Structural stability of a Mitotic Spindle: parametric Finite element approach

Mitotic spindles are mechanical structures that play a critical role in cell division by generating forces to separate chromosomes. They are ordered assemblages of proteins that make up microtubules (MT) and microtubule connectors whose mechanical properties are responsible for their structural integrity under mitotic forces. We use a continuum mechanics approach to study the stability of equilibrium of a mitotic spindle as a whole. We create and apply a finite element (FE) parameterised model of interpolar MTs, astral MTs and MT connectors varying the number of MT filaments and the arrangement of their interconnections. The model is based on the experimental data on Fission Yeast spindles in late anaphase B and mitotic HeLa cells [1]–[3]. We account for the complex interactions between interpolar MTs, astral MTs, connectors and centrosomes through mechanical coupling. Comparing the results with experiments and Molecular dynamics-based simulations [1], we demonstrate the great potential of Structural mechanics methods to address the stability of spindles. Here we report how buckling states of the spindle get localised towards either of centrosomes due to the irregular placement of microtubules and irregularities in MT coupling. In certain cases, such behaviour may result in nuclear misplacement, asymmetric division or other abnormalities.[1] J. J. Ward, H. Roque, C. Antony, and F. Nédélec, “Mechanical design principles of a mitotic spindle,” eLife, vol. 3, p. e03398, 2014.[2] F. Pampaloni, G. Lattanzi, A. Jonas, T. Surrey, E. Frey, and E.-L. Florin, “Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length,” Proc. Natl. Acad. Sci., vol. 103, no. 27, pp. 10248–10253, 2006.[3] F. M. Nixon, C. Gutiérrez-Caballero, F. E. Hood, D. G. Booth, I. A. Prior, and S. J. Royle, “The mesh is a network of microtubule connectors that stabilizes individual kinetochore fibers of the mitotic spindle,” eLife, vol. 4, no. JUNE2015, pp. 1–21, 2015.