Optimizing likelihood models for particle trajectory segmentation in multi-state systems

Particle tracking offers significant insight into the molecular mechanics that govern the behavior of living cells. The analysis of molecular trajectories that transition between different motive states, such as diffusive, driven and tethered modes, is of considerable importance, with even single trajectories containing significant amounts of information about a molecule's environment and its interactions with cellular structures. Hidden Markov models (HMM) have been widely adopted to perform the segmentation of such complex tracks. In this paper, we show that extensive analysis of hidden Markov model outputs using data derived from multi-state Brownian dynamics simulations can be used both for the optimization of likelihood models describing the states of the system and for characterization of the technique's failure mechanisms. The major drivers of HMM failure were found to be likelihood overlap, which was visualized using the Bhattacharyya coefficient, and state mixing caused by state transitions that occur between time points in a particle's trajectory both of which are intrinsically associated with the multi-state nature of the data. This approach provides critical information for the visualization of HMM failure and successful design of particle tracking experiments where trajectories contain multiple mobile states.