Limits...
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.


Fit of a two-state diffusion model with measurement noise to an LFA-1 trajectory (PMA+Cal-I treatment).MCMC output (12 independent chains of 20000 MCMC steps with a 10000 step burn-in). (A) The posteriors for the two diffusion coefficients, (B) corresponding samples (12 chains plotted in the same colour) for D0 (red) and D1 (blue) including burn-in (dashed line). (C) Posteriors for the switching probabilities per frame, (D) corresponding samples (12 chains) for p01 (red) and p10 (blue) including burn-in (dashed line). (E) State inference shown as the probability of being in the low diffusion state. (F) Trajectory coloured by the probability of being in the low diffusion state. Colour scale represents π(z = 1∣X) from 0 (blue, high diffusion state) to 1 (green, low diffusion state). Colorbar length: 100nm. Priors, see Methods.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4608688&req=5

pone.0140759.g003: Fit of a two-state diffusion model with measurement noise to an LFA-1 trajectory (PMA+Cal-I treatment).MCMC output (12 independent chains of 20000 MCMC steps with a 10000 step burn-in). (A) The posteriors for the two diffusion coefficients, (B) corresponding samples (12 chains plotted in the same colour) for D0 (red) and D1 (blue) including burn-in (dashed line). (C) Posteriors for the switching probabilities per frame, (D) corresponding samples (12 chains) for p01 (red) and p10 (blue) including burn-in (dashed line). (E) State inference shown as the probability of being in the low diffusion state. (F) Trajectory coloured by the probability of being in the low diffusion state. Colour scale represents π(z = 1∣X) from 0 (blue, high diffusion state) to 1 (green, low diffusion state). Colorbar length: 100nm. Priors, see Methods.

Mentions: We fitted the one-state and two-state diffusion models with measurement noise to each trajectory in the four treatments (36–75 trajectories depending on treatment, 4 s trajectories at 1000 frames s−1), thereby estimating parameters for these models for each trajectory. Convergence was confirmed using a multiple chain protocol, see Methods. An example of a fit to the two-state diffusion model with measurement noise is shown in Fig 3; inference of the hidden state shows clear evidence of state switching in this trajectory with a high probability of being in one or other of the two diffusion states and tight switching times. There is a large separation in the posterior distributions for the low and high diffusion coefficients, with the ratio of the posterior mean estimates being around 10.


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)

Fit of a two-state diffusion model with measurement noise to an LFA-1 trajectory (PMA+Cal-I treatment).MCMC output (12 independent chains of 20000 MCMC steps with a 10000 step burn-in). (A) The posteriors for the two diffusion coefficients, (B) corresponding samples (12 chains plotted in the same colour) for D0 (red) and D1 (blue) including burn-in (dashed line). (C) Posteriors for the switching probabilities per frame, (D) corresponding samples (12 chains) for p01 (red) and p10 (blue) including burn-in (dashed line). (E) State inference shown as the probability of being in the low diffusion state. (F) Trajectory coloured by the probability of being in the low diffusion state. Colour scale represents π(z = 1∣X) from 0 (blue, high diffusion state) to 1 (green, low diffusion state). Colorbar length: 100nm. Priors, see Methods.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0140759.g003: Fit of a two-state diffusion model with measurement noise to an LFA-1 trajectory (PMA+Cal-I treatment).MCMC output (12 independent chains of 20000 MCMC steps with a 10000 step burn-in). (A) The posteriors for the two diffusion coefficients, (B) corresponding samples (12 chains plotted in the same colour) for D0 (red) and D1 (blue) including burn-in (dashed line). (C) Posteriors for the switching probabilities per frame, (D) corresponding samples (12 chains) for p01 (red) and p10 (blue) including burn-in (dashed line). (E) State inference shown as the probability of being in the low diffusion state. (F) Trajectory coloured by the probability of being in the low diffusion state. Colour scale represents π(z = 1∣X) from 0 (blue, high diffusion state) to 1 (green, low diffusion state). Colorbar length: 100nm. Priors, see Methods.
Mentions: We fitted the one-state and two-state diffusion models with measurement noise to each trajectory in the four treatments (36–75 trajectories depending on treatment, 4 s trajectories at 1000 frames s−1), thereby estimating parameters for these models for each trajectory. Convergence was confirmed using a multiple chain protocol, see Methods. An example of a fit to the two-state diffusion model with measurement noise is shown in Fig 3; inference of the hidden state shows clear evidence of state switching in this trajectory with a high probability of being in one or other of the two diffusion states and tight switching times. There is a large separation in the posterior distributions for the low and high diffusion coefficients, with the ratio of the posterior mean estimates being around 10.

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.