Stochastic Modeling Yields a Mechanistic Framework for Spindle Attachment Error Correction in Budding Yeast Mitosis.

Proper segregation of the replicated genome requires that kinetochores form and maintain bioriented, amphitelic attachments to microtubules from opposite spindle poles and eliminate erroneous, syntelic attachments to microtubules from the same spindle pole. Phosphorylation of kinetochore proteins destabilizes low-tension kinetochore-microtubule attachments, yet tension stabilizes bioriented attachments. This conundrum for forming high-tension amphitelic attachments is recognized as the "initiation problem of biorientation (IPBO)." A delay before kinetochore-microtubule detachment solves the IPBO, but it lacks a mechanistic framework. We developed a stochastic mathematical model for kinetochore-microtubule error correction in yeast that reveals: (1) under low chromatin tension, requiring a large number of phosphorylation events at multiple sites to achieve detachment provides the necessary delay; and (2) kinetochore-induced microtubule depolymerization generates tension in amphitelic, but not syntelic, attachments. With these requirements, the model provides a mechanistic framework for the delay before detachment to solve the IPBO and demonstrates the high degree of amphitely observed experimentally for wild-type spindles under optimal conditions.

Physical limits on kinesin-5-mediated chromosome congression in the smallest mitotic spindles.

A characteristic feature of mitotic spindles is the congression of chromosomes near the spindle equator, a process mediated by dynamic kinetochore microtubules. A major challenge is to understand how precise, submicrometer-scale control of kinetochore micro-tubule dynamics is achieved in the smallest mitotic spindles, where the noisiness of microtubule assembly/disassembly will potentially act to overwhelm the spatial information that controls microtubule plus end-tip positioning to mediate congression. To better understand this fundamental limit, we conducted an integrated live fluorescence, electron microscopy, and modeling analysis of the polymorphic fungal pathogen Candida albicans, which contains one of the smallest known mitotic spindles (<1 µm). Previously, ScCin8p (kinesin-5 in Saccharomyces cerevisiae) was shown to mediate chromosome congression by promoting catastrophe of long kinetochore microtubules (kMTs). Using C. albicans yeast and hyphal kinesin-5 (Kip1p) heterozygotes (KIP1/kip1∆), we found that mutant spindles have longer kMTs than wild-type spindles, consistent with a less-organized spindle. By contrast, kinesin-8 heterozygous mutant (KIP3/kip3∆) spindles exhibited the same spindle organization as wild type. Of interest, spindle organization in the yeast and hyphal states was indistinguishable, even though yeast and hyphal cell lengths differ by two- to fivefold, demonstrating that spindle length regulation and chromosome congression are intrinsic to the spindle and largely independent of cell size. Together these results are consistent with a kinesin-5-mediated, length-dependent depolymerase activity that organizes chromosomes at the spindle equator in C. albicans to overcome fundamental noisiness in microtubule self-assembly. More generally, we define a dimensionless number that sets a fundamental physical limit for maintaining congression in small spindles in the face of assembly noise and find that C. albicans operates very close to this limit, which may explain why it has the smallest known mitotic spindle that still manifests the classic congression architecture.