Blink and you’ll miss it: a comparison of Bayesian statistical methods to model photobleaching events in single molecule imaging

Lung cancer is currently one of the leading causes of cancer deaths worldwide and as many as 85% of these cases are Non-Small Cell Lung Cancer (NSCLC) (Cancer.net, 2023). Epidermal Growth Factor Receptors (EGFRs) are proteins known to play a role in the development of several types of cancer, including NSCLC. EGFR is involved in normal cell growth and development processes, and so mutations in the DNA of EGFR, which can cause uncontrolled or erroneous clustering of this protein, lead to the development of cancer. Measuring the separations of populations of EGFR clusters can be used as a novel diagnostic test to determine the most appropriate treatment for individual cancer patients and can provide important information for the development of novel drugs to control undesirable EGFR clustering.

Single molecule imaging techniques such as Fluorescence Localisation Imaging with Photobleaching (FLImP, Needham et al. (2016)), enable the study of protein complexes such as EGFR. FLImP relies on the successive photobleaching of fluorescent molecules, known as fluorophores, bound to the EGFR on the cell surface. As each fluorophore is bleached, the emitted light intensity decreases in a stepwise pattern. Counting these bleaching events over time can be used to estimate the number of fluorophores active in each observation frame. This information can then be used alongside assumptions about the shape of a single fluorophore to determine the separations between EGFR clusters to which the fluorophores are bound.

The behaviour of fluorophores in these systems can be described by a Markov process, and as such statistical models can therefore be developed for each intensity trace to estimate the most likely number of active fluorophores. However, the development of these models is non-trivial due to multiple noise sources and the existence of temporary “dark” or “blink” states in which fluorophores briefly stop emitting light.

A variety of methods to achieve this have been proposed in the last decade, ranging from simple change-point algorithms to more complex methods considering hidden and factorial Markov models or Bayesian statistical models. Two of the most influential methods within this area of research were developed by Tsekouras et al. (2016) and Garry et al. (2020). Both methods use a Bayesian approach with well-informed priors, using maximum a posteriori estimation to identify the most likely location and number of fluorophore photobleaching events. These methods, however, differ in several fundamental ways. This research focuses on the comparison of these two methods when applied to simulated intensity tracks and how they perform in terms of both accuracy and computational efficiency.

“Lung Cancer - Small Cell: Statistics.” Cancer.Net, 20 Mar. 2023, https://www.cancer.net/cancertypes/lung-cancer-small-cell/statistics.

Needham, Sarah R., et al. "EGFR oligomerization organizes kinase-active dimers into competent signalling platforms." Nature communications 7.1 (2016): 13307.

Tsekouras, Konstantinos, et al. "A novel method to accurately locate and count large numbers of steps by photobleaching." Molecular biology of the cell 27.22 (2016): p.3601-3615.

Garry, Jon, et al. "Bayesian counting of photobleaching steps with physical priors." The Journal of chemical physics 152.2 (2020): The Journal of chemical physics 152(2), p.024110.