Maximum likelihood-based analysis of single-molecule photon arrival trajectories

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Biophysics

Background:

• Photon arrival time analysis is crucial for understanding molecular dynamics.
• Maximum likelihood estimation (MLE) offers a powerful, unbinned approach to analyze complex kinetic processes.
• Model selection criteria like AIC and BIC are essential for distinguishing between competing kinetic models.

Purpose of the Study:

• To investigate the statistical properties of unbinned, maximum likelihood-based analysis of photon arrival trajectories.
• To evaluate the accuracy and precision of parameter estimation in kinetic modeling.
• To assess the efficiency of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for kinetic model selection.

Main Methods:

• Utilizing maximum likelihood estimation on one-color photon arrival trajectories.
• Modeling photon trajectories as Markov modulated Poisson processes in the low excitation regime.
• Analyzing the impact of the number of observed photons on parameter estimation and model selection.

Main Results:

• The Bayesian Information Criterion (BIC) successfully identifies the correct kinetic model (e.g., a three-state model) even with short trajectories (2x10^3 photons).
• Parameter estimation precision reaches approximately 10% for two-state models and 20% for three-state models with 10^4 photons and well-separated intensity levels.
• Unbinned analysis leverages all information within photon trajectories for improved accuracy.

Conclusions:

• Unbinned maximum likelihood analysis provides accurate parameter estimates and robust model selection for kinetic processes.
• The number of observed photons is a critical factor for successful model identification and precise parameter estimation.
• Information criteria like BIC are effective tools for discerning true kinetic models from competing hypotheses in photon trajectory analysis.