Mechanical stability of bipolar spindle assembly

TL;DR

This paper presents a minimal mechanical model of bipolar spindle assembly, deriving analytical expressions for forces and stability, and revealing conditions for bistability and the roles of motor proteins during cell division.

Contribution

It introduces a comprehensive minimal model that analytically describes spindle stability, including force interactions and bistability, advancing understanding of mitotic spindle mechanics.

Findings

Derived a closed-form force expression between centrosomes.

Mapped the stability diagram based on interaction parameters.

Predicted bistability regimes in spindle assembly.

Abstract

Assembly and stability of mitotic spindle is governed by the interplay of various intra-cellular forces, e.g. the forces generated by motor proteins by sliding overlapping anti-parallel microtubules (MTs) polymerized from the opposite centrosomes, the interaction of kinetochores with MTs, and the interaction of MTs with the chromosomes arms. We study the mechanical behavior and stability of spindle assembly within the framework of a minimal model which includes all these effects. For this model, we derive a closed--form analytical expression for the force acting between the centrosomes as a function of their separation distance and we show that an effective potential can be associated with the interactions at play. We obtain the stability diagram of spindle formation in terms of parameters characterizing the strength of motor sliding, repulsive forces generated by polymerizing MTs, and the forces arising out of interaction of MTs with kinetochores. The stability diagram helps in quantifying the relative effects of the different interactions and elucidates the role of motor proteins in formation and inhibition of spindle structures during mitotic cell division. We also predict a regime of bistability for certain parameter range, wherein the spindle structure can be stable for two different finite separation distances between centrosomes. This occurrence of bistability also suggests mechanical versatility of such self-assembled spindle structures.