Stochastic Model Building of Photophysics using Hidden Markov Model

Abstract

Exogenous fluorescence probes have been widely employed in studying complex biological dynamics with high temporal and spatial resolution. A photoinduced dark state can be useful if it can be utilized for a particular purpose through optical modulation. Transferring this concept to more traditional fluorophores requires a detailed understanding of the photophysical dynamics. Because photon emission is a random process corresponding to underlying photophysical state transitions, a robust, probabilistic method is required to uncover the most probable model. This thesis focuses on a generalized hidden Markov model (HMM)-based method to build a proper photophysical model, and calculate model parameters from simulated and experimental data. The conventional algorithm in HMMs is modified to analyze Poisson-distributed intensity trajectories. By modifying the conventional algorithm to introduce photophysical relevance and localization error, we have improved HMM performance both in determining the dimensions of unknown systems and in robustness even if the intensity trajectory is very short. Experimental conditions including non-unity detection efficiency and background noise lead to non-Poisson distribution of intensity counts, which cannot be explained by Poisson statistics. Photon-by-photon HMM (PbPHMM) was developed to build a photophysical model from non-Poisson distributed photon time traces, with the goal of incorporating the information often discarded by time-binning. Additionally, in PbPHMM, the solution of the master equation is not required, which is often long and complicated, to explain state connectivity. The fitting ability of PbPHMM was evaluated by analyzing simulated time traces of fluorescence photons, varying experimental and photophysical parameters. The relation between photophysical parameters and the trained model parameters were formulated based on probabilistic theory. The number of dark states was determined by Bayesian information criteria. The fitting performance of PbPHMM could be improved when multiple time traces are available. PbPHMM was applied to build a photophysical model building from photon time traces from optically-modulated silver nanodots. One bright and one dark state were predicted from photon trajectories from silver nanodots.