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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.


Posterior estimates of diffusion coefficients for single LFA-1 trajectories.(A-D) Pooled posterior samples of logeD0 and logeD1 for trajectories preferring the two-state diffusion model (fast switching,  or , trajectories removed). The posterior means for logeD0 (red squares) and logeD1 (green triangles), are also shown. Black line indicates value of σ2/2Δt. Dashed line indicates threshold used to categorise immobile and mobile diffusion states. Treatments: (A) DMSO, two-state model preferred for 13 trajectories; (B) Cyto D, 3 trajectories; (C) PMA, 8 trajectories; (D) PMA+Cal-I, 6 trajectories. (E) Pooled logeD estimates and posterior means (blue circles) over all treatments, for trajectories where one-state diffusion model was preferred (132 trajectories).
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pone.0140759.g005: Posterior estimates of diffusion coefficients for single LFA-1 trajectories.(A-D) Pooled posterior samples of logeD0 and logeD1 for trajectories preferring the two-state diffusion model (fast switching, or , trajectories removed). The posterior means for logeD0 (red squares) and logeD1 (green triangles), are also shown. Black line indicates value of σ2/2Δt. Dashed line indicates threshold used to categorise immobile and mobile diffusion states. Treatments: (A) DMSO, two-state model preferred for 13 trajectories; (B) Cyto D, 3 trajectories; (C) PMA, 8 trajectories; (D) PMA+Cal-I, 6 trajectories. (E) Pooled logeD estimates and posterior means (blue circles) over all treatments, for trajectories where one-state diffusion model was preferred (132 trajectories).

Mentions: We next analysed the consistency of the diffusion coefficient estimates between trajectories. We note that the diffusion coefficients can be estimated below the measurement noise effective diffusion coefficient of σ2/(2Δt) since estimates are based on multiple time points, the error falling as σ2/(2nΔt) for n displacements. On the 4000 time points this gives a lower threshold of log(D) = 1.64, so well below the lowest inferred diffusion coefficient. For both sets of trajectories, those that preferred the one-state diffusion (D) or two-state diffusion (D0, D1), we computed the posterior mean diffusion coefficient and pooled their posterior distributions (in the full likelihood model, Figs 5 and 6). All four conditions demonstrated similar features:


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)

Posterior estimates of diffusion coefficients for single LFA-1 trajectories.(A-D) Pooled posterior samples of logeD0 and logeD1 for trajectories preferring the two-state diffusion model (fast switching,  or , trajectories removed). The posterior means for logeD0 (red squares) and logeD1 (green triangles), are also shown. Black line indicates value of σ2/2Δt. Dashed line indicates threshold used to categorise immobile and mobile diffusion states. Treatments: (A) DMSO, two-state model preferred for 13 trajectories; (B) Cyto D, 3 trajectories; (C) PMA, 8 trajectories; (D) PMA+Cal-I, 6 trajectories. (E) Pooled logeD estimates and posterior means (blue circles) over all treatments, for trajectories where one-state diffusion model was preferred (132 trajectories).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0140759.g005: Posterior estimates of diffusion coefficients for single LFA-1 trajectories.(A-D) Pooled posterior samples of logeD0 and logeD1 for trajectories preferring the two-state diffusion model (fast switching, or , trajectories removed). The posterior means for logeD0 (red squares) and logeD1 (green triangles), are also shown. Black line indicates value of σ2/2Δt. Dashed line indicates threshold used to categorise immobile and mobile diffusion states. Treatments: (A) DMSO, two-state model preferred for 13 trajectories; (B) Cyto D, 3 trajectories; (C) PMA, 8 trajectories; (D) PMA+Cal-I, 6 trajectories. (E) Pooled logeD estimates and posterior means (blue circles) over all treatments, for trajectories where one-state diffusion model was preferred (132 trajectories).
Mentions: We next analysed the consistency of the diffusion coefficient estimates between trajectories. We note that the diffusion coefficients can be estimated below the measurement noise effective diffusion coefficient of σ2/(2Δt) since estimates are based on multiple time points, the error falling as σ2/(2nΔt) for n displacements. On the 4000 time points this gives a lower threshold of log(D) = 1.64, so well below the lowest inferred diffusion coefficient. For both sets of trajectories, those that preferred the one-state diffusion (D) or two-state diffusion (D0, D1), we computed the posterior mean diffusion coefficient and pooled their posterior distributions (in the full likelihood model, Figs 5 and 6). All four conditions demonstrated similar features:

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.