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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.


Related in: MedlinePlus

Dependences of parameter estimates from two-state diffusion model.(A-D) Scatter plots of posterior means for the two-state model with measurement noise, for trajectories where the approximate two-state diffusion model was preferred (fast switching,  or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red crosses; PMA, black circles; PMA+Cal-I, green triangles. In panel (A) the black solid line is a linear fit with two outlier trajectories removed, D1 = aD0 + b, a = 0.68, b = −1.5 × 104 nm2 s−1; black dashed line is the double iterate, D1 = a(aD0 + b) + b.
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pone.0140759.g007: Dependences of parameter estimates from two-state diffusion model.(A-D) Scatter plots of posterior means for the two-state model with measurement noise, for trajectories where the approximate two-state diffusion model was preferred (fast switching, or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red crosses; PMA, black circles; PMA+Cal-I, green triangles. In panel (A) the black solid line is a linear fit with two outlier trajectories removed, D1 = aD0 + b, a = 0.68, b = −1.5 × 104 nm2 s−1; black dashed line is the double iterate, D1 = a(aD0 + b) + b.

Mentions: For trajectories where the two-state diffusion model was preferred, (excluding the fast-switching trajectories), we examined if the diffusion coefficients between the two diffusive states are related (Fig 7A). The correlation coefficient is high (r = 0.84), whilst a linear relation is strongly suggested, D1 = 0.68D0 − 1.5 × 104 nm2s−1, independent of treatment, using all points except the 2 outliers. This suggests that the switching events we are detecting are likely due to a single process. We also examined the relationship between D0 and p10, D0 and the time in the high (z = 0) diffusion state and D1 and the time in the low (z = 1) diffusion state, but found no correlation, Fig 7B–7D.


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)

Dependences of parameter estimates from two-state diffusion model.(A-D) Scatter plots of posterior means for the two-state model with measurement noise, for trajectories where the approximate two-state diffusion model was preferred (fast switching,  or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red crosses; PMA, black circles; PMA+Cal-I, green triangles. In panel (A) the black solid line is a linear fit with two outlier trajectories removed, D1 = aD0 + b, a = 0.68, b = −1.5 × 104 nm2 s−1; black dashed line is the double iterate, D1 = a(aD0 + b) + b.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0140759.g007: Dependences of parameter estimates from two-state diffusion model.(A-D) Scatter plots of posterior means for the two-state model with measurement noise, for trajectories where the approximate two-state diffusion model was preferred (fast switching, or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red crosses; PMA, black circles; PMA+Cal-I, green triangles. In panel (A) the black solid line is a linear fit with two outlier trajectories removed, D1 = aD0 + b, a = 0.68, b = −1.5 × 104 nm2 s−1; black dashed line is the double iterate, D1 = a(aD0 + b) + b.
Mentions: For trajectories where the two-state diffusion model was preferred, (excluding the fast-switching trajectories), we examined if the diffusion coefficients between the two diffusive states are related (Fig 7A). The correlation coefficient is high (r = 0.84), whilst a linear relation is strongly suggested, D1 = 0.68D0 − 1.5 × 104 nm2s−1, independent of treatment, using all points except the 2 outliers. This suggests that the switching events we are detecting are likely due to a single process. We also examined the relationship between D0 and p10, D0 and the time in the high (z = 0) diffusion state and D1 and the time in the low (z = 1) diffusion state, but found no correlation, Fig 7B–7D.

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.


Related in: MedlinePlus