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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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Average force decomposition across the population of trajectories.(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 (n = 843).
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pcbi.1004607.g007: Average force decomposition across the population of trajectories.(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 (n = 843).

Mentions: To obtain insight into the forces governing LIDS and TIDS events we computed the average contribution of each force component throughout the trajectory. The distributions of these forces clearly show that the spring force is the lowest contributor, followed by the PEF, while the force from the K-fibre is the largest contribution (Fig 7A). The K-fibre forces comprise 64% of the combined (absolute) forces on average (Fig 7B), with the spring force being only 11% on average (17%, 8% during poleward, antipoleward movements, respectively). However, these forces vary dynamically over the trajectory (see Fig 5). We therefore used the detected switching time as a temporal fiducial marker to align force profiles from multiple switch events. We performed this procedure after separating events into LIDS and TIDS thereby obtaining an averaged profile for each event type. Although the spring force was the least in magnitude during the run (Fig 7A), it had the strongest pre-switch signature discriminating between LIDS and TIDS (Fig 8A). The PEF profile was identical regardless of which sister switched first (Fig 8B), although there was a tendency for TIDS to occur at a slightly increased distance from the metaphase plate. For LIDS, the spring force increased significantly in the 20 s leading up to the switch, peaking at around -4 s with an increase of over 150% relative to that at -20 s (Fig 8A). This high spring tension (deduced in prior studies from changes in the inter-sister distance) has been suggested as the trigger for lead sister switching [7, 12, 45, 46]. During a LIDS both K-fibres are in a polymerising state, since the previously depolymerising lead sister switches first, which causes a reduction in spring force immediately post-switch (Fig 8A). This loss of tension is thought to be the trigger for the switch of the second sister [7, 12, 45, 46]. Conversely, for a TIDS an increase of the spring force occurs post-switch as the two sisters are attached to depolymerising K-fibres, stretching the centromeric spring (Fig 8B); this stretch relaxing over 20 s post-switch. This high tension 2 s post-switch could trigger the initially leading sister to switch thereby completing the directional switch of the two sisters. However, TIDS events cannot be explained by the tension arguments above; the spring tension (and inter-sister stretch) reach their maximum after the trailing sister has switched so a tension trigger on the trailing sister cannot be the cause of a TIDS event. Another mechanism must be in place to cause the trailing sister to switch first. Examining the force contributions across events indicates that the spring force, despite its high level of change across the switching event, remains a minor component rising to at most 20% during a LIDS. In fact, examination of the opposing forces (sum of PEF and spring force) to the depolymerising K-fibre attached to the leading sister indicate that they are rarely sufficient to stall the leading sister, only resisting on average 50% of the pulling force at the switch (Fig 8C).


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

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

Average force decomposition across the population of trajectories.(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 (n = 843).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004607.g007: Average force decomposition across the population of trajectories.(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 (n = 843).
Mentions: To obtain insight into the forces governing LIDS and TIDS events we computed the average contribution of each force component throughout the trajectory. The distributions of these forces clearly show that the spring force is the lowest contributor, followed by the PEF, while the force from the K-fibre is the largest contribution (Fig 7A). The K-fibre forces comprise 64% of the combined (absolute) forces on average (Fig 7B), with the spring force being only 11% on average (17%, 8% during poleward, antipoleward movements, respectively). However, these forces vary dynamically over the trajectory (see Fig 5). We therefore used the detected switching time as a temporal fiducial marker to align force profiles from multiple switch events. We performed this procedure after separating events into LIDS and TIDS thereby obtaining an averaged profile for each event type. Although the spring force was the least in magnitude during the run (Fig 7A), it had the strongest pre-switch signature discriminating between LIDS and TIDS (Fig 8A). The PEF profile was identical regardless of which sister switched first (Fig 8B), although there was a tendency for TIDS to occur at a slightly increased distance from the metaphase plate. For LIDS, the spring force increased significantly in the 20 s leading up to the switch, peaking at around -4 s with an increase of over 150% relative to that at -20 s (Fig 8A). This high spring tension (deduced in prior studies from changes in the inter-sister distance) has been suggested as the trigger for lead sister switching [7, 12, 45, 46]. During a LIDS both K-fibres are in a polymerising state, since the previously depolymerising lead sister switches first, which causes a reduction in spring force immediately post-switch (Fig 8A). This loss of tension is thought to be the trigger for the switch of the second sister [7, 12, 45, 46]. Conversely, for a TIDS an increase of the spring force occurs post-switch as the two sisters are attached to depolymerising K-fibres, stretching the centromeric spring (Fig 8B); this stretch relaxing over 20 s post-switch. This high tension 2 s post-switch could trigger the initially leading sister to switch thereby completing the directional switch of the two sisters. However, TIDS events cannot be explained by the tension arguments above; the spring tension (and inter-sister stretch) reach their maximum after the trailing sister has switched so a tension trigger on the trailing sister cannot be the cause of a TIDS event. Another mechanism must be in place to cause the trailing sister to switch first. Examining the force contributions across events indicates that the spring force, despite its high level of change across the switching event, remains a minor component rising to at most 20% during a LIDS. In fact, examination of the opposing forces (sum of PEF and spring force) to the depolymerising K-fibre attached to the leading sister indicate that they are rarely sufficient to stall the leading sister, only resisting on average 50% of the pulling force at the switch (Fig 8C).

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