Markov chain models of emitter activations in single molecule localization microscopy

A well-reasoned model of data movie in single molecule localization microscopy (SMLM) is desired. A model of data movie can be decomposed into a model of emitter activation process and a model of data frame. In this paper, we focus on Markov chain modeling and analyzing of emitter activation process for both cycled and continuous illuminations. First, a two-phase Markov chain is proposed to model the activation process for a pair of conjugated activator and emitter with cycled illumination. By converting the frame-based Markov chain into several cycle-based Markov chains, the stationary state distribution in the photoactivatable period is derived. Further obtained are several formulas that capture the characterization of the two-phase Markov chain. Second, the Markov chain and analytical result are extended to the continuous illumination where an emitter is excited continuously in all frames. Finally, incorporating the model of emitter activation process with our previous model of data frame, the model of data movie for both cycled and continuous illuminations in 3D and 2D imaging are simulated by custom codes. It is shown that the model can synthesize data movies well and the analytical formulas predict the simulation results accurately. The models provide a means to be broadly utilized in generating well-reasoned data movies for training of neural networks and evaluation of localization algorithms.