Positioning the nucleus at the bud neck during Saccharomyces cerevisiae mitosis involves pulling forces of cytoplasmic dynein localized in the daughter cell. Although genetic analysis has revealed a complex network positioning the nucleus, quantification of the forces acting on the nucleus and the number of dyneins driving the process has remained difficult. To better understand the collective forces involved in nuclear positioning, we compare a model of dyneins-driven microtubule (MT) pulling, MT pushing, and cytoplasmic drag to experiments. During S. cerevisiae mitosis, MTs interacting with the cortex nucleated by the daughter spindle pole body (SPB) (SPB-D) are longer than the mother SPB (SPB-M), increasing further during spindle elongation in anaphase. Interphasic SPB mobility is effectively diffusive, while the mitotic mobility is directed. By optimizing a computational model of the mobility of the nucleus due to diffusion and MTs pushing at the cell membrane to experiment, we estimate the viscosity governing the drag force on nuclei during positioning. A force balance model of mitotic SPB mobility compared to experimental mobility suggests that even one or two dynein dimers are sufficient to move the nucleus in the bud neck. Using stochastic computer simulations of a budding cell, we find that punctate dynein localization can generate sufficient force to reel in the nucleus to the bud neck. Compared to uniform motor localization, puncta involve fewer motors suggesting a functional role for motor clustering. Stochastic simulations also suggest that a higher number of force generators than predicted by force balance may be required to ensure the robustness of spindle positioning. Take Away• Saccharomyces cerevisiaea cytoplasmic viscosity is estimated by quantifying the in vivo mobility of the nucleus and comparing to simulations.• The in vivo length dynamics of microtubules (MTs) interacting with daughter bud cortex during nuclear positioning in mitosis are measured.• We developed a model of astral MT interactions with cortical dynein in the process of nuclear positioning during mitosis.• A force balance model predicts the minimal force required for nuclear positioning. Kunalika Jain and Neha Khetan contributed equally to the manuscript.

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Flagellar and ciliary oscillations result from a combination of stereotypical axonemal geometry, collective mechanics of motors, microtubules (MTs), elastic linkers and biochemical regulation. However, the minimal essential components and constraints resulting in flagellar oscillations remain unclear. Here, we demonstrate that periodic, low-frequency waves of flagella-like oscillations in vitro emerge from a ATP-driven collective molecular motor transport of MTs clamped at one end. The spontaneous oscillations arise without any external forcing and can be explained by an in silico model of molecular motor binding driven MT bending and buckling followed by motor detachment driven 'recovery' stroke. We demonstrate that transitions in single MT patterns between flapping, flagellar-beating and looping are determined solely by the self-organization of collective motor transport and filament elasticity.

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