A preprint reports that two classes of BK ion-channel records can look different depending on how memory is measured. Conventional dwell-time analysis gave cell-BK patches the larger memory signal, but a response-based measure of how event consequences varied with history gave mitoBK patches the larger residual.
The finding comes from a theory for non-Markovian jump dynamics—systems in which transition rates can depend on earlier observed events—combined with an analysis of thresholded open–closed BK trajectories. It retains an exact trajectory-level description even when equations for state probabilities do not close.
Memory is more than a dwell time
Under the theory’s stated assumptions, transition rates are determined by the observed history. That lets the analysis work directly with a full event record rather than relying only on the current state.
The same event-consequence kernel describes the future consequence of one event, supplies that event’s contribution to observed fluctuations, and becomes the response when weighted by the event rate.
When histories are averaged together, exact fluctuation-response relations leave a nonnegative response-heterogeneity gap—the variation in event consequences that the averaging discards. The gap can test whether a proposed memory coordinate is enough for one chosen observable and perturbation; refining the coordinate cannot increase the residual, and a zero residual means sufficiency only for that task.
The framework also derives uncertainty bounds for response that are controlled by the process’s dynamical activity, when sensitivity to a logarithmic rate perturbation is bounded.
When the question changed, the ranking changed
The initial BK dataset contained 30 cell-BK and 26 mitoBK patches. After quality control, 52 patches remained for the fixed-horizon comparison: 27 cell-BK and 25 mitoBK.
The analysis compared what followed an observed event with a matched continuation branch in which that event did not occur. Within each patch, the researchers also shuffled dwell order while preserving marginal dwell distributions, open fraction and recording time; this removed serial order without changing those basic quantities.
On conventional dwell-memory excess, the median was 0.205 for cell-BK and 0.129 for mitoBK. On the state-and-age excess residual, the medians were 0.0065 and 0.292, respectively. The two measures therefore reversed the apparent ordering of the channel classes.
The mitoBK residual was larger than the cell-BK residual in the reported comparison, with a one-sided p-value of 3.57 × 10−9. It also exceeded the shuffled control in all 25 quality-controlled mitoBK patches, with an exact two-sided p-value of 5.96 × 10−8. As preceding dwell history was added, the reported residual fell from 0.292 to 0.237 and then 0.198.
On the study’s frequency scale, mitoBK residuals were largest at the lowest tested frequency: the median was 0.263 at Ω = 0.5, 0.178 at Ω = 2 and 0.103 at Ω = 16. Cell-BK medians were 0.087 at Ω = 0.5 and 0.007 at Ω = 2, remaining close to the shuffled baseline at higher frequencies. No monotone voltage dependence was resolved.
A result with a narrow reach
The BK response analysis was observational, not an external intervention. It used a finite number of preceding dwells rather than the complete history and relied on thresholded dwell sequences rather than raw currents.
The reported three-dwell reference is zero by construction, so it cannot establish that three preceding dwells are response-sufficient. More broadly, a zero residual applies only to the selected observable and perturbation family; it does not by itself establish full Markovianity or complete predictive sufficiency.
In a solvable coarse-grained network, a candidate state could match standard kinetic statistics yet fail a response-based test, and the memory needed depended on the observable and perturbation. The broader warning is that matching ordinary kinetics may not be enough to capture every response.
Controlled perturbations would be needed to test whether the observational event–continuation kernels predict physical responses. Replication with raw currents and alternative event-detection procedures would help assess the effects of thresholded dwell sequences.
Paper data and sources
Original title: The Memory Hidden in Response Fluctuations: Trajectory-Level Fluctuation-Response Theory and Inequalities for Non-Markovian Jump Dynamics
Authors: Jiming Zheng, Zhiyue Lu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text