed. With two steps of similar length, close to the most favorable two-step case, the event-list check rejected a passive mixture in 91.2% of simulated runs of 100 bursts, at a 1% false-alarm level. When one step was five times faster than the other, that fell to 32% at 100 bursts and 76% at 300.

• It has not been tested on CFTR recordings.
• In simulation under a correctly specified two-step model, likelihood fitting reached about 100% power at 300 bursts, where the three-point check reached 29.5%. The event-list check has not been compared with likelihood fitting below 300 bursts.
• No single ingredient is new. The briefing lists the earlier work for each.
• Several reported results are weak or unsupported, and the briefing says which.

One untested question is whether the event-list check rejects a passive mixture on real wild-type CFTR burst durations. A table of burst durations per patch is enough, with each patch's resolution, filter cut-off, burst criterion and number of active channels; raw traces are not needed.

The plan for the event-list check is fixed in writing before any recording is seen. A script runs steps 3 to 5 of that plan on a laboratory's own computer. To get in touch, write through the Contact page.

• The briefing: claims, results, limits and earlier work. Also as a PDF of the briefing.
• The data request and analysis plan.
• The methods note for the event-list check.
• The curvature-screen folder on GitHub: two estimators that remove the bias caused by squaring a noisy reading and cancel an unknown constant background, the event-list check, control analyses, a false-alarm calibration, and scripts for every number in the note.

Code is MIT. The text of the note is CC0-1.0. The public datasets, and the small derived files made from them, keep their own licences, listed in the folder.