In search of an optimal ring to couple microtubule depolymerization to processive chromosome motions

Abstract

Mitotic chromosome motions are driven by microtubules (MTs) and associated proteins that couple kinetochores to MT ends. A good coupler should ensure a high stability of attachment, even when the chromosome changes direction or experiences a large opposing force. The optimal coupler is also expected to be efficient in converting the energy of MT depolymerization into chromosome motility. As was shown years ago, a "sleeve"-based, chromosome-associated structure could, in principle, couple MT dynamics to chromosome motion. A recently identified kinetochore complex from yeast, the "Dam1" or "DASH" complex, may function as an encircling coupler in vivo. Some features of the Dam1 ring differ from those of the "sleeve," but whether these differences are significant has not been examined. Here, we analyze theoretically the biomechanical properties of encircling couplers that have properties of the Dam1/DASH complex, such as its large diameter and inward-directed extensions. We demonstrate that, if the coupler is modeled as a wide ring with links that bind the MT wall, its optimal performance is achieved when the linkers are flexible and their binding to tubulin dimers is strong. The diffusive movement of such a coupler is limited, but MT depolymerization can drive its motion via a "forced walk," whose features differ significantly from those of the mechanisms based on biased diffusion. Our analysis identifies key experimental parameters whose values should determine whether the Dam1/DASH ring moves via diffusion or a forced walk.

Fig. 1.

Structure of kinetochore MT ends and models for force-bearing ring-like coupling. (A) Axial slices from electron tomograms of kinetochore MTs from PtK1 (a and b), Schizosaccharomyces pombe (c), S. cerevisiae (d and e). PFs have extensive flare (arrows) but different lengths. (B) In Hill's model, a sleeve has 65 low-affinity-binding sites along each PF (20). This mechanism does not use the PF's power stroke, because a MT tip is buried in a narrow sleeve. (C) A PF power stroke pushes with maximal force on a ring, which is ≈10-nm wider than the MT. This mechanism has no restrictions on PF length. (D) In the electrostatic model, the ring moves at the ends of the curved PFs, which therefore extend only ≈1 dimer beyond the ring (based on ring diameter and PF curvature). (E) A model that combines the power stroke, as in C, and attributes ring–MT interaction to site-specific protein–protein bonds, as in B, but the bonds are now formed by the linkers. The resulting motions are significantly different from those in other models.

Fig. 2.

Ring with linkers on a 13_3 MT. (A) Interaction points between dimers (light, β tubulins; dark, α tubulins). Each dimer interacts at seven points; four are lateral bonds (blue dots) with adjacent PFs (green), and three are longitudinal junctions, one within the dimer and two with dimers in the same PF (red dots). The Dam1 linker binds to a tubulin monomer (yellow dot). Axis z coincides with the MT axis and points to its plus end; x and y axes lie in a perpendicular plane, and x points to PF no. 13. (B) Angular variables of ring orientation. (C) MT wall-ring configurations as calculated in the model. Purple lines show ring backbones. (D) Shown is a 13-fold ring, but similar models can be drawn for a range of ring symmetries, because the number of bonds is defined by the MT surface, which has a lower radial symmetry than the ring. (E) Preferred ring orientations. A ring that is perfectly perpendicular to the MT axis would correspond to a central dot, where θ = 0. The ring is sensitive to the MT seam, as seen from the nonsymmetric distribution of data points relative to the orange line. (F) Experimental tilting angles were estimated from electron micrographs of Dam1 rings decorating taxol-stabilized MTs (29, 30). The resulting distribution is statistically identical (95% confidence, Mann–Whitney t test) to that calculated from our model, assuming a single binding site per dimer. Highly tilted rings in some EM images could have resulted from specimen distortions that frequently accompany the negative staining procedure.

Fig. 3.

Role of the ring-MT-binding energy. (A) Ring diffusion on the MT surface is fast only for k_DAM < 6 k_BT. (B) Thermal motions of a weakly bound ring (k_DAM 3 k_BT) are biased by the shortening MT end (shown is the z coordinate of the uppermost lateral bond between two adjacent PFs). (C) Force-velocity curves for weak and strong binding. (D) Detachment force grows for stronger linker-tubulin binding, but the stalling force gets smaller.

Fig. 4.

Forced walk of the ring. (A) With increasing ring-tubulin affinity, the ring steps slower. The irregular features of ring forward motion are caused by the stochasticity and asynchrony in PF splitting and walking of different linkers. (B) The linkers step asynchronously (shown are the z coordinates of their MT-associated ends) and in 8-nm steps (arrows point to some), whereas the steps of the ring's center are more variable in size. (C) With increasing load, the duration of ring pauses increases, and the ring walks more slowly (k_DAM 13 k_BT). (D) The rate of coupler's movement with the depolymerizing MT end is a blueprint for the strength of its affinity to the MT wall and thus for the mechanism of its motion.