A Hidden Markov Model for Single Particle Tracks Quantifies Dynamic Interactions between LFA-1 and the Actin Cytoskeleton
Figure 5
Parameter optimization for two-state model.
A typical MCMC parameter optimization for an ensemble of 20 simulated 2-state particle tracks with model parameters ,
,
and
. Each track consists of 1000 frames sampled at 1 ms intervals. (A., B.) HMM parameter values are plotted for an MCMC trajectory that starts with a random initial guess and stochastically evolves in the parameter space according to Algorithm 3 (Fig. 4). The shaded part of the plots indicate the burn-in phase during which the trajectory approaches the log likelihood maxima. (C., D.) Histogram of parameter values from the MCMC trajectory above after excluding the burn-in phase.
and
are in units of
. The gray vertical lines in (D.) mark the values of transition probabilities that were used for simulating the particle tracks. (E., F.) Typical errors and dispersions in maximum likelihood parameter estimates using the stochastic MCMC optimization scheme described in the text. Ten independent particle tracks consisting of 1000 steps each, sampled at 5 ms intervals were simulated with
, different values of
, indicated by the colored dots in the left panel,
and
. These parameter combinations correspond to the first four rows in Table S1. MCMC parameter estimates and 95% coverage intervals of parameter histograms are shown by the corresponding colored crosses that are centered at the maximum likelihood parameter values.