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Cytoskeleton and Cell Motility


V.1 Coordinators
V.2 Participants
V.3 Introduction
V.4 Specific Research Objectives
V.5 Background and Significance
V.6 Research Plan V.7 Relation with Organogenesis (project 3) and Biological Networks (project 1)
V.8 Timeline

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V.6.ii.c.3 Mathematical models of rotational alignment, spindle asymmetry, and spindle rocking, based on measurements and predictions:

Recent studies have suggested that the dynein/dynactin complex acting on astral microtubules provides the motive force for driving rotational alignment, spindle rocking, and the anaphase B separation of the poles (Gonczy et al., 1999; Grill et al., 2001; Skop and White, 1998). Foci of accumulated dynactin components in the cortex might act as localized tethers that competitively capture microtubules from the asters and cause them to move towards the focus. When one aster has more microtubule attachments than the other, it will move closer to the cortical patch causing the other aster (on the opposite pole of the nucleus) to move away (Hyman and White, 1987). The proximal aster will then make more cortical attachments whereas the distal aster will make fewer, causing the whole centrosomal/nucleus complex to rotate until one of the asters is adjacent to the dynactin focus. Although observed foci of dynactin are located consistently with this scenario (Skop and White, 1998), this model remains hypothetical.

Experiments in which ablation or mutations eliminate the spindle midzone have shown that, contrary to expectations (Grill et al., 2001), the microtubule motors in this organelle have no significant role in driving anaphase separation of the poles. A plausible working hypothesis is that interactions of the microtubule ends with the cortically distributed dynactin complex mediate the poleward movement of asters. The PAR segregation system may lower the concentration of dynactin at one pole. Such an asymmetry could give rise to force differences on the asters with consequent differences in their poleward migration, leading to a net axial movement of the spindle and asymmetric cleavage. The White lab has been developing GFP-tagged versions of the individual components of the dynactin complex and using multiphoton microscopy to visualize dynactin complex dynamics. As for rotational alignment, we will soon have fairly detailed information on the dynamics of the astral movements and changing distributions of dynactin, together with a plausible hypothesis. The next challenge is to see whether these hypotheses are self-consistent and capable of explaining observed phenomena.

The rocking movements observed during anaphase B spindle elongation are not seen when the expression of dynactin components is suppressed by RNAi (White lab, unpublished). Although the Strome lab has shown that these rocking movements are not essential, explaining them may reveal important insights into astral/cortical interactions. For example, the White lab has found that mutants in let-99, a gene originally identified as required for rotational alignment (Rose and Kemphues, 1998), have rapid, random excursions of the centrosomal/nucleus complex that are highly reminiscent of the excursions of the posterior centrosome during anaphase B. Thus asters may be innately unstable when they interact with the cortex A computer model of astral cortical interactions that is able to simulate these instabilities would provide insight into the factors causing or suppressing these instabilities.

Our model will treat the aster as a spherical array of microtubules aligned with minus ends adjacent to the centrosome. These microtubules will experience dynamic instability. Non-uniformly distributed cytoplasmic factors (e.g. katanin) will locally modify the kinetics of this instability. In addition, plus-end binding factors at the distal ends of the microtubules (e.g. CLIP-170 and MCAK/XKCM1) may modify the interaction of microtubule ends with factors in the cortex. We will assume that the microtubule ends interact with discrete complexes on the cell cortex including the dynactin system. These complexes tether and cap captured microtubules, thereby modulating their dynamic instability. The cortical complex may then act to "reel in" the captured microtubule, generating a force that pulls the centrosome towards the cortex. The net movement of the aster/centrosome will depend on the balance of all the forces that the captured microtubules apply.

Rather than trying to define a set of differential equations, we will directly simulate the mechanics of the cytoskeletal components, assuming random distributions of individual microtubules and cortical complexes with long-range changes of density of some components produced by the PAR segregation system. We have previously used this discrete mechanistic approach to simulate cytokinesis (White and Borisy, 1983) and found it to be very effective. We will explore the dynamic behavior of various postulated microtubule/cortical interactions. For example, the microtubule capture complexes could be sparsely distributed so that most elongating microtubules do not encounter a complex when they reach the cortex. These microtubules might act to push the centrosome away and counter the forces generated by the few microtubules that interact with cortical complexes. Alternatively, touching the cortex in the absence of an attachment complex may trigger the catastrophic depolymerization of the microtubule, which would then generate no force.

The aim of the simulations is to test our hypotheses by searching for a set of parameters that will enable us to simulate all the dynamic behaviors that we observe in embryos. If we cannot, our hypotheses are incomplete. On the other hand, if our computer model reproduces the observed dynamics, the parameters (e.g. density of microtubule capture complexes) give us predictions that we can verify experimentally. We expect that initial models will reproduce only a subset of phenomena, leading us to further experimentation that will allow refinement of the model.