In this study, we use tools of theoretical physics and numerical simulations to investigate the regulation of microtubule dynamics by molecular motors and wetting proteins. Control of microtubule abundance, stability, and length is crucial to regulate intracellular transport as well as cell polarity and division.

We study the effect of molecular motors on microtubule rescue, the event when a microtubule switches from shrinking to growing, by developing a stochastic theoretical description. It has been recently shown that microtubule rescues happen at tubulin exchange sites along the shaft and that molecular motors are able to induced such exchanges. We study how microtubule stability and length depend on motor-induced tubulin exchange within the microtubule shaft, by using analytical derivations and stochastic simulations. Our theoretical description matches in vitro experiments on microtubule dynamics in the presence of kinesin-1 molecular motors. The overall dynamics of a population of microtubules can be captured by an effective rescue rate. However, by considering rescue happening only at exchange sites, we reveal that the dynamics of individual microtubules within the population differ dramatically from the effective description, as can be seen by computing the correlation function between the lengths of the growing phases and those of the subsequent shrinking phases. Furthermore, we study in detail a transition from bounded to unbounded microtubule growth. Additionally, we study the dynamics of microtubules on a finite domain. We find that in such a case, the microtubule length distribution becomes peaked at high motor concentrations. Our results provide novel insights into how molecular motors imprint information of microtubule stability on the microtubule network and on how cells could control the lengthscale of their microtubules.

It is currently accepted that some proteins, such as the End Binding (EB) proteins, have the ability to bind specifically to the tip of growing microtubules, forming a film that is often referred to as a comet. Recent results suggest that these comets might be liquid droplets resulting from phase separation. We study the wetting of growing microtubules by phase separating proteins. We employed a diffusive interface model to describe the phase separating protein and the microtubule is described as a fiber with an attractive surface. Our hydrodynamic description agrees well with in vitro observations. We also uncover what we suspect is a phase transition between the nucleation of droplets at the tip and the formation of a film extending from the tip over a finite length. We investigate this film phase with numerical computations and derive an analytical approximation of the film profile close to the tip. This film formation mechanism could explain the comets observed in cells. In cells, droplets emerging from comets are not persistent. However, the precise dissolution mechanism is still unknown. We implement a simple droplets dissolution process which allows us to reproduce qualitatively the dissolution of droplets observed in cells.