Fig 1.
Model for transitions of sister chromatids between different KT-MT attachment states.
Double-headed arrows denote reversible transitions, whereas the single-headed arrow denotes an irreversible transition from the amphitelic state (centromere not under tension) to the biorientation state (centromere under tension).
Fig 2.
Scheme for kinase and phosphatase activities at the KT.
Kinases are Ipl1 and Mps1 (shown in green), and phosphatases are PP1 and PPX (shown in red). Phosphorylation of MELT motifs by Mps1 starts the SAC signaling cascade and its dephosphorylation by RVSF-bound PP1 promotes silencing of the SAC signal. Phosphorylation of Ndc80 by Ipl1 weakens KT-MT attachment, and its dephosphorylation by PPX promotes KT-MT attachment.
Fig 3.
Molecular interactions at the KT.
(A) Model of kinase (green) and phosphatase (red) activities at the KT, derived from the scheme in Fig 2. The full scheme can be divided into two modules (shown within boxes), namely, Ndc80 and MELT modules. See text for a detailed description of each module. ‘P’ (blue color) is used to depict the phosphorylation status of different motifs. The dashed arrow between the boxes indicates that Mps1 bound to either Ndc80 or Ndc80P phosphorylates MELT repeats. (B) Scheme showing binding of Ndc80 to MT. The reactions on the first line show that Ndc80 (unphosphorylated) binds reversibly to a MT, stabilizing the attachment, and that Ndc80:Mps1 can also bind to a MT, which displaces Mps1 in an irreversible reaction. (MTs and Mps1 compete for the same binding site on Ndc80; therefore, upon MT binding, Mps1 is displaced from Ndc80.) We assume that Ndc80P (and Ndc80P:Mps1) can also bind to MTs (second line of reactions), but with a much larger dissociation constant, i.e., phosphorylation of Ndc80 promotes detachment of the MT from a KT.
Fig 4.
A model of MT attachment to sister KTs through Ndc80.
(A) The vector (m,n) represents the numbers of Ndc80s bound to a MT at a pair of sister KTs. The attachment can be monotelic (black), syntelic (red with subscript s) or amphitelic (green with subscript a). The start and finish points of the chromosome-alignment process are shown with blue boxes. We assume that the process stops (KTs reach biorientation) when the KTs spend more than 1 s in the finish box without coming out. (B) Traces showing four time-courses of KT-MT attachment status calculated using the scheme in (A). A black vertical bar indicates the time of biorientation.
Fig 5.
Probability of biorientation in a simplified model.
Probability that sister KTs reach biorientation within 10 min, starting from the syntelic attachment state, as a function of an effective MT-Ndc80 dissociation rate (kd,eff). Different curves correspond to different numbers of Ndc80s used in the biorientation criterion. The highest value of the probability of biorientation in each case is 1 (or very close to 1). The optimal value of kd,eff, shown with an arrow, was determined using the minimum value of the mean-time for biorientation (S1 Fig in S2 File).
Table 1.
Optimal value of effective dissociation rate constant (kd,eff) and the error rate (1−Pbio) per chromosome at that value*.
Fig 6.
Analysis of the kinase-phosphatase balance point.
Probability of sister KTs reaching biorientation within 10 min, starting from the syntelic attachment state. The location of the maximum in biorientation probability (balance point) is indicated with arrows. The value of phosphatase activity is set to kPPX = 1 s−1. (A) When the minimum number of Ndc80s needed to reach biorientation is lowered, the balance point occurs at higher values of kIpl1. For this analysis we chose Ndc80:MT and Ndc80P:MT dissociation rates as kd,ndc = 0.1 s−1 and kd,ndcp = 1.5 s−1 respectively. (B) Depending on the values of the MT-Ndc80 dissociation rates, the balance point occurs at values smaller or greater than one. For this analysis the minimum number of Ndc80s needed for biorientation was chosen to be four.
Fig 7.
Dissociation scheme of Ndc80-MT attachment.
Fig 8.
Dependence of kinase-phosphatase balance point on MT-Ndc80 dissociation rates.
(A) The blue curve corresponds to variation in the Ndc80:MT dissociation rate when the Ndc80P:MT dissociation rate is fixed at 1.5 s−1. As the Ndc80:MT dissociation rate is increased towards the optimal value of kd,eff (0.7 s−1), the balance point drops to zero. The red curve corresponds to variation in the Ndc80P:MT dissociation rate, when the Ndc80:MT dissociation rate is fixed at 0.1 s−1. As the Ndc80P:MT dissociation rate is decreased towards optimal kd,eff, the balance point becomes much larger than one. (B) Curves on which the effective MT-Ndc80 dissociation rate keff is constant. The curves were calculated using Eq 3. At a fixed value of kPPX, the interval between the red and the blue curves is the range of kIpl1 over which the biorientation probability is high (see Fig 5). This range increases with increasing kPPX.
Table 2.
Mean number of transitions (N) from amphitelic (amp) to monotelic (mon) state at two different kinase-phosphatase balance points*.
Fig 9.
Effect of geometrical orientation of KTs on biorientation probability.
Probability of biorientation within 10 min for different values of Psyn. KTs start in unattached state. Psyn = 0.5 corresponds to the case in which KTs in monotelic state transition to syntelic and amphitelic states with equal probability. The lowest error rate in this case is 4.5×10−2 per chromosome (occurs at kIpl1/kPPX = 1). Psyn = 0.1 corresponds to the case in which KTs in monotelic state transition to amphitelic state 10 times more often than syntelic state. The error rate in this case at kIpl1/kPPX = 1 is 10−4 per chromosome.
Table 3.
Average number of Mps1 and SAC signaling proteins bound per KT*.