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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.


Observed variation in the diffusion coefficient of LFA-1 in single particle tracking trajectories, with proposed mechanisms.
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pone.0140759.g012: Observed variation in the diffusion coefficient of LFA-1 in single particle tracking trajectories, with proposed mechanisms.

Mentions: The high variability of the estimated diffusion coefficients among both fast and slow trajectories may provide biological insight into the organisation of LFA-1 in the membrane. Clustering and cytoskeletal contacts are central to the regulation of LFA-1 in the membrane [51]. Previous work has found that the movement of clusters on live cells is dependent on the conformation of the receptor [5, 41]. We propose that the multi-state diffusion observed in the current analysis is a result of changes in the size of clusters, or the number of cytoskeletal contacts for those clusters. The relationship in Fig 7A suggests that the switching events we are detecting are all due to a common process. One interpretation is that we are observing diffusing aggregates of LFA-1, either in protein islands [52], or due to multiple attachments of LFA-1 molecules with the bead, a change in the aggregate size by 1 corresponding to a switch in the diffusion coefficient. We hypothesise that the diffusion coefficient reflects the size of the aggregate; the cross section of a receptor or complex in the membrane has a predictable effect on its diffusion [53]. However, the variability in the (high) diffusion coefficients that we observe is inconsistent with this process alone. Since diffusion coefficients are observed along the straight line in Fig 7A, there is an heterogeneity that determines the diffusion coefficient by smaller increments, and is presumably also responsible for the large variability in the switching frequency, (Fig 8). We thus have a hierarchy of processes: on time scales less than 4 s we observe changes in the aggregate size producing large changes in the diffusion coefficient according to Fig 7A, and these aggregates are also affected by a slower process that results in a finer heterogeneity (Figs 6 and 12). A potential mechanism is cytoskeletal attachment, with the number of attachments increasing with aggregate size thereby increasing the drag, and a sufficiently large number of these interactions making the receptor aggregate immobile, giving an interpretation of the non-zero intercept of the D0/D1 relationship in Fig 7. This is consistent with calpain inhibition having the highest level of immobility, Table 1, since calpain cleaves the talin head domain and releases LFA-1 from the cytoskeleton [42]. The fact that the mobile diffusion coefficient is reduced under calpain treatment, Table 1, also supports the fact that cytoskeletal interactions are contributing to the aggregate drag. We also demonstrated that the immobile states (detected predominantly as immobile throughout) typically have a slow linear drift, with speeds of around 110 nm s−1. We suggest that these correspond to LFA-1 (possibly clusters) strongly bound to the actin cortex, and these drift phases correspond to cortex remodelling under actin (de)polymerisation, myosin contraction or retrograde flux, [50]. Such drift was also detected by MSD analysis as super-diffusion (α > 1) [5].


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)

Observed variation in the diffusion coefficient of LFA-1 in single particle tracking trajectories, with proposed mechanisms.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0140759.g012: Observed variation in the diffusion coefficient of LFA-1 in single particle tracking trajectories, with proposed mechanisms.
Mentions: The high variability of the estimated diffusion coefficients among both fast and slow trajectories may provide biological insight into the organisation of LFA-1 in the membrane. Clustering and cytoskeletal contacts are central to the regulation of LFA-1 in the membrane [51]. Previous work has found that the movement of clusters on live cells is dependent on the conformation of the receptor [5, 41]. We propose that the multi-state diffusion observed in the current analysis is a result of changes in the size of clusters, or the number of cytoskeletal contacts for those clusters. The relationship in Fig 7A suggests that the switching events we are detecting are all due to a common process. One interpretation is that we are observing diffusing aggregates of LFA-1, either in protein islands [52], or due to multiple attachments of LFA-1 molecules with the bead, a change in the aggregate size by 1 corresponding to a switch in the diffusion coefficient. We hypothesise that the diffusion coefficient reflects the size of the aggregate; the cross section of a receptor or complex in the membrane has a predictable effect on its diffusion [53]. However, the variability in the (high) diffusion coefficients that we observe is inconsistent with this process alone. Since diffusion coefficients are observed along the straight line in Fig 7A, there is an heterogeneity that determines the diffusion coefficient by smaller increments, and is presumably also responsible for the large variability in the switching frequency, (Fig 8). We thus have a hierarchy of processes: on time scales less than 4 s we observe changes in the aggregate size producing large changes in the diffusion coefficient according to Fig 7A, and these aggregates are also affected by a slower process that results in a finer heterogeneity (Figs 6 and 12). A potential mechanism is cytoskeletal attachment, with the number of attachments increasing with aggregate size thereby increasing the drag, and a sufficiently large number of these interactions making the receptor aggregate immobile, giving an interpretation of the non-zero intercept of the D0/D1 relationship in Fig 7. This is consistent with calpain inhibition having the highest level of immobility, Table 1, since calpain cleaves the talin head domain and releases LFA-1 from the cytoskeleton [42]. The fact that the mobile diffusion coefficient is reduced under calpain treatment, Table 1, also supports the fact that cytoskeletal interactions are contributing to the aggregate drag. We also demonstrated that the immobile states (detected predominantly as immobile throughout) typically have a slow linear drift, with speeds of around 110 nm s−1. We suggest that these correspond to LFA-1 (possibly clusters) strongly bound to the actin cortex, and these drift phases correspond to cortex remodelling under actin (de)polymerisation, myosin contraction or retrograde flux, [50]. Such drift was also detected by MSD analysis as super-diffusion (α > 1) [5].

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.