An extension to reversible jump Markov chain Monte Carlo for change point problems with heterogeneous temporal dynamics

TL;DR

CRJMCMC extends reversible jump MCMC with compound moves to robustly detect short-lived, heterogeneous change points in time-series data, enabling accurate per-frame fluorophore counting in photobleach step analysis. The method jointly estimates active fluorophore counts and intensity parameters without heavy filtering or calibration, validated on simulated FLImP traces and experimental DNA origami ruler data. Across extensive simulations and experiments, CRJMCMC outperforms existing MAP-based and FHMM approaches in RMSE and per-frame accuracy, while enabling higher-order fluorophore counting and recovering more usable data frames. Beyond FLImP, the approach offers a general framework for time-series change-point problems with heterogeneous state persistence, with broad potential applications in biology, engineering, and finance.

Abstract

Detecting brief changes in time-series data remains a major challenge in fields where short-lived states carry meaning. In single-molecule localisation microscopy, this problem is particularly acute as fluorescent molecules used to tag protein oligomers display heterogenous photophysical behaviour that can complicate photobleach step analysis; a key step in resolving nanoscale protein organisation. Existing methods often require extensive filtering or prior calibration, and can fail to accurately account for blinking or reversible dark states that may contaminate downstream analysis. In this paper, an extension to RJMCMC is proposed for change point detection with heterogeneous temporal dynamics. This approach is applied to the problem of estimating per-frame active fluorophore counts from one-dimensional integrated intensity traces derived from Fluorescence Localisation Imaging with Photobleaching (FLImP), where compound change point pair moves are introduced to better account for short-lived events known as blinking and dark states. The approach is validated using simulated and experimental data, demonstrating improved accuracy and robustness when compared with current photobleach step analysis methods and with the existing analysis approach for FLImP data. This Compound RJMCMC (CRJMCMC) algorithm performs reliably across a wide range of fluorophore counts and signal-to-noise conditions, with signal-to-noise ratio (SNR) down to 0.001 and counts as high as seventeen fluorophores, while also effectively estimating low counts observed when studying EGFR oligomerisation. Beyond single molecule imaging, this work has applications for a variety of time series change point detection problems with heterogeneous state persistence. For example, electrocorticography brain-state segmentation, fault detection in industrial process monitoring and realised volatility in financial time series.

Figures (7)

• Figure 1: Visualisation of complex photophysical behaviour of fluorophores. (a) Markov chain describing fluorophore state transitions. Fluorophores typically exist in one of four states: bright (fluorescent), blinking (short-term dark), long-lived dark, or photobleached, and they transition between these as indicated by the arrows. Bright fluorophores emit detectable photons; blinking and dark states involve temporary loss of fluorescence, and photobleaching is a permanent transition to an off-state. Probabilities presented here have been obtained from needham2013measuring. Note that there can be multiple dark states, but for the purposes of this study, this simplified model is implemented based on Alexa Fluor 488 fluorophores iyer2024drug. (b) Examples of blink and dark states. Blink and dark states are reversible events which produce temporary drops in fluorescence that are visually indistinguishable from the irreversible photobleaching. Blink states are very short, typically only lasting 1-2 frames, whereas dark states are longer lived, with dwell time depending on the type of fluorophore used.
• Figure 2: Performance of CRJMCMC across simulated integrated intensity traces. CRJMCMC is compared with previously published methods by tsekouras2016novel (green line), garry2020bayesian (purple line), and bryan2022diffraction (orange line). Panels a, c, and e show representative integrated intensity traces under increasing fluorophore number (a), decreasing SNR (c), and increasing frequency of short-lived states (e). Corresponding average root mean squared error (RMSE) values and 95% confidence intervals are summarised in panels b, d, and f across each scenario.
• Figure 3: Analysed intensity traces from GATTAquant DNA origami rulers. (a) CRJMCMC (red) detects additional fluorophore levels exceeding those identified by iyer2024drug (black). (b) CRJMCMC recovers state transitions excluded by the filtering in Iyer et al. (2024) iyer2024drug.
• Figure 4: Schematic of the pipeline used to estimate population-level hyperparameters and how it feeds into CRJMCMC iterations. Hyperparameters governing the prior distributions are estimated during a pre-processing step and pooled across traces within each experiment to account for shared experimental conditions and mitigate the influence of noisy data. In CRJMCMC, at each iteration, a change point move is carried out, following by an update of the continuous parameters for fluorophore and background mean and variance ($\mu_f$, $\mu_b$, $\sigma_f^2$, $\sigma_b^2$) using Gibbs-sampling. White: Population-level, Grey: Dataset-level.
• Figure 5: Posterior estimates of change point locations and corresponding simulated intensity trace. (a) Posterior kernel density estimates (standard deviation of 2) for change point locations, conditioned on the number of change points, from a single Markov chain with 20,000 iterations following a burn-in of 10,000 iterations. (b) Corresponding simulated intensity trace (turquoise), CRJMCMC model estimation (red line), with four fluorophores and an SNR of 0.1.