Figure 1.
A. During metaphase, microtubules from the mitotic spindles stochastically search for the kinetochores (red dots) located on the chromosomes. Once microtubules have attached in a bipolar manner, tension (green arrows) is applied and the kinetochore-microtubule connection is stabilized. Meanwhile, the unattached kinetochore sends out a signal that stops anaphase commencement (red-blue gradient). B. After some variable time, all kinetochores are properly attached to the mitotic spindles and the “stop-anaphase” signal ceases. C. Anaphase commences rapidly after proper attachment. D. If a kinetochore pair is attached in a non-proper way (here a synthelic attachment is shown) the checkpoint detaches the faulty kinetochore-microtubule connection.
Figure 2.
The main function of the stalling part of the SAC is to prevent premature activation of APCCdc20. Failure to do so results in premature anaphase entry which leads to chromosome missegregation. A general model connecting the phenotype (chromosome missegregation) with the interactions of the SAC proteins on the kinetochore and in the cytoplasm was formulated. A–B All SAC proteins assemble on the unattached kinetochores, interact, and promote the creation of activated diffusible factors (proteins and complexes) composed of Mad2, Mad3 and Bub3. C These factors inhibit the Cdc20 by degradation and sequestering. The relative contribution of each SAC-protein to the sequestering and degradation rates is determined. D Cooperation between Cdc20 sequestering and degradation minimizes the APCCdc20 (arrow) and determines the actual level of the inhibition rates. E Further, a quantitative relation between the APCCdc20 and the CMR is assumed. Hence the SAC topology is connected to the phenotype. Knowing the CMR rate and the rate for all single SAC-deletions it is possible to compare any given putative topology with the real CMR values and thus search for solutions whose behavior is consistent with the observed phenotype.
Figure 3.
The SAC-proteins promote Cdc20 sequestering and degradation.
A. A model representing the interactions of the SAC core proteins on the kinetochores was formulated. Each SAC protein was represented by a node and each node was connected to five edges. The edges represented possible activations from the four other SAC proteins or from some external source. The ten edges connecting the SAC proteins were all assigned a direction and a value between 0 and 1, representing the relative strength of the interaction. The five external activations were only assigned a value. An interaction whose value is set to zero does not exist. Hence by randomizing the interaction directions and their weights our model can capture a vast number of different kinetochore interaction networks. In the end the relative activity of Mad2, Mad3 and Bub3 was obtained. B. An example kinetochore interaction network. C. Mad2, Mad3 and Bub3, whose relative activity level was determined by the kinetochore interactions, can inhibit Cdc20, either by forming complexes or by themselves. Each activated factor (protein/complex) is assigned two values: one for its relative sequestering strength and one for its relative strength of degradation. Again, the values varied between 0 and 1. The relative degree of sequestration and degradation for each factor was calculated as the product of the kinetochore activities of all its components multiplied by the specific sequestration/degradation rate for this factor and normalized with the ‘total’ sequestering/degradation (see Equations 2–6). It is known that Bub3 alone does not promote Cdc20 inhibition [51] and that Mad2 alone does not degrade Cdc20 [52] hence we exclude these activated proteins from the computational screen. D. An example set of sequestering and degrading proteins and complexes: for simplicity, the constant contributions are omitted here.
Figure 4.
Interplay between sequestering and degradation ensures minimal APCCdc20.
A. A general model for the Cdc20 sequestering and degradation interplay was formulated. The action of the diffusible SAC-proteins/complexes is generalized as a diffusible inhibitor ‘M’. Hence Cdc20 is being spontaneously generated at some rate k0 and can either bind a free APC, forming active APCCdc20 or be sequestered forming M-Cdc20. The sequestered Cdc20 can also bind APC forming an inactive APCMCdc20. Both Cdc20 and MCdc20 are degraded by the APC. The degradation of the inhibited complex is enhanced by the checkpoint (kdeg>k2). For simplicity it was assumed that APC binds free and sequestered Cdc20 at the same rate (k1). In order to make the model general it was also assumed that Cdc20 can degrade in an APC independent manner (k-0) and that Cdc20 can desequester (k-seq). Both these rates are small compared to the sequestering and degradation rates. B. The relation between the sequestering, the degradation and the APCCdc20 level: The level of APCCdc20 varies with the sequestration and degradation rates. We note that for any sequestering rate there is a degradation rate for which the APCCdc20 inhibition is optimal. See the right panel for the relation between APCCdc20 and the degradation rate for three different fixed sequestration rates (units are molecules−1s−1). This holds true for all cases where inhibition is good (APCCdc20/APCtotal<0.01). We conclude that the wild type sequestering and degradation rates are such that they minimize the APCCdc20. The reason behind this optimization of the inhibition is that the degradation regulates the balance between the amount of free inhibiting complexes, Cdc20 and APC. C. The level of APCCdc20 drives the chromosomal missegregation rate: An impaired ability to inhibit APCCdc20 is translated into an increase in the chromosomal missegregation rate (see main text and supporting information S1 for details).
Table 1.
See supporting information S1 for a comparison with previous measurements of chromosome missegregation and for an explanation about the rescaling of the Bub1, Bub3 and Mad1 rates.
Figure 5.
A. A kinetochore network is chosen and its weights and the contribution from external sources (here denoted ‘Ipl1’ and ‘Mps1’, see main text for details) are randomized. B. One or several activated factors (proteins/complexes) composed of Bub3 Mad2 and Mad3 contribute in a varying degree to the sequestering and degradation rates. Next, the relative contribution of each factor to the total Cdc20 sequestering and/or degradation was calculated. Note that the same complex can contribute to both sequestering and degradation (here MCC does that). C. The total sequestration and degradation rates from all factors are normalized so that they correspond to rates giving an optimal (minimal) level of APCCdc20. Here the relationship between the APCCdc20 and the degradation rate is shown for a fixed sequestration rate. D–E. Once the wild-type network was defined we proceeded to sequentially delete all the SAC-proteins. The impact of deleting Bub3 is shown here. On the kinetochore Mad3 is less activated and all complexes containing Bub3 also disappears. F. The decrease of the sequestering and degradation is translated into a new APCCdc20 level. This decrease is represented here by a shift on the x-axis (degradation) and from the blue curve (stronger sequestering) to the green curve (weaker sequestering). G. The relative impact on the APCCdc20 is than translated into a predicted change in the chromosomal missegregation rate for this network and this mutation and compared (H.) with the experimental values. The bub3 deletion here does not fall within the accepted range thus disqualifying this particular topology. For details about the screen see the supporting information S1.
Figure 6.
Experimental versus predicted values for the double deletions.
A. The experimental (green) versus the predicted (blue) values. The x- and y-axis represent chromosome missegregation rates for the mad1mad3 and the mad2mad3 double deletions whereas the lines extending from each point represent one standard deviation. B. A zoom-in on the lower left corner of A. The rightmost (worse) predicted value is not likely to represent the real topology since it contains many highly unlikely interactions (see main text for details).
Figure 7.
A proposed mechanism for the SAC.
On the kinetochore, Bub1 is activated either endogenously or by Ipl1 or some other factor. Once in place, Bub1 together with Mps1 promotes Mad1 activation which in turn activates Mad2. Bub1 also activates Bub3 that, together with Ipl1, activates Mad3. Subsequently, the active Mad2 diffuses and sequesters Cdc20. The resulting Mad2-Cdc20 complex then binds to the activated Bub3-Mad3 complex and forms the MCC. The MCC proceeds to bind the APC where the Cdc20 gets ubiquinated and degraded. The degradation of the Cdc20 recycles the other MCC components which restarts the process.