Dependences of parameter estimates from two-state diffusion model.

<p>(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, <math><mrow><msub><mi>p</mi><mo>^</mo><mn>01</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math> or <math><mrow><msub><mi>p</mi><mo>^</mo><mn>10</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math>, 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, <i>D</i>₁ = <i>aD</i>₀ + <i>b</i>, <i>a</i> = 0.68, <i>b</i> = −1.5 × 10⁴ nm² s⁻¹; black dashed line is the double iterate, <i>D</i>₁ = <i>a</i>(<i>aD</i>₀ + <i>b</i>) + <i>b</i>.</p

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

<p>Observed variation in the diffusion coefficient of LFA-1 in single particle tracking trajectories, with proposed mechanisms.</p

Model selection for one-state and two-state diffusion models on simulated stationary beads and stationary latex bead trajectories.

<p>Blue bars: Bayes factors from model selection on simulated stationary beads (<i>n</i> = 240) with added Gaussian noise (<i>σ</i>² = 41.09nm²). Single data points on axis: Bayes factors from model selection on stationary latex bead trajectories, both without (red asterisks) and with (green circles, <i>σ</i>² = 41.09nm²) measurement noise incorporated into the inference algorithm. Priors, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140759#sec002" target="_blank">Methods</a>.</p

Comparison of parameter estimates for exact and approximate two-state diffusion models with measurement noise.

<p>(A-D) Scatter plots of two-state parameter estimates for exact model against approximate model, for 30 trajectories preferring the approximate two-state model (fast-switching, <math><mrow><msub><mi>p</mi><mo>^</mo><mn>01</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math> or <math><mrow><msub><mi>p</mi><mo>^</mo><mn>10</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math> in the exact model, trajectories removed). Line of equality is shown as dashed. Treatments: DMSO (blue asterisks), Cyto D (red squares), PMA (black circles), PMA+Cal-I (green triangles).</p

Fit of a two-state diffusion model without measurement noise to three stationary latex bead trajectories.

<p>MCMC output from chains of 20000 MCMC steps with a 10000 step burn-in. (A-C) Inference of the hidden state <b>z</b> shown as the probability of being in the low diffusion state. (D-F) Posterior distributions for the two diffusion coefficients: <i>D</i>₀ (red) and <i>D</i>₁ (blue). See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140759#sec002" target="_blank">Methods</a> for priors and initial conditions.</p

Pooled posterior distribution of diffusion coefficients for single LFA-1 trajectories.

<p>(A) Pooled posterior samples of <i>D</i> for trajectories where one-state diffusion model was preferred, restricted to log_<i>e</i><i>D</i> > 8 (99 trajectories). The posterior distribution from a single trajectory (black line, DMSO treatment) is also plotted, normalised to equal height. (B) Pooled posterior samples of <i>D</i>₀ and <i>D</i>₁ for trajectories where two-state diffusion model was preferred, restricted to log_<i>e</i><i>D</i>₁ > 8 (29 trajectories), with fast switching (<math><mrow><msub><mi>p</mi><mo>^</mo><mn>01</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math> or <math><mrow><msub><mi>p</mi><mo>^</mo><mn>10</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math>) trajectories removed. One data point with <i>D</i>₀ > 2 × 10⁵ nm² s⁻¹ not shown.</p

Model selection between approximate one-state and two-state diffusion models with measurement noise on LFA-1 trajectories.

<p>(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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140759#sec002" target="_blank">Methods</a>.</p

Fit of a two-state diffusion model with measurement noise to an LFA-1 trajectory (PMA+Cal-I treatment).

<p>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 <i>D</i>₀ (red) and <i>D</i>₁ (blue) including burn-in (dashed line). (C) Posteriors for the switching probabilities per frame, (D) corresponding samples (12 chains) for <i>p</i>₀₁ (red) and <i>p</i>₁₀ (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 <i>π</i>(<b>z</b> = 1∣<b>X</b>) from 0 (blue, high diffusion state) to 1 (green, low diffusion state). Colorbar length: 100nm. Priors, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140759#sec002" target="_blank">Methods</a>.</p

Posterior estimates of diffusion coefficients for single LFA-1 trajectories.

<p>(A-D) Pooled posterior samples of log_<i>e</i><i>D</i>₀ and log_<i>e</i><i>D</i>₁ for trajectories preferring the two-state diffusion model (fast switching, <math><mrow><msub><mi>p</mi><mo>^</mo><mn>01</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math> or <math><mrow><msub><mi>p</mi><mo>^</mo><mn>10</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math>, trajectories removed). The posterior means for log_<i>e</i><i>D</i>₀ (red squares) and log_<i>e</i><i>D</i>₁ (green triangles), are also shown. Black line indicates value of <i>σ</i>²/2Δ<i>t</i>. Dashed line indicates threshold used to categorise immobile and mobile diffusion states. Treatments: (A) DMSO, two-state model preferred for 13 trajectories; (B) Cyto D, 3 trajectories; (C) PMA, 8 trajectories; (D) PMA+Cal-I, 6 trajectories. (E) Pooled log_<i>e</i><i>D</i> estimates and posterior means (blue circles) over all treatments, for trajectories where one-state diffusion model was preferred (132 trajectories).</p

Model selection and proportion of time spent in the immobile state.

<p>Diffusion coefficient units are nm² s⁻¹ with standard error based on the number of trajectories.</p><p>¹ Model selection between approximate one-state and two-state diffusion models with measurement noise, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140759#sec002" target="_blank">Methods</a>, with trajectories with no strong model preference (−3 < log_<i>e</i><i>B</i>_{1<i>D</i>, 2<i>D</i>} < 3) removed.</p><p>² Fast switching trajectories (<math><mrow><msub><mi>p</mi><mo>^</mo><mn>01</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math> or <math><mrow><msub><mi>p</mi><mo>^</mo><mn>10</mn></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math>) also removed.</p><p>³ Defined as log_<i>e</i><i>D</i> < 8 or log_<i>e</i><i>D</i>₁ < 8, for mean posterior parameters <i>D</i>, <i>D</i>₁ nm² s⁻¹ from one-state and two-state diffusion models with measurement noise.</p><p>⁴ Over all trajectories with either one-state or two-state model preference, with fast switching trajectories removed (i.e. Table notes 1 and 2 apply). For one-state preference, the proportion in the immobile state is 0 if log_<i>e</i><i>D</i> > 8, 1 if log_<i>e</i><i>D</i> > 8. For two-state preference, the proportion is 0 if log_<i>e</i><i>D</i>₁ > 8, and if log_<i>e</i><i>D</i>₁ < 8 the proportion of time that was spent in the <i>z</i> = 1 state (diffusion with <i>D</i> = <i>D</i>₁), i.e. <math><mrow><mn>1</mn><mo>/</mo><mi>N</mi><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><mi>π</mi><mrow><mo>(</mo><msub><mi>z</mi><mi>i</mi></msub><mo>|</mo><mi>X</mi><mo>)</mo></mrow></mrow></math>.</p><p>⁵ Over all posterior samples, for trajectories with two-state model preference, with fast switching trajectories removed.</p><p>⁶ Over all posterior samples, for trajectories with one-state model preference, restricted to log_<i>e</i><i>D</i> > 8.</p><p>⁷ Over all posterior samples, for trajectories with one-state model preference, restricted to log_<i>e</i><i>D</i> < 8.</p><p>Model selection and proportion of time spent in the immobile state.</p