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

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.Author Summary: To achieve proper cell division, newly duplicated chromosomes must be segregated into daughter cells with high fidelity. This occurs in mitosis where during the crucial metaphase stage chromosomes are aligned on an imaginary plate, called the metaphase plate. Chromosomes are attached to a structural scaffold—the mitotic spindle, which is composed of dynamic fibres called microtubules—by protein machines called kinetochores. Observation of kinetochores during metaphase reveals they undergo a series of forward and backward movements. The mechanical system generating this oscillatory motion is not well understood. By tracking kinetochores in live cell 3D confocal microscopy and reverse engineering their trajectories we decompose the forces acting on kinetochores into the three main force generating components. Kinetochore dynamics are dominated by K-fibre forces, although changes in the minor spring force over time suggests an important role in controlling directional switching. In addition, we show that the strength of forces can vary both spatially within cells throughout the plate and between cells.