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

Slator PJ, Cairo CW, Burroughs NJ - PLoS ONE (2015)

Bottom Line: Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 10(2) - 2.6 × 10(5) 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.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.

View Article: PubMed Central - PubMed

Affiliation: Systems Biology Centre, University of Warwick, Coventry, United Kingdom; Systems Biology Doctoral Training Centre, University of Warwick, Coventry, United Kingdom.

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 D1 = 0.68D0 - 1.5 × 10(4) 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 × 10(2) - 2.6 × 10(5) 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.

No MeSH data available.


Fit of a two-state diffusion model without measurement noise to three stationary latex bead trajectories.MCMC output from chains of 20000 MCMC steps with a 10000 step burn-in. (A-C) Inference of the hidden state z shown as the probability of being in the low diffusion state. (D-F) Posterior distributions for the two diffusion coefficients: D0 (red) and D1 (blue). See Methods for priors and initial conditions.
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pone.0140759.g001: Fit of a two-state diffusion model without measurement noise to three stationary latex bead trajectories.MCMC output from chains of 20000 MCMC steps with a 10000 step burn-in. (A-C) Inference of the hidden state z shown as the probability of being in the low diffusion state. (D-F) Posterior distributions for the two diffusion coefficients: D0 (red) and D1 (blue). See Methods for priors and initial conditions.

Mentions: The stationary beads also provide an opportunity to check that the measurement noise does not affect model selection: stationary beads should prefer a one-state diffusion model since the time series is homogeneous. If the two-state diffusion model is preferred then measurement noise, the tracking algorithm, or instrument noise contributes to the heterogeneity in the trajectory. We applied the one-state and two-state diffusion model algorithms (without measurement noise) to the three stationary beads. The two-state diffusion model showed high frequency switching behaviour (Fig 1A–1C), with two distinct (well separated) diffusion coefficients, (Fig 1D–1F). Crucially, the two-state diffusion model is strongly preferred for all 3 trajectories (Fig 2, red asterisks). Therefore there is evidence that tracked bead displacements are not unstructured and an analysis of LFA-1 trajectories using the models without allowing for measurement noise may be unreliable, due to this inherent inhomogeneity.


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

Slator PJ, Cairo CW, Burroughs NJ - PLoS ONE (2015)

Fit of a two-state diffusion model without measurement noise to three stationary latex bead trajectories.MCMC output from chains of 20000 MCMC steps with a 10000 step burn-in. (A-C) Inference of the hidden state z shown as the probability of being in the low diffusion state. (D-F) Posterior distributions for the two diffusion coefficients: D0 (red) and D1 (blue). See Methods for priors and initial conditions.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4608688&req=5

pone.0140759.g001: Fit of a two-state diffusion model without measurement noise to three stationary latex bead trajectories.MCMC output from chains of 20000 MCMC steps with a 10000 step burn-in. (A-C) Inference of the hidden state z shown as the probability of being in the low diffusion state. (D-F) Posterior distributions for the two diffusion coefficients: D0 (red) and D1 (blue). See Methods for priors and initial conditions.
Mentions: The stationary beads also provide an opportunity to check that the measurement noise does not affect model selection: stationary beads should prefer a one-state diffusion model since the time series is homogeneous. If the two-state diffusion model is preferred then measurement noise, the tracking algorithm, or instrument noise contributes to the heterogeneity in the trajectory. We applied the one-state and two-state diffusion model algorithms (without measurement noise) to the three stationary beads. The two-state diffusion model showed high frequency switching behaviour (Fig 1A–1C), with two distinct (well separated) diffusion coefficients, (Fig 1D–1F). Crucially, the two-state diffusion model is strongly preferred for all 3 trajectories (Fig 2, red asterisks). Therefore there is evidence that tracked bead displacements are not unstructured and an analysis of LFA-1 trajectories using the models without allowing for measurement noise may be unreliable, due to this inherent inhomogeneity.

Bottom Line: Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 10(2) - 2.6 × 10(5) 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.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.

View Article: PubMed Central - PubMed

Affiliation: Systems Biology Centre, University of Warwick, Coventry, United Kingdom; Systems Biology Doctoral Training Centre, University of Warwick, Coventry, United Kingdom.

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 D1 = 0.68D0 - 1.5 × 10(4) 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 × 10(2) - 2.6 × 10(5) 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.

No MeSH data available.