MCAK recognizes the nucleotide-dependent feature at growing microtubule ends

Here, we presented a simple model to calculate the relative contribution of the direct and EB-dependent end-binding of MCAK (Appendix 1—figure 1).

Based on the model, we had the dissociation constants:

(6)

${\displaystyle {\displaystyle K_0=\frac{\left[MCAK\right]\cdot \left[EB1\right]}{\left[MCAK\cdot EB1\right]}}}$

(7)

${\displaystyle {\displaystyle K_1=\frac{\left[MCAK\right]\cdot \left[MTE\right]}{\left[MCAK-MTE\right]}}}$

(8)

${\displaystyle {\displaystyle K_2=\frac{\left[EB1\right]\cdot \left[MTE\right]}{\left[EB1-MTE\right]}}}$

(9)

${\displaystyle {\displaystyle K_3=\frac{\left[MCAK\cdot EB1\right]\cdot \left[MTE\right]}{\left[MCAK\cdot EB1-MTE\right]}}}$

Then, the relative contribution of the direct and EB-dependent end-binding of MCAK can be expressed as α:

(10)

${\displaystyle {\displaystyle \alpha =\frac{\left[MCAK-MTE\right]}{\left[MCAK\cdot EB1-MTE\right]}=\frac{K_3\cdot \left[MCAK\right]}{K_1\cdot \left[MCAK\cdot EB1\right]}=\frac{K_3\cdot K_0}{K_1\cdot \left[EB1\right]}}}$

Here, we considered two scenarios. In the cytoplasm, both EB1 and MCAK undergo free diffusion and can associate with each other without restrictions. The relative concentrations of MCAK and EB1 are critical parameters, but they may vary across different cell types and remain unknown. We also considered the second scenario in which MCAK is locally enriched at specific cellular localizations through an EB-independent mechanism. For example, EB1 does not affect the localization of MCAK at centromere and centrosome, nor does EB1 significantly affect the function of MCAK there (Domnitz et al., 2012). Here, we assumed that the local concentration of anchored-state MCAK is relatively high, and EB1 remains diffusive and its concentration is nearly constant, as it is continuously replenished in the local space from the vast cytoplasmic pool. In both cases, the ratio of K₃ to K₁ emerges as a key determinant.

K₃ is the end-binding affinity of the MCAK·EB1 complex. Intuitively, it depends on the respective microtubule-binding affinities of MCAK and EB1, as well as the cooperativity, if any, of their microtubule-binding behaviors. K₃ can be expressed as:

(11)

${\displaystyle {\displaystyle \frac{1}{K_3}=a\frac{1}{K_1}+b\frac{1}{K_2}}}$

(12)

${\displaystyle {\displaystyle K_3=\frac{K_2\cdot K_1}{a{K}_2+b{K}_1}}}$

where a and b represent the weighting factors of binding sites or cooperativity factors of the binding behaviors. Therefore, K₃ shows a positively correlated, monotonically increasing dependence on K₁, indicating that the increase in the end-binding affinity of MCAK contributes to that of the MCAK·EB1 complex. Therefore, we think that MCAK’s functional impact at microtubule ends derives not only from its intrinsic end-binding capacity, but also its ability to strengthen the EB1-mediated end association pathway.

In the simplest case, the formation of the MCAK·EB1-MTE complex arises from the binding of either MCAK or EB1 to microtubule ends, and the binding behaviors for MCAK and EB1 are independent (a=1; b=1). Consequently, K₃ can be expressed as:

(13)

${\displaystyle {\displaystyle K_3=\frac{K_2\cdot K_1}{K_2+K_1}}}$

if $K_1\ll K_2$, then

(14)

$K_3\approx K_1$

if $K_1\gg K_2$, then

(15)

$K_3\approx K_2$

If $K_1\approx K_2$, then

(16)

$K_3\approx \frac{K_1}{2}$

In our experiments, we measured the dissociation constants of MCAK to growing microtubule ends is 69 µM (K₁). We also performed similar experiments with EB1 and found that EB1 showed the dissociation constant of 722 µM (K₂) for growing microtubule ends (Appendix 1—figure 2), similar to the value reported in our previous report (Song et al., 2020). Therefore, substituting Equation 14 into Equation 10, we obtained

(17)

$\alpha \approx \frac{K_0}{\left[EB1\right]}$

Here, if we assume that the cytoplasmic concentration of EB1 is twice the value of K₀, then α=0.5, indicating that 50% of MCAK binds to microtubule ends via the direct binding pathway; even if the EB1 concentration reaches ten times the value of K₀, 10% of MCAK still utilizes the direct binding pathway. Overall, as the EB1 concentration increases relative to K₀, α decreases, reflecting a decline in the proportion of MCAK that associates with microtubule ends through the direct binding mechanism.