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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.


Model selection between approximate one-state and two-state diffusion models with measurement noise on LFA-1 trajectories.(A) Box and whisker plot of log Bayes factors by treatment, trajectories with log Bayes factor outside 1.5 times IQR are plotted as outliers (red crosses). The thresholds ±3 (red lines) are shown. (B) Stacked bar plot showing proportions for each preferred model and trajectories which demonstrate fast switching between diffusive states. A log Bayes factor of ±3 ((A), red lines) is considered preference for the relevant model. MCMC runs comprise 12 parallel chains of 20000 steps with a 10000 step burn-in. Priors, see Methods.
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pone.0140759.g004: Model selection between approximate one-state and two-state diffusion models with measurement noise on LFA-1 trajectories.(A) Box and whisker plot of log Bayes factors by treatment, trajectories with log Bayes factor outside 1.5 times IQR are plotted as outliers (red crosses). The thresholds ±3 (red lines) are shown. (B) Stacked bar plot showing proportions for each preferred model and trajectories which demonstrate fast switching between diffusive states. A log Bayes factor of ±3 ((A), red lines) is considered preference for the relevant model. MCMC runs comprise 12 parallel chains of 20000 steps with a 10000 step burn-in. Priors, see Methods.

Mentions: By calculating the marginal likelihood for the approximate one-state and two-state diffusion models with measurement noise, and hence the Bayes factor , we then ascertained for each trajectory the evidence for a two-state compared to a one-state diffusion process. As described in Methods, we used fairly stringent criteria: if the log (base e) Bayes factor is smaller than -3 then we consider this preference for the two-state diffusion model, and greater than 3 as preference for the one-state diffusion model [49]. The number of trajectories with preference for each model was robust to the choice of Bayes factor threshold (S1 Table). Fig 4 shows the Bayes factor estimates for each condition, and the number of trajectories which preferred each model, grouped by treatment. There are a total of 16 DMSO (out of a total of 75, 21%), 8 Cyto D (out of 36, 22%), 13 PMA (out of 19, 33%) and 8 PMA+Cal-I (out of 46, 17%) trajectories where the two-state diffusion model is preferred, Table 1. Thus, in all treatments we detected evidence of switching within trajectories with a similar level of preference. However, a proportion of the trajectories that preferred the two-state diffusion model showed extremely fast switching; we define fast switching as either or , giving counts: DMSO, 3 trajectories; Cyto D, 5 trajectories; PMA, 5 trajectories; PMA+Cal-I, 2 trajectories, Table 1. Thus, over all treatments, for trajectories where the two-state diffusion model was preferred, we saw fast switching in 33% of trajectories.


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)

Model selection between approximate one-state and two-state diffusion models with measurement noise on LFA-1 trajectories.(A) Box and whisker plot of log Bayes factors by treatment, trajectories with log Bayes factor outside 1.5 times IQR are plotted as outliers (red crosses). The thresholds ±3 (red lines) are shown. (B) Stacked bar plot showing proportions for each preferred model and trajectories which demonstrate fast switching between diffusive states. A log Bayes factor of ±3 ((A), red lines) is considered preference for the relevant model. MCMC runs comprise 12 parallel chains of 20000 steps with a 10000 step burn-in. Priors, see Methods.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0140759.g004: Model selection between approximate one-state and two-state diffusion models with measurement noise on LFA-1 trajectories.(A) Box and whisker plot of log Bayes factors by treatment, trajectories with log Bayes factor outside 1.5 times IQR are plotted as outliers (red crosses). The thresholds ±3 (red lines) are shown. (B) Stacked bar plot showing proportions for each preferred model and trajectories which demonstrate fast switching between diffusive states. A log Bayes factor of ±3 ((A), red lines) is considered preference for the relevant model. MCMC runs comprise 12 parallel chains of 20000 steps with a 10000 step burn-in. Priors, see Methods.
Mentions: By calculating the marginal likelihood for the approximate one-state and two-state diffusion models with measurement noise, and hence the Bayes factor , we then ascertained for each trajectory the evidence for a two-state compared to a one-state diffusion process. As described in Methods, we used fairly stringent criteria: if the log (base e) Bayes factor is smaller than -3 then we consider this preference for the two-state diffusion model, and greater than 3 as preference for the one-state diffusion model [49]. The number of trajectories with preference for each model was robust to the choice of Bayes factor threshold (S1 Table). Fig 4 shows the Bayes factor estimates for each condition, and the number of trajectories which preferred each model, grouped by treatment. There are a total of 16 DMSO (out of a total of 75, 21%), 8 Cyto D (out of 36, 22%), 13 PMA (out of 19, 33%) and 8 PMA+Cal-I (out of 46, 17%) trajectories where the two-state diffusion model is preferred, Table 1. Thus, in all treatments we detected evidence of switching within trajectories with a similar level of preference. However, a proportion of the trajectories that preferred the two-state diffusion model showed extremely fast switching; we define fast switching as either or , giving counts: DMSO, 3 trajectories; Cyto D, 5 trajectories; PMA, 5 trajectories; PMA+Cal-I, 2 trajectories, Table 1. Thus, over all treatments, for trajectories where the two-state diffusion model was preferred, we saw fast switching in 33% of trajectories.

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.