Limits...
Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics.

Armond JW, Harry EF, McAinsh AD, Burroughs NJ - PLoS Comput. Biol. (2015)

Bottom Line: We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature.There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude.Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

View Article: PubMed Central - PubMed

Affiliation: Warwick Systems Biology Centre and Mathematics Institute, University of Warwick, Coventry, United Kingdom.

ABSTRACT
Kinetochores are multi-protein complexes that mediate the physical coupling of sister chromatids to spindle microtubule bundles (called kinetochore (K)-fibres) from respective poles. These kinetochore-attached K-fibres generate pushing and pulling forces, which combine with polar ejection forces (PEF) and elastic inter-sister chromatin to govern chromosome movements. Classic experiments in meiotic cells using calibrated micro-needles measured an approximate stall force for a chromosome, but methods that allow the systematic determination of forces acting on a kinetochore in living cells are lacking. Here we report the development of mathematical models that can be fitted (reverse engineered) to high-resolution kinetochore tracking data, thereby estimating the model parameters and allowing us to indirectly compute the (relative) force components (K-fibre, spring force and PEF) acting on individual sister kinetochores in vivo. We applied our methodology to thousands of human kinetochore pair trajectories and report distinct signatures in temporal force profiles during directional switches. We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature. There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude. This data driven reverse engineering approach is sufficiently flexible to allow fitting of more complex mechanistic models; mathematical models of kinetochore dynamics can therefore be thoroughly tested on experimental data for the first time. Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

Show MeSH
Population parameter analysis.Posterior means for (A) K-fibre (de)polymerisation velocities v+ (blue) and v− (red); (B) spring constant κ; (C) anti-poleward force gradient α; (D) noise parameter τ = s−2; (E) natural length L (blue); (F) the probabilities of not switching state per time-point when sisters are coherent (blue) and incoherent (red). The informed Gaussian prior on L 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 (n = 843).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4664287&req=5

pcbi.1004607.g004: Population parameter analysis.Posterior means for (A) K-fibre (de)polymerisation velocities v+ (blue) and v− (red); (B) spring constant κ; (C) anti-poleward force gradient α; (D) noise parameter τ = s−2; (E) natural length L (blue); (F) the probabilities of not switching state per time-point when sisters are coherent (blue) and incoherent (red). The informed Gaussian prior on L 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 (n = 843).

Mentions: As shown in Fig 2, the posterior distributions for the model parameters can be computed for single trajectories, typically giving high confidence parameter estimates. To summarise across the dataset, we used the posterior means of each trajectory (Fig 4); these show that there is significant heterogeneity between trajectories in their parameter values, with ranges over an order of magnitude in many cases. The natural length is the exception because it is constrained by the informed nocodazole prior and thus the means are tightly clustered (mean 795 ± 31 nm; Fig 4E) about the prior mean (775 ± 110 nm). These parameter estimates can be used to unravel the forces driving kinetochore movements as follows.


Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics.

Armond JW, Harry EF, McAinsh AD, Burroughs NJ - PLoS Comput. Biol. (2015)

Population parameter analysis.Posterior means for (A) K-fibre (de)polymerisation velocities v+ (blue) and v− (red); (B) spring constant κ; (C) anti-poleward force gradient α; (D) noise parameter τ = s−2; (E) natural length L (blue); (F) the probabilities of not switching state per time-point when sisters are coherent (blue) and incoherent (red). The informed Gaussian prior on L 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 (n = 843).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4664287&req=5

pcbi.1004607.g004: Population parameter analysis.Posterior means for (A) K-fibre (de)polymerisation velocities v+ (blue) and v− (red); (B) spring constant κ; (C) anti-poleward force gradient α; (D) noise parameter τ = s−2; (E) natural length L (blue); (F) the probabilities of not switching state per time-point when sisters are coherent (blue) and incoherent (red). The informed Gaussian prior on L 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 (n = 843).
Mentions: As shown in Fig 2, the posterior distributions for the model parameters can be computed for single trajectories, typically giving high confidence parameter estimates. To summarise across the dataset, we used the posterior means of each trajectory (Fig 4); these show that there is significant heterogeneity between trajectories in their parameter values, with ranges over an order of magnitude in many cases. The natural length is the exception because it is constrained by the informed nocodazole prior and thus the means are tightly clustered (mean 795 ± 31 nm; Fig 4E) about the prior mean (775 ± 110 nm). These parameter estimates can be used to unravel the forces driving kinetochore movements as follows.

Bottom Line: We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature.There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude.Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

View Article: PubMed Central - PubMed

Affiliation: Warwick Systems Biology Centre and Mathematics Institute, University of Warwick, Coventry, United Kingdom.

ABSTRACT
Kinetochores are multi-protein complexes that mediate the physical coupling of sister chromatids to spindle microtubule bundles (called kinetochore (K)-fibres) from respective poles. These kinetochore-attached K-fibres generate pushing and pulling forces, which combine with polar ejection forces (PEF) and elastic inter-sister chromatin to govern chromosome movements. Classic experiments in meiotic cells using calibrated micro-needles measured an approximate stall force for a chromosome, but methods that allow the systematic determination of forces acting on a kinetochore in living cells are lacking. Here we report the development of mathematical models that can be fitted (reverse engineered) to high-resolution kinetochore tracking data, thereby estimating the model parameters and allowing us to indirectly compute the (relative) force components (K-fibre, spring force and PEF) acting on individual sister kinetochores in vivo. We applied our methodology to thousands of human kinetochore pair trajectories and report distinct signatures in temporal force profiles during directional switches. We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature. There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude. This data driven reverse engineering approach is sufficiently flexible to allow fitting of more complex mechanistic models; mathematical models of kinetochore dynamics can therefore be thoroughly tested on experimental data for the first time. Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

Show MeSH