Modeling dual pathways for the metazoan spindle assembly checkpoint

Abstract

Using computational modeling, we investigate mechanisms of signal transduction. We focus on the spindle assembly checkpoint, where a single unattached kinetochore is able to signal to prevent cell cycle progression. The inhibitory signal switches off rapidly once spindle microtubules have attached to all kinetochores. This requirement tightly constrains the possible mechanisms. Here we investigate two possible mechanisms for spindle checkpoint operation in metazoan cells, both supported by recent experiments. The first involves the free diffusion and sequestration of cell cycle regulators. This mechanism is severely constrained both by experimental fluorescence recovery data and by the large volumes involved in open mitosis in metazoan cells. By using a simple mathematical analysis and computer simulation, we find that this mechanism can generate the inhibition found in experiment but likely requires a two-stage signal amplification cascade. The second mechanism involves spatial gradients of a short-lived inhibitory signal that propagates first by diffusion but then primarily by active transport along spindle microtubules. We propose that both mechanisms may be operative in the metazoan spindle assembly checkpoint, with either able to trigger anaphase onset even without support from the other pathway.

Fig. 1.

Plot, for the model of Eq. 1 showing the fraction of molecules N_e/N (solid line), N_c*/N (dashed line), and N_e*/N (dotted line) as a function of time, with the final kinetochore attaching at time t = 0, i.e., initial steady-state concentrations, but k_k then set to zero at t = 0. (Inset) The same fractions but starting with all N molecules in the e form and with k_k set to 20 μm³·s⁻¹ at t = 0. For comparison, in the main plot, the fractions N_c/N for the production only at kinetochores and autocatalytic models are plotted as gray curves. They should be compared with the solid black curve. The gray solid curve is with a reaction only at a kinetochore, and the gray dotted-dashed curve is with autocatalysis. Note that with a reaction only at a kinetochore the initial inhibition is weak, whereas with autocatalysis inhibition is near total, even when k_k is set to zero. The values of k (for the autocatalytic rate), α, and k_k in the single-species models are the same as they are for the model of Eq. 1.

Fig. 2.

A schematic of the diffusive two-step reaction model (A) and the active-transport model (B). Kinetochores are shown in green; red dashed lines denote diffusion; and solid red arrows denote motion via active transport. Sister chromatids are shown in blue, and the black lines are microtubules.