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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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Lead or the trailing sister can initiate directional switching.(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 pLIDS = pTIDS.
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pcbi.1004607.g006: Lead or the trailing sister can initiate directional switching.(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 pLIDS = pTIDS.

Mentions: In addition to inferring the force parameters, our method also estimates the probability of each K-fibre being in a + or − state at each time-point (). From these state probabilities we estimated the switching times for going into and out of coherent runs (the pair of states +/– or –/+; see example of Fig 6A)—these correspond to switches in direction. We used coherent runs to define switching since the oscillations are comprised of periods of coherence separated by a directional switching event. We defined coherent runs in as a consecutive sequence of at least 5 time points in the same direction, although we allow for transient changes of direction because of noise (see Materials and Methods). The end of these coherent runs then defines the initiation of a directional switch. As trajectory stochasticity increases, coherent runs become less frequent; as expected we saw an increase in the number of detected switches as EV increases from 025% (S3E Fig). However, paradoxically the number of switches fell again for trajectories with EV > 25%.


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

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

Lead or the trailing sister can initiate directional switching.(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 pLIDS = pTIDS.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004607.g006: Lead or the trailing sister can initiate directional switching.(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 pLIDS = pTIDS.
Mentions: In addition to inferring the force parameters, our method also estimates the probability of each K-fibre being in a + or − state at each time-point (). From these state probabilities we estimated the switching times for going into and out of coherent runs (the pair of states +/– or –/+; see example of Fig 6A)—these correspond to switches in direction. We used coherent runs to define switching since the oscillations are comprised of periods of coherence separated by a directional switching event. We defined coherent runs in as a consecutive sequence of at least 5 time points in the same direction, although we allow for transient changes of direction because of noise (see Materials and Methods). The end of these coherent runs then defines the initiation of a directional switch. As trajectory stochasticity increases, coherent runs become less frequent; as expected we saw an increase in the number of detected switches as EV increases from 025% (S3E Fig). However, paradoxically the number of switches fell again for trajectories with EV > 25%.

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