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.

Author Summary

Many important biological processes begin when a target molecule binds to a cell surface receptor protein. This event leads to a series of biochemical reactions involving the receptor and signalling molecules, and ultimately a cellular response. Surface receptors are mobile on the cell surface and their mobility is influenced by their interaction with intracellular proteins. We wish to understand the details of these interactions and how they are affected by cellular activation. An experimental technique called single particle tracking (SPT) uses optical microscopy to study the motion of cell-surface receptors, revealing important details about the organization of the cell membrane. In this paper, we propose a new method of analyzing SPT data to identify reduced receptor mobility as a result of transient binding to intracellular proteins. Using our analysis we are able to reliably differentiate receptor motion when a receptor is freely diffusing on the membrane versus when it is interacting with an intracellular protein. By observing the frequency of transitions between free and bound states, we are able to estimate reaction rates for the interaction. We apply our method to the receptor LFA-1 in T cells and draw conclusions about its interactions with the T cell cytoskeleton.