Mechanics of multi-centrosomal clustering in bipolar mitotic spindles

Abstract

To segregate chromosomes in mitosis, cells assemble mitotic spindle, a molecular machine with centrosomes at two opposing cell poles and chromosomes at the equator. Microtubules and molecular motors connect the poles to kinetochores, specialized protein assemblies on the centromere regions of the chromosomes. Bipolarity of the spindle is crucial for the proper cell division, and two centrosomes in animal cells naturally become two spindle poles. Cancer cells are often multi-centrosomal, yet they are able to assemble bipolar spindles by clustering centrosomes into two spindle poles. Mechanisms of this clustering are debated. In this study, we computationally screen effective forces between a) centrosomes, b) centrosomes and kinetochores, c) centrosomes and chromosome arms, d) centrosomes and cell cortex, to understand mechanics that determines three-dimensional spindle architecture. To do this, we use stochastic Monte Carlo search for stable mechanical equilibria in effective energy landscape of the spindle. We find that the following conditions have to be met to robustly assemble the bipolar spindle in a multi-centrosomal cell: 1) strengths of centrosomes' attraction to each other and to the cell cortex have to be proportional to each other; 2) strengths of centrosomes' attraction to kinetochores and repulsion from the chromosome arms have to be proportional to each other. We also find that three other spindle configurations emerge if these conditions are not met: a) collapsed, b) monopolar, c) multipolar spindles, and the computational screen reveal mechanical conditions for these abnormal spindles. Running title: Multi-centrosomal clusteringSignificance statement: To segregate chromosomes, cells assemble bipolar mitotic spindle. Multiple mechanical forces generated by microtubules and molecular motors in the spindle govern the spindle architecture, but it is unclear what force balances support the bipolarity of the spindle. This problem is especially difficult and important in cancer cells, which often have multiple centrosomes that somehow are able to cluster into two spindle poles. By using stochastic energy minimization in an effective energy landscape of the spindle and computationally screening forces, we find mechanical conditions for mono-, multi-and bi-polar spindles. We predict how microtubule and motor parameters have to be regulated in mitosis in multi-centrosomal cells.

Mechanics of MTOC clustering and spindle positioning in budding yeast Cryptococcus neoformans

“…To have a better understanding of the spindle positioning, we also set up a simple one-dimensional analytical model with closed-form expressions for various averaged forces (Fig 3B-3C). By screening these forces, we estimate the plausible force balance for proper spindle positioning in a confinement mimicking a budded cell [36,49,55]. These two models not only complement the primary experimental observations of spindle localization in C. neoformans, but reasonably corroborates with each other in a qualitative manner.…”

“…Further, in the model, we considered exponentially decaying spatial dependence of forces, a straightforward and widely used choice [36,49,55]. We derived closed-form expressions for various MT-mediated forces (instantaneous cortical push, cortical dynein pull, the force due to MT buckling) on the spindle due to MT-cell cortex interaction.…”

“…A spindle is constantly acted upon by molecular forces arising from the interactions of its components with the surrounding [14,16,36,43,48,64,76,77], e.g., cMTs interacting with the cell cortex via dynein generates a pull on the nucleus toward the cell periphery; similarly, cMTs buckling in contact with the cell membrane pushes the nucleus away from the membrane. These interactions are plausible in both mother and daughter bud cell cortices.…”

“…Basic characteristics of the clustering mechanisms are shared across a diverse set of organisms as well as several organelle assemblies (e.g. Golgi assembly and stacking, mitochondrial assembly, multi-centrosomal clustering [36] etc.) and are not necessarily organism-specific [8].…”

Modeling reveals cortical dynein-dependent fluctuations in bipolar spindle length

“…where N c,dcor is the total number of MTs on centrosome c that bind to cortical dynein, K is a scaling factor, and d cor is the minimum distance from the centrosome to the cell cortex. The force acting on the centrosome from a MT bound to dynein decreases exponentially with increased MT length [56], and we use this for every MT-motor interaction considered in this model. MTs will stay bound to cortical dynein until the end of the MT is greater than a distance D dcor from the cell cortex, at which time it begins depolymerizing.…”