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

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.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

“…Recent work on spindle and MT organization includes studies of spindle elongation and force balance [59,68], the formation and maintenance of antiparallel MT overlaps [69,70], MT bundling and sliding [15], spindle movements and positioning [71,72], spindle length and shape [15,51,52,73,74], MT organization [75], and spindle assembly from a bipolar initial condition [32,76]. Models of kinetochore-MT attachment and biorientation have examined capture of lost kinetochores [63,77], chromosome reorientation after MT attachment [31], attachment error correction [33,39,78,79], and chromosome movement on the spindle [52,61,[80][81][82]. Most spindle models have started with a bipolar structure or separated spindle poles, and most previous chromosome models have begun with chromosomes attached to the spindle or near a pre-formed spindle.…”

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

“…Recent work on spindle and MT organization includes studies of spindle elongation and force balance [59,68], the formation and maintenance of antiparallel MT overlaps [69,70], MT bundling and sliding [15], spindle movements and positioning [71,72], spindle length and shape [15,51,52,73,74], MT organization [75], and spindle assembly from a bipolar initial condition [32,76]. Models of kinetochore-MT attachment and biorientation have examined capture of lost kinetochores [63,77], chromosome reorientation after MT attachment [31], attachment error correction [33,39,78,79], and chromosome movement on the spindle [52,61,[80][81][82]. Most spindle models have started with a bipolar structure or separated spindle poles, and most previous chromosome models have begun with chromosomes attached to the spindle or near a pre-formed spindle.…”

The dynamics of centromere motion through the metaphase-to-anaphase transition reveal a centromere separation order

“…The dynamics of centromere motion during metaphase has been the focus of many quantitative studies [13][14][15][16][17][18][19] . The development of automated centromere tracking, advanced image analysis, and datadriven mathematical modelling has provided novel mechanistic and molecular insights into metaphase centromere dynamics 20,21 . However, the dynamic behaviour of centromeres during the metaphase-toanaphase transition and during anaphase has been largely overlooked due of the lack of appropriate quantitative tools.…”