Figure 2. Mathematical model predicts recruitment of Kip2 to the microtubule minus-end.

(a) Schematic of the mathematical model. Free Kip2 (with concentration ${\left[\text{Kip2}\right]}_{\text{free}}\le {\left[\text{Kip2}\right]}_{\text{total}}$) binds to the microtubule minus-end anchored at the SPB with rate $r_{\text{in}}=k_{\text{in}}{\left[\text{Kip2}\right]}_{\text{free}}$ if the minus-end site is free, and to any free lattice site with rate $r_{\text{on}}=k_{\text{on}}{\left[\text{Kip2}\right]}_{\text{free}}$. A bound motor can detach with rate $k_{\text{off}}$, and it can advance with rate $k_{\text{step}}$ if the next site towards the plus-end is free. At the plus end, the motor detaches with a different rate, $k_{\text{out}}$. (b) Experimental Kip2-3xsfGFP fluorescence (a.u.) mean profile (black) and standard error (gray) with respective mean in silico model fits (red) for microtubules binned by length. Red dashed lines past plus-end and SPB indicate model extrapolations without support by data. (c) Likelihood of total Kip2 concentration ${\left[\text{Kip2}\right]}_{\text{total}}$ estimated from fit in (b). (d) Likelihood of on rate constant $k_{\text{on}}$ and in rate constant $k_{\text{in}}$ estimated from in silico model fit in (b). Statistical significance for $k_{\text{in}}>k_{\text{on}}$, ****, (p<5∙10⁻⁵) determined by sampling from the likelihood (see Appendix 1), difference in median as indicated. (e) Likelihood of out rate $k_{\text{out}}$ constant estimated from in silico model fit in (b). For in silico model parameter estimate plots (cde), median parameter values are indicated as circles, inter-quartile range ($IQR$) by thick gray bars and $1.5\times IQR$ by thin gray bars. Kernel density estimates are computed from 20’000 samples from the likelihood function. Sampled parameter ranges are indicated by dashed black lines. See also Figure 2—figure supplement 2, Figure 2—figure supplement 1, and Figure 2—figure supplement 3.

Figure 2—figure supplement 1. Median parameter value model simulations for static and growing microtubules.

(a) In silico model simulated as in the main text, according to the measurement model section in the Supplementary Material. Briefly, the microtubule length is static and discrete microtubule lengths with 88 nm steps are considered. (b) Growing in silico microtubule model with prescribed growth rate of 0.05 s⁻¹, corresponding to a growth speed of 0.4 nm s⁻¹. (c) Growing in silico microtubule model with prescribed growth rate of 2.875 s⁻¹, corresponding to the mean in vivo growth speed of 23 nm s⁻¹ given in Figure 2—figure supplement 2d.

Figure 2—figure supplement 2. Measurements of kinesin movement speeds, as well as the speeds of b-microtubule growth and shrinkage in living cells.

(a) Representative kymographs and highlighted trajectories (red dashed lines) of Kip3-3xsfGFP (left), Kip2-3xsfGFP (middle), and Kip2-S63A-3xsfGFP (right) speckles moving along a preanaphase b-microtubule. Unlike Kip2, Kip3-3xsfGFP rarely forms obvious speckles. (b) A collection of kymographs was generated to quantify the speed of speckles moving towards microtubule plus-ends for each mutant. Kip3-3xsfGFP speckles move at a speed of 3.0 ± 1.8 µm min⁻¹ (n = 10 speckles), Kip2-3xsfGFP at 6.3 ± 2.1 µm min⁻¹ (n = 192), and Kip2-S63A-3xsfGFP at 6.0 ± 2.0 µm min⁻¹ (n = 66). (c, d) The speeds of b-microtubule growth (1.4 ± 1.1 µm min⁻¹, n = 250 phases) and shrinkage (2.0 ± 1.4 µm min⁻¹, n = 409 phases) were derived from the 3D b-microtubule length over 85.6 s. Growth and shrinkage phases were annotated manually. All cells were cultivated and imaged at 25 °C. All values are reported as mean ± s.d.. Statistical significances were calculated using two-tailed Student’s t-test. For all panels, ****p<0.0001, n.s., not significant.

Figure 2—figure supplement 3. Concentration and out rate estimates for bfa1Δbub2Δ and Kip2-S63A strains.

(a) Likelihood of total Kip2 concentrations estimated from model fits in (cd) and Figure 2b. (b) Likelihood of out rate constant estimated from model fits in (cd) and Figure 2b. (c) Experimental Kip2-3xsfGFP fluorescence (a.u.) mean profile (black) and standard error (gray) in bfa1Δbub2Δ cells with respective mean of the best model fits (red). Red dashed lines past plus-end and SPB indicate model extrapolations without support by data. (d) Experimental Kip2-S63A-3xsfGFP fluorescence (a.u.) mean profile (black) and standard error (gray) with respective mean of the best model fits (red). Red dashed lines past plus-end and SPB indicate model extrapolations without support by data. (e) Western blot analysis of endogenously expressed GFP fusion proteins. Pgk1 was blotted as loading control. Lysates were prepared from cycling cells of indicated genotype.