Detection of Diffusion Heterogeneity in Single Particle Tracking Trajectories Using a Hidden Markov Model with Measurement Noise Propagation

Abstract

We develop a Bayesian analysis framework to detect heterogeneity in the diffusive behaviour of single particle trajectories on cells, implementing model selection to classify trajectories as either consistent with Brownian motion or with a two-state (diffusion coefficient) switching model. The incorporation of localisation accuracy is essential, as otherwise false detection of switching within a trajectory was observed and diffusion coefficient estimates were inflated. Since our analysis is on a single trajectory basis, we are able to examine heterogeneity between trajectories in a quantitative manner. Applying our method to the lymphocyte function-associated antigen 1 (LFA-1) receptor tagged with latex beads (4 s trajectories at 1000 frames s−1), both intra- and inter-trajectory heterogeneity were detected; 12–26% of trajectories display clear switching between diffusive states dependent on condition, whilst the inter-trajectory variability is highly structured with the diffusion coefficients being related by D 1 = 0.68D 0 − 1.5 × 104 nm2 s−1, suggestive that on these time scales we are detecting switching due to a single process. Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 102 − 2.6 × 105 nm2 s−1) is very much larger than the measurement uncertainty within trajectories, suggesting that LFA-1 aggregation and cytoskeletal interactions are significantly affecting mobility, whilst the timescales of these processes are distinctly different giving rise to inter- and intra-trajectory variability. There is also an ‘immobile’ state (defined as D < 3.0 × 103 nm2 s−1) that is rarely involved in switching, immobility occurring with the highest frequency (47%) under T cell activation (phorbol-12-myristate-13-acetate (PMA) treatment) with enhanced cytoskeletal attachment (calpain inhibition). Such ‘immobile’ states frequently display slow linear drift, potentially reflecting binding to a dynamic actin cortex. Our methods allow significantly more information to be extracted from individual trajectories (ultimately limited by time resolution and time-series length), and allow statistical comparisons between trajectories thereby quantifying inter-trajectory heterogeneity. Such methods will be highly informative for the construction and fitting of molecule mobility models within membranes incorporating aggregation, binding to the cytoskeleton, or traversing membrane microdomains.

How Receptor Surface Diffusion and Cell Rotation Increase Association Rates

“…For example, not only do receptors diffuse, but their diffusion coefficient can randomly fluctuate (sometimes due to being trapped in membrane subdomains such as lipid rafts [80,65]). Two key examples are (i) LFA-1 receptors that alternate between fast and slow diffusive states [34,81] and (ii) AMPA receptors on the postsynaptic membrane that alternate within seconds between rapid diffusive and stationary states [16]. To extend the present work to such heterogeneous diffusion, one could assume the receptor diffusivity fluctuates between discrete states, as in [27,28,61].…”

A Hidden Markov Model for Detecting Confinement in Single Particle Tracking Trajectories

“…Specifically, models must approximate well the behaviour of different dynamic states in the data. For instance, confinement is often associated with a decrease in the effective diffusion coefficient, suggesting that models that switch diffusivities (25)(26)(27)(28)(29)(30) should also be able to detect confinement in these iSCAT particle trajectories. However, we found that a two-state diffusion coefficient switching HMM (30) could not segment these trajectories (data not shown).…”

“…This has led to the development of a range of statistical methods that detect deviations from Brownian motion, such as mean square displacement (MSD) (8)(9)(10)(11)(12)(13), and confinement (14)(15)(16)(17)(18)(19) analyses. A new breed of methods model switching in the movement dynamics between various dynamic states (20)(21)(22)(23)(24), often within a hidden Markov chain framework (25)(26)(27)(28)(29)(30). For high resolution data the latter techniques can utilise the high level of information present in the trajectory to extract detailed motion characteristics, and potentially infer underlying biophysical mechanisms.…”

Protein concentration gradients and switching diffusions

“…Nevertheless, if one takes the switching rates to depend on spatial position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Ito form. Advances in single-particle tracking (SPT) and statistical methods suggest that particles within the plasma membrane, for example, can switch between different discrete conformational states with different diffusivities [15][16][17]. Such switching could be due to interactions between proteins and the actin cytoskeleton [18,19] or due to protein-lipid interactions [20].…”