A Hidden Markov Model for Single Particle Tracks Quantifies Dynamic Interactions between LFA-1 and the Actin Cytoskeleton

Abstract

The extraction of hidden information from complex trajectories is a continuing problem in single-particle and single-molecule experiments. Particle trajectories are the result of multiple phenomena, and new methods for revealing changes in molecular processes are needed. We have developed a practical technique that is capable of identifying multiple states of diffusion within experimental trajectories. We model single particle tracks for a membrane-associated protein interacting with a homogeneously distributed binding partner and show that, with certain simplifying assumptions, particle trajectories can be regarded as the outcome of a two-state hidden Markov model. Using simulated trajectories, we demonstrate that this model can be used to identify the key biophysical parameters for such a system, namely the diffusion coefficients of the underlying states, and the rates of transition between them. We use a stochastic optimization scheme to compute maximum likelihood estimates of these parameters. We have applied this analysis to single-particle trajectories of the integrin receptor lymphocyte function-associated antigen-1 (LFA-1) on live T cells. Our analysis reveals that the diffusion of LFA-1 is indeed approximately two-state, and is characterized by large changes in cytoskeletal interactions upon cellular activation.

Dynamic Regulation of CD45 Lateral Mobility by the Spectrin-Ankyrin Cytoskeleton of T Cells

“…4). (21). This analysis provides an improved resolution of the two underlying diffusion coefficients compared with the population analysis described above (supplemental Fig.…”

“…For population analysis of D micro and D M values, a population density analysis was performed to determine the relative proportion and center of two log normal subpopulations, as described previously (18). To estimate the maximum likelihood parameters of a two-state HMM for a set of tracks, we used a stochastic Markov Chain Monte Carlo optimization scheme as described previously (21). The Markov Chain Monte Carlo optimization scheme yields a distribution for each model parameter whose mean is the maximum likelihood parameter estimate.…”

Single-molecule tracking of small GTPase Rac1 uncovers spatial regulation of membrane translocation and mechanism for polarized signaling

“…Furthermore, to evaluate the kinetics of interconversion between the two diffusive states (D 1 and D 2 ), we analyzed the SPT trajectories from dnRac1 and RDB-Rac1 with a two-state Hidden-Markovian model (HMM). The HMM analysis had been previously applied to single-molecule trajectories to study dimerization kinetics in growth factor receptors (31), protein-RNA interactions (32), and also integrin-cytoskeletal interactions (33). In our case, it allows us to extract the association and dissociation kinetics between Rac1 and its interacting GEFs.…”

Segmentation of 3D Trajectories Acquired by TSUNAMI Microscope: An Application to EGFR Trafficking

“…Considerable effort has been devoted to the identification of change points in motion (36) or diffusivity (38) along the same trajectory and to the visualization of spatial regions with different dynamic behaviors (34,35,38,42). Such an analysis is called trajectory segmentation and classification (11), which is often carried out by calculating a number of classification parameters over the trajectory using methods such as rolling window analysis (34,36,43), supervised segmentation (44), mean-squareddisplacement (MSD) curvature (34,35,45,46), maximum likelihood estimator (38), Bayesian methods (47,48), F-statistics (49), hidden Markov model (50,51), and wavelet analysis (42,52).…”