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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.

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Force decomposition profile.(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 Fig 1C; (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.
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pcbi.1004607.g005: Force decomposition profile.(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 Fig 1C; (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.

Mentions: From the parameter estimates and inferred K-fibre state determined for each trajectory, we can use Eq (3) to calculate effective contributions to the total force on each kinetochore (recall that in our model the parameterisation of forces and velocities are commensurate; we quote forces in μm s−1). Specifically we can estimate the contributions of the 3 component forces: the PEF, the K-fibre forces and the spring force (Fig 5A) throughout the trajectory. In Fig 5B and 5C we show the forces acting on one sister (sister 1) of the sister pair of Fig 1C; Fig 5D and 5E show the same for the second sister (sister 2). The K-fibre force on sister 1 was by far the dominant force on the kinetochores and because it corresponds to the K-fibre state, it changes sign at directional switches (Fig 5B). The PEF and spring force were a minor contribution, and were in phase every period, the spring force having double the period of the oscillation as previously observed [8, 12]. A comparison between the sisters (Fig 5B and 5D) clearly demonstrates the approximate anti-phase of the K-fibre state, although this is not exact and extended periods of incoherence did occur; in this example, both sisters have polymerising K-fibres during incoherence. This is reflected in the spring force profile (Fig 5C and 5E) since +/+ incoherence causes relaxation of the spring to near zero spring tension and apparent compression (Fspring < 0) during the extended period of incoherence. The PEF force, being positional and linearised in our model, corresponds to the kinetochore position thereby reflecting the off-plate position of the sister pair (Fig 1C).


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

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

Force decomposition profile.(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 Fig 1C; (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.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004607.g005: Force decomposition profile.(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 Fig 1C; (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.
Mentions: From the parameter estimates and inferred K-fibre state determined for each trajectory, we can use Eq (3) to calculate effective contributions to the total force on each kinetochore (recall that in our model the parameterisation of forces and velocities are commensurate; we quote forces in μm s−1). Specifically we can estimate the contributions of the 3 component forces: the PEF, the K-fibre forces and the spring force (Fig 5A) throughout the trajectory. In Fig 5B and 5C we show the forces acting on one sister (sister 1) of the sister pair of Fig 1C; Fig 5D and 5E show the same for the second sister (sister 2). The K-fibre force on sister 1 was by far the dominant force on the kinetochores and because it corresponds to the K-fibre state, it changes sign at directional switches (Fig 5B). The PEF and spring force were a minor contribution, and were in phase every period, the spring force having double the period of the oscillation as previously observed [8, 12]. A comparison between the sisters (Fig 5B and 5D) clearly demonstrates the approximate anti-phase of the K-fibre state, although this is not exact and extended periods of incoherence did occur; in this example, both sisters have polymerising K-fibres during incoherence. This is reflected in the spring force profile (Fig 5C and 5E) since +/+ incoherence causes relaxation of the spring to near zero spring tension and apparent compression (Fspring < 0) during the extended period of incoherence. The PEF force, being positional and linearised in our model, corresponds to the kinetochore position thereby reflecting the off-plate position of the sister pair (Fig 1C).

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