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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.


Mean waiting times and example trajectories showing confinement for two-state diffusion model fit to LFA-1 trajectories.(A) Mean waiting time in seconds ( for z = 0 state, ) for z = 1 state) for trajectories where approximate two-state diffusion model was preferred (fast switching,  or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red squares; PMA black circles; PMA+Cal-I, green triangles. Labels B-F correspond to example confinement state trajectories in B-F. (B) DMSO treatment (mean waiting time in z = 0 state 0.02s, in z = 1 state 0.04s) (C) PMA treatment (z = 0 state 0.32s, z = 1 state 0.16s) (D) PMA treatment (z = 0 state 0.09s, z = 1 state 0.12s) (E) PMA+Cal-I treatment (z = 0 state 1.48s, z = 1 state 0.39s) (F) DMSO treatment (z = 0 state 0.04s, z = 1 state 0.72s).
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pone.0140759.g008: Mean waiting times and example trajectories showing confinement for two-state diffusion model fit to LFA-1 trajectories.(A) Mean waiting time in seconds ( for z = 0 state, ) for z = 1 state) for trajectories where approximate two-state diffusion model was preferred (fast switching, or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red squares; PMA black circles; PMA+Cal-I, green triangles. Labels B-F correspond to example confinement state trajectories in B-F. (B) DMSO treatment (mean waiting time in z = 0 state 0.02s, in z = 1 state 0.04s) (C) PMA treatment (z = 0 state 0.32s, z = 1 state 0.16s) (D) PMA treatment (z = 0 state 0.09s, z = 1 state 0.12s) (E) PMA+Cal-I treatment (z = 0 state 1.48s, z = 1 state 0.39s) (F) DMSO treatment (z = 0 state 0.04s, z = 1 state 0.72s).

Mentions: We also examined the frequency of switching events for trajectories where the two-state diffusion model was preferred, excluding fast switching trajectories. Fig 8A plots the exponentially distributed waiting times in each state (i.e. the reciprocal of the inferred transition probabilities), demonstrating a broad range of values. Some trajectories exhibit fast transient switching (Fig 8A, trajectories clustered around origin, example in Fig 8B), although slower than that in stationary beads. Another group of trajectories switch less frequently, with the time in a single state on the order of tenths of seconds (Fig 8C and 8D). We also observe trajectories with very slow switching, Fig 8E is an example of a trajectory with a single switch point, whilst some trajectories spend the majority of time in the z = 0 (fast) state, with transient switching to the z = 1 (slow) state (Fig 8F). This variety suggests that multiple processes are affecting the waiting times since this range of behaviours would not be observed in a single exponential waiting time model.


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)

Mean waiting times and example trajectories showing confinement for two-state diffusion model fit to LFA-1 trajectories.(A) Mean waiting time in seconds ( for z = 0 state, ) for z = 1 state) for trajectories where approximate two-state diffusion model was preferred (fast switching,  or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red squares; PMA black circles; PMA+Cal-I, green triangles. Labels B-F correspond to example confinement state trajectories in B-F. (B) DMSO treatment (mean waiting time in z = 0 state 0.02s, in z = 1 state 0.04s) (C) PMA treatment (z = 0 state 0.32s, z = 1 state 0.16s) (D) PMA treatment (z = 0 state 0.09s, z = 1 state 0.12s) (E) PMA+Cal-I treatment (z = 0 state 1.48s, z = 1 state 0.39s) (F) DMSO treatment (z = 0 state 0.04s, z = 1 state 0.72s).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4608688&req=5

pone.0140759.g008: Mean waiting times and example trajectories showing confinement for two-state diffusion model fit to LFA-1 trajectories.(A) Mean waiting time in seconds ( for z = 0 state, ) for z = 1 state) for trajectories where approximate two-state diffusion model was preferred (fast switching, or , trajectories removed). Treatments: DMSO, blue asterisks; Cyto D, red squares; PMA black circles; PMA+Cal-I, green triangles. Labels B-F correspond to example confinement state trajectories in B-F. (B) DMSO treatment (mean waiting time in z = 0 state 0.02s, in z = 1 state 0.04s) (C) PMA treatment (z = 0 state 0.32s, z = 1 state 0.16s) (D) PMA treatment (z = 0 state 0.09s, z = 1 state 0.12s) (E) PMA+Cal-I treatment (z = 0 state 1.48s, z = 1 state 0.39s) (F) DMSO treatment (z = 0 state 0.04s, z = 1 state 0.72s).
Mentions: We also examined the frequency of switching events for trajectories where the two-state diffusion model was preferred, excluding fast switching trajectories. Fig 8A plots the exponentially distributed waiting times in each state (i.e. the reciprocal of the inferred transition probabilities), demonstrating a broad range of values. Some trajectories exhibit fast transient switching (Fig 8A, trajectories clustered around origin, example in Fig 8B), although slower than that in stationary beads. Another group of trajectories switch less frequently, with the time in a single state on the order of tenths of seconds (Fig 8C and 8D). We also observe trajectories with very slow switching, Fig 8E is an example of a trajectory with a single switch point, whilst some trajectories spend the majority of time in the z = 0 (fast) state, with transient switching to the z = 1 (slow) state (Fig 8F). This variety suggests that multiple processes are affecting the waiting times since this range of behaviours would not be observed in a single exponential waiting time model.

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.