14 research outputs found

    Average force decomposition across the population of trajectories.

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    <p>(A) Distributions of absolute forces (spring, PEF and K-fibre) averaged over trajectories (and sisters). (B) Mean force partition averaged over all time-points, time-points where the kinetochore is attached to a polymerising or depolymerising K-fibre. Absolute force values are averaged over respective sister and time-points across all trajectories (<i>n</i> = 843).</p

    Force profiles during directional switches.

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    <p>Time-dependent estimation of (A) spring force and (B) PEF. Switch events from trajectories where the lead (LIDS, <i>n</i> = 1614; magenta) or trail (TIDS, <i>n</i> = 449; black) kinetochore switched first were aligned at their median switching time (the time origin is marked by vertical blue line). Solid lines indicate mean, dashed lines ±s.e.m.. Forces are given as velocities by rescaling by the viscosity coefficient. (C) Opposing force (spring + PEF) on lead sister during a LIDS (magenta) or TIDS (black) is plotted relative to the depolymerisation force <i>F</i><sub>−</sub>. Solid lines indicate mean, dashed lines 5% and 95% percentiles of the population. (D) Spring force heat map across switching events partitioned by difference between probability of LIDS (<i>p</i><sub>LIDS</sub>) or TIDS (<i>p</i><sub>TIDS</sub>). Events above zero on right <i>y</i>-axis are classified as LIDS; those below as TIDS.</p

    Population parameter analysis.

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    <p>Posterior means for (A) K-fibre (de)polymerisation velocities <i>v</i><sub>+</sub> (blue) and <i>v</i><sub>−</sub> (red); (B) spring constant <i>κ</i>; (C) anti-poleward force gradient <i>α</i>; (D) noise parameter <i>τ</i> = <i>s</i><sup>−2</sup>; (E) natural length <i>L</i> (blue); (F) the probabilities of not switching state per time-point when sisters are coherent (blue) and incoherent (red). The informed Gaussian prior on <i>L</i> is shown in red in (E). Dashed line and shaded areas in (A-F) indicate mean and ±s.d., respectively. (G-L) Trajectories binned by radial distance from the centre of metaphase plate (with approximately equal numbers per bin; alternating grey and white boxes) for parameters as in (A-F). Circles indicate mean of bin and lines show ±s.d.. All panels include all converged and filtered trajectories (<i>n</i> = 843).</p

    Force decomposition profile.

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    <p>(A) Schematic of the forces acting on kinetochore sisters. (B-E) Estimated decomposition of kinetochore velocity into its force components over time for the trajectory in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.g001" target="_blank">Fig 1C</a>; (B, D) sister 1 and (C, E) sister 2. Polymerisation/depolymerisation force on kinetochores attributable to the K-fibre (blue/red, respectively); spring force (green); polar ejection forces (orange) and the total force (purple). Time-series overlaid with inferred end (black dashed) and start (green dashed) times of coherence periods (runs). Between end and start times K-fibres are incoherent (in this case +/+) Note that forces are positive in the anti-poleward direction.</p

    Oscillating stochastic kinetochore model.

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    <p>(A) Model schematic showing the orientation of the two sisters and the respective forces (arrows). Sister kinetochores are connected by a linear spring (producing force <i>F</i><sub>spring</sub>, green) and are attached to a K-fibre in either a polymerising (<i>F</i><sub>+</sub>, blue) or depolymerising (<i>F</i><sub>−</sub>, red) state. The direction of polar ejection forces (PEF, <i>F</i><sub>PEF</sub>) is indicated by orange arrows. Sisters may be off-axis (twist angle <i>θ</i>); the spring force (and natural length) are then projected onto the metaphase plate normal. A directional switch is shown with the trailing sister (left) switching first (K-fibre catastrophe), followed by the originally leading sister (K-fibre rescue). See main text for details. (B) Simulated trajectory from model <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.e020" target="_blank">Eq (5)</a> showing the (normal) distance from the metaphase plate of the two sisters. Parameters used were <i>p</i><sub><i>c</i></sub> = 0.94, <i>p</i><sub><i>ic</i></sub> = 0.61, <i>v</i><sub>+</sub> = 0.05 μm s<sup>−1</sup>, <i>v</i><sub>−</sub> = −0.03 μm s<sup>−1</sup>, <i>L</i> = 0.8 μm, <i>κ</i> = 0.05 s<sup>−1</sup>, <i>α</i> = 0.03 s<sup>−1</sup> and <i>τ</i> = 1000 s<sup>2</sup> μm<sup>−2</sup>, (Δ<i>t</i> = 2<i>s</i>). See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#sec002" target="_blank">Methods</a> for parameter explanation. (C) Example sister pair trajectory, from kinetochore tracking of live-cell imaging data, showing the (normal) distance from the metaphase plate of the two sisters. (D) The hidden Markov chain transition network for K-fibres switching between polymerising (+) and depolymerising (–) states used in the MCMC algorithm model. <i>p</i><sub><i>c</i></sub>, <i>p</i><sub><i>ic</i></sub> are the probabilities of remaining coherent and incoherent, respectively, and <i>q</i><sub><i>c</i></sub> = 1−<i>p</i><sub><i>c</i></sub> and <i>q</i><sub><i>ic</i></sub> = 1−<i>p</i><sub><i>ic</i></sub>. (E) Time-lapse sequence of kinetochores. Kinetochores are marked by eGFP-CENP-A. Yellow bordered panel at right shows single kinetochore pair indicated by yellow box in first image.</p

    Lead or the trailing sister can initiate directional switching.

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    <p>(A) Example trajectory exhibiting lead initiated directional switching (LIDS; magenta dashed lines) and trail initiated directional switching (TIDS; black dashed lines). (B) Probability of the trailing vs. lead sister switching first (n = 2063 switch events). Dotted white line indicates the boundary where <i>p</i><sub>LIDS</sub> = <i>p</i><sub>TIDS</sub>.</p

    Determination of oscillatory trajectories using three quality statistics.

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    <p>(A) Histogram of explained variance (EV) of each trajectory. (B) Explained variance of each trajectory arranged by cell. (C) Histogram of log Bayes factor of the kinetochore model <i>M</i><sub>coh</sub> against Brownian motion <i>M</i><sub>BM</sub> (log <i>B</i>[<i>M</i><sub>coh</sub>/<i>M</i><sub>BM</sub>]) of each trajectory. (D) log <i>B</i>[<i>M</i><sub>coh</sub>/<i>M</i><sub>BM</sub>] of each trajectory arranged by cell. (E) Histogram of directional correlation statistic <i>D</i><sub>Δ<i>t</i></sub> of each trajectory. (F) <i>D</i><sub>Δ<i>t</i></sub> of each trajectory arranged by cell. (G) log <i>B</i>[<i>M</i><sub>coh</sub>/<i>M</i><sub>BM</sub>] plotted against EV for each trajectory. Trajectories are coloured according to <i>D</i><sub>Δ<i>t</i></sub>; blue have significant directional correlations. (H) Mean trajectory positions within the metaphase plate viewed along the spindle axis (Y, Z) coloured by EV. All converged trajectories are shown in panels (A-G) (<i>n</i> = 1169); only those from grey area in (G) are shown in (H) (<i>n</i> = 843).</p

    PEF variation over the metaphase plate impacts oscillation amplitude and deviation from alignment.

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    <p>(A) Average absolute PEF (on sister 1) binned by distance <i>r</i> from the centre of the metaphase plate (bins of approximately equal number; alternating grey and white boxes). (B) Average profile of the proportion of the opposing force (spring + PEF) to <i>F</i><sub>−</sub> on lead sister during a LIDS for trajectories with <i>r</i> ≥ 4 μm (cyan) and <i>r</i> ≤ 3 μm (blue). Switch events aligned as described under <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.g008" target="_blank">Fig 8</a>. Solid and dashed lines indicate mean and ±s.e.m., respectively. (C-F) Trajectories binned by distance <i>r</i> as in (A) with bin mean of (C) alignment deviation; (D) oscillation amplitude; (E) metaphase plate thickness; (F) inter-sister distance shown. Lines in (D,F) indicate s.d., <i>n</i> = 843, see text for definitions.</p

    Posterior distribution from a trajectory with strong oscillations.

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    <p>Inferred posterior distributions and model parameters for the single trajectory shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.g001" target="_blank">Fig 1C</a> for (A) the K-fibre (de)polymerisation velocities <i>v</i><sub>+</sub> (blue) and <i>v</i><sub>−</sub> (red); (B) spring constant <i>κ</i>; (C) anti-poleward force gradient <i>α</i>; (D) noise parameter <i>τ</i> = <i>s</i><sup>−2</sup>; (E) natural length <i>L</i>; (F) probabilities of not switching state per time-point when sisters are coherent (blue) and incoherent (red). The informed Gaussian prior for <i>L</i> determined through nocodazole treatment (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.s002" target="_blank">S1 Fig</a>) is shown in red in (E). Posterior distributions consist of over 5,000 samples (see section 1.2 of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.s001" target="_blank">S1 Text</a> for convergence protocols). (G) Trajectories for sisters of trajectory in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004607#pcbi.1004607.g001" target="_blank">Fig 1C</a> with switching points marked by dashed lines. (H) Probability of switching per frame shown for each sister. (I) Posterior probabilities of sister state over the course of the trajectory. Incoherent state –/– does not occur during this particular trajectory.</p

    The number of single-cell states in the MCF-7 response to estrogen.

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    <p>(<b>A</b>) The mean squared error of the model fit to the microarray data decreases as function of the number of states: as expected, when the number of parameters increases, the quality of the fit improves. (<b>B</b>) The condition number is a measure of the similarity of the transcriptional profiles of the states. It increases as function of the number of states, , highlighting that over-fitting also increases with . A good balance between fit quality and over-fitting must be found. (<b>C</b>) The model posterior probability, derived by a Bayesian approach, has a peak at , which shows that a model with six states strikes a good balance between fit-to-data and model parsimony.</p
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