Pivot-and-bond model explains microtubule bundle formation

Abstract

During mitosis, microtubules form a spindle, which is responsible for proper segregation of the genetic material. A common structural element in a mitotic spindle is a parallel bundle, consisting of two or more microtubules growing from the same origin and held together by cross-linking proteins. An interesting question is what are the physical principles underlying the formation and stability of such microtubule bundles. Here we show, by introducing the pivot-and-bond model, that random angular movement of microtubules around the spindle pole and forces exerted by cross-linking proteins can explain the formation of microtubule bundles as observed in our experiments. The model predicts that stable parallel bundles can form in the presence of either passive crosslinkers or plus-end directed motors, but not minus-end directed motors. In the cases where bundles form, the time needed for their formation depends mainly on the concentration of cross-linking proteins and the angular diffusion of the microtubule. In conclusion, the angular motion drives the alignment of microtubules, which in turn allows the cross-linking proteins to connect the microtubules into a stable bundle.

Microtubule pivoting enables mitotic spindle assembly in S. cerevisiae

“…But close proximity of the poles and the relatively short lengths of pole-anchored microtubules preclude direct observation of pivoting in vivo during this fundamental stage of spindle assembly. Moreover, while microtubules in S. pombe appear to pivot freely ( Kalinina et al, 2013 ; Prelogović et al, 2019 ; Winters et al, 2019 ; Cojoc et al, 2016 ), mechanical flexibility at the microtubule–pole interface has not been directly measured or modified in any organism. Thus, the importance of pivoting specifically during initial establishment of spindle bipolarity remains uncertain.…”

Controlling particle currents with evaporation and resetting from an interval

“…Our work indicates new avenues for understanding the nonequilibrium features of resetting, e.g., in the study of optimization of resetting pathways for efficient particle transport. Furthermore, we expect that our formalism could be extended to shed light on various biophysical problems described by onedimensional diffusion with suitable boundary and/or resetting conditions, such as microtubule dynamics [43,44], molecular motors [2,45,46], single-file diffusion of water in carbon nanorings [47], or polymer translocation through nanopores [48,49] In this Appendix, we report the solution for the Laplace transform of Eq. (1) for P(x, t|x 0 , x r ), the probability distribution of the Brownian particle position in one dimension, initially at x 0 , resetting to x r according the space-dependent resetting rate r c (x).…”

Microtubule pivoting driven by spindle elongation rescues polar chromosomes to ensure faithful mitosis

“…The pivoting of microtubules attached to polar chromosomes may also play a role in spindle assembly, potentially involving mechanisms similar to those observed in yeast for the formation of parallel and antiparallel bundles (Prelogović et al, 2019;Winters et al, 2019). Typical polar chromosomes arrive at the spindle surface with mono-lateral attachments.…”