Model of chromosome motility in Drosophila embryos: adaptation of a general mechanism for rapid mitosis.

During mitosis, ensembles of dynamic MTs and motors exert forces that coordinate chromosome segregation. Typically, chromosomes align at the metaphase spindle equator where they oscillate along the pole-pole axis before disjoining and moving poleward during anaphase A, but spindles in different cell types display differences in MT dynamicity, in the amplitude of chromosome oscillations and in rates of chromatid-to-pole motion. Drosophila embryonic mitotic spindles, for example, display remarkably dynamic MTs, barely detectable metaphase chromosome oscillations, and a rapid rate of "flux-pacman-dependent" anaphase chromatid-to-pole motility. Here we develop a force-balance model that describes Drosophila embryo chromosome motility in terms of a balance of forces acting on kinetochores and kMTs that is generated by multiple polymer ratchets and mitotic motors coupled to tension-dependent kMT dynamics. The model shows that i), multiple MTs displaying high dynamic instability can drive steady and rapid chromosome motion; ii), chromosome motility during metaphase and anaphase A can be described by a single mechanism; iii), high kinetochore dynein activity is deployed to dampen metaphase oscillations, to augment the basic flux-pacman mechanism, and to drive rapid anaphase A; iv), modulation of the MT rescue frequency by the kinetochore-associated kinesin-13 depolymerase promotes metaphase chromosome oscillations; and v), this basic mechanism can be adapted to a broad range of spindles.

Model of coupled transient changes of Rac, Rho, adhesions and stress fibers alignment in endothelial cells responding to shear stress.

Interactions of cell adhesions, Rho GTPases and actin in the endothelial cells' response to external forces are complex and not fully understood, but a qualitative understanding of the mechanosensory response begins to emerge. Here, we formulate a mathematical model of the coupled dynamics of cell adhesions, small GTPases Rac and Rho and actin stress fibers guiding a directional reorganization of the actin cytoskeleton. The model is based on the assumptions that the interconnected cytoskeleton transfers the shear force to the adhesion sites, which in turn transduce the force into a chemical signal that activates integrins at the basal surface of the cell. Subsequently, activated and ligated integrins signal and transiently de-activate Rho, causing the disassembly of actin stress fibers and inhibiting the maturation of focal complexes into focal contacts. Focal complexes and ligated integrins activate Rac, which in turn enhances focal complex assembly. When Rho activity recovers, stress fibers re-assemble and promote the maturation of focal complexes into focal contacts. Merging stress fibers self-align, while the elevated level of Rac activity at the downstream edge of the cell is translated into an alignment of the cells and the newly forming stress fibers in the flow direction. Numerical solutions of the model equations predict transient changes in Rac and Rho that compare well with published experimental results. We report quantitative data on early alignment of the stress fibers and its dependence on cell shape that agrees with the model.

Model for anaphase B: role of three mitotic motors in a switch from poleward flux to spindle elongation.

It has been proposed that the suppression of poleward flux within interpolar microtubule (ipMT) bundles of Drosophila embryonic spindles couples outward forces generated by a sliding filament mechanism to anaphase spindle elongation. Here, we (i) propose a molecular mechanism in which the bipolar kinesin KLP61F persistently slides dynamically unstable ipMTs outward, the MT depolymerase KLP10A acts at the poles to convert ipMT sliding to flux, and the chromokinesin KLP3A inhibits the depolymerase to suppress flux, thereby coupling ipMT sliding to spindle elongation; (ii) used KLP3A inhibitors to interfere with the coupling process, which revealed an inverse linear relation between the rates of flux and elongation, supporting the proposed mechanism and demonstrating that the suppression of flux controls both the rate and onset of spindle elongation; and (iii) developed a mathematical model using force balance and rate equations to describe how motors sliding the highly dynamic ipMTs apart can drive spindle elongation at a steady rate determined by the extent of suppression of flux.