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Abstract

The mitotic spindle is a bipolar structure that segregates the chromosomes during mitosis. The main components of the spindle are microtubules: polymers that can grow and shrink at their ends. Microtubule length and spatio-temporal organisation are regulated by proteins that can crosslink microtubules, slide them with respect to each other, and affect their polymerization dynamics.

During anaphase, the spindle elongates to separate the two chromosome masses into the daughter cells. This is driven by the simultaneous sliding and growth of microtubules organised into antiparallel bundles. Since microtubule growth increases overlap length, and sliding decreases it, they have to be coordinated to maintain the microtubule overlap. Importantly, diffusible crosslinkers can slow down microtubule sliding \textit{in vitro}, leading to the formation of stable overlaps that resemble those of the spindle. Two important questions remain unanswered to understand these processes: \mbox{1. How} do diffusible crosslinkers work as brakes against microtubule sliding to form stable overlaps? \mbox{2. How} are microtubule dynamics regulated in cells to maintain overlaps while sliding?

In the first part of this thesis, we produced a continuous theory that explains how diffusible crosslinkers affect sliding by molecular motors and produce stable overlaps. We verified the validity of this approach by comparing the theory with computer simulations containing individual motors, crosslinkers and microtubules. Our findings suggest that braking by diffusible crosslinkers results from the drag associated to their diffusive tails, as previously proposed. However, we find that occupancy of binding sites in the microtubule lattice plays an important role in this process. In addition, we propose a mechanism by which diffusible crosslinkers can coordinate sliding and microtubule growth. Finally, we apply this theory to an \textit{in vitro} setup containing dynamic microtubules, diffusive crosslinkers and molecular motors. Such system can self organise into bundles that resemble anaphase spindles. Our theory can explain why a complex of motor and diffusive crosslinker can produce sliding, and drive the system to a state in which all the lattice sites are occupied by crosslinkers. It predicts that in overlaps which are kept at very high crosslinker density by the action of motors, crosslinker unbinding drives the sliding of microtubules at a much slower speed than motor sliding, and this prediction is matched by the experimental data.

In the second part, we studied anaphase microtubule dynamics in fission yeast. In this organism, no microtubule nucleation occurs during anaphase, so rescues are required to maintain the microtubule overlap of the spindle. Since not all microtubules that undergo catastrophe are rescued, the number of microtubules decreases during anaphase. We found that, as anaphase progresses, microtubule growth speed decreases and rescue rate increases. Our data supports a model in which this is mediated by the progressive enrichment of the rescue factor Cls1 on the spindle, which increases microtubule stability in time, and prevents the collapse of spindles at late anaphase, when the number of microtubules is around 4. Additionally, we found that the organisation of rescues that results from the recruitment of Cls1 to the midzone by the microtubule crosslinker Ase1 ensures the maintenance of microtubule overlap without the need for feedback between microtubule growth and sliding. Finally, we studied how microtubule dynamics change with cell size, and with deletion of kinesin-6 klp9, the main driver of microtubule sliding during anaphase. We found that klp9 deletion increases rescue rate, and that cell size increases the duration of microtubule growth events and decreases the rate at which microtubules are lost.