Mathematical model of the KMT interface. (A) NDC80–MT binding is characterized by three molecular parameters: association rate (k_on), dissociation rate (k_off), and cooperativity parameter (ω). (B) Calculated kinetics of the increase in K-fiber size for the kinetochore with 1D NDC80 complexes for the repetitive sites model and lawn model. Values of other model parameters are provided in Table 1 and Table 2. Both models correctly predict that formation of a K fiber with a mean of 27 KMTs takes ∼20 min in PtK1 cells (McEwen et al., 1997). (C) Histogram distribution of the number of KMTs at a steady state in the repetitive sites model and lawn model relative to metaphase cells (experimental data are from McEwen et al., 1997). (D) K-fiber size for different numbers of phosphomimetic substitutions predicted in the two models normalized relative to the normal K-fiber size (27 KMTs in PtK1 cells). Error bars here and for all theoretical plots are SDs. Here and in Fig. 6 (A and B), experimental data for K-fiber size are the same as in Fig. 3 C. (E) Snapshots from theoretical videos for kinetochores with different NDC80 complexes (Video 1 for 1D mutant in the repetitive sites model and Video 2 in the lawn model). Each image is a fragment of a kinetochore cross section at steady state. The exact positions of attached MTs change with time, but the mean number of MTs bound to the kinetochores stays roughly the same at steady state. (F) Mean KMT half-life calculated for kinetochores with different phosphomutants and normalized relative to KMT half-life for 1D NDC80 complexes, which was 9 min in both models (owing to calibration) and was taken as 1 on this graph. Experimental data for single NDC80 complexes are mean residency times in vitro, which is an inverse of the dissociation rate (Table 1). Residency time for 1D NDC80 is 240 ms (taken as 1 on this graph). Note that time is plotted on a logarithmic scale. (G) Schematic of the KMT interface in the lawn model, in which the sites of MT attachment to the kinetochore do not have a predetermined location or molecular makeup, and they form via stochastic contacts between MTs and the NDC80 complexes that can reach them (black circles). The hatched area shows an overlap between two such circles; molecules from this area (in blue) can engage in binding to either of the two MTs.