A Likelihood based Approach for Building Trajectories from Intermittent Observations

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Single Particle Tracking (SPT) using probes that blink, bleach, activate, bind or are otherwise not consistently observed throughout an experiment presents a challenge when connecting the set of observed positions into trajectories. One method for approaching the connection problem is to assign each possible connection, fluorophore ‘birth' and ‘death' a cost and arrange these costs into a ‘cost matrix [1].' Connections, as well as ‘birth' and ‘death' events are found by minimizing the total cost. We show that when the costs are calculated using the known kinetic behavior of the probes and a known diffusion constant this approach can be used to find the set of connections, etc. that approximates the global maximum likelihood solution. Although this method can find the approximate maximum likelihood solution, in many cases a favored trajectory assignment has a likelihood that is not significantly larger than a conflicting trajectory assignment. This ambiguity arises when the probe density increases such that the likelihood cannot reliably distinguish between true and false connections. using an iterative method to relax the costs of a chosen set of connections, we have been able to dramatically reduce the number of false connections with the trade off being trajectories broken at places of ambiguity and therefore more, but shorter trajectories. In order to demonstrate the effectiveness of removing such ambiguities, we show results from simulations as well as experimental data from tracking membrane proteins labeled with quantum dots or a fluorogen activating peptide system. [1] Jaqaman, K. et al. Nature Methods v.5 no.8, (August 2008): 695-702