Displacement-weighted velocity analysis of gliding assays reveals that Chlamydomonas axonemal dynein preferentially moves conspecific microtubules

Abstract

In vitro gliding assays, in which microtubules are observed to glide over surfaces coated with motor proteins, are important tools for studying the biophysics of motility. Gliding assays with axonemal dyneins have the unusual feature that the microtubules exhibit large variations in gliding speed despite measures taken to eliminate unsteadiness. Because axonemal dynein gliding assays are usually done using heterologous proteins, i.e., dynein and tubulin from different organisms, we asked whether the source of tubulin could underlie the unsteadiness. By comparing gliding assays with microtubules polymerized from Chlamydomonas axonemal tubulin with those from porcine brain tubulin, we found that the unsteadiness is present despite matching the source of tubulin to the source of dynein. We developed a novel, to our knowledge, displacement-weighted velocity analysis to quantify both the velocity and the unsteadiness of gliding assays systematically and without introducing bias toward low motility. We found that the quantified unsteadiness is independent of tubulin source. In addition, we found that the short Chlamydomonas microtubules translocate significantly faster than their porcine counterparts. By modeling the effect of length on velocity, we propose that the observed effect may be due to a higher rate of binding of Chlamydomonas axonemal dynein to Chlamydomonas microtubules than to porcine microtubules.

Figure 1

Microtubule translocation unsteadiness is a characteristic of both conspecific and heterogeneous dynein-tubulin experiments. (a) Kymographs showing example Chlamydomonas microtubules (left two images) and example porcine microtubules (right two images) gliding on outer-arm dynein from Chlamydomonas axonemes. These kymographs were made by collecting intensity line scans of the translocation path of the rhodamine-labeled microtubule from each frame imaged at 100 ms frame rate and projecting them sequentially such that the x axis of these plots becomes time. (b) The displacement along an example microtubule’s path (corresponding to the leftmost kymograph in a) plotted as a function of time, as tracked in each frame by FIESTA. (c) The instantaneous velocity of the same example microtubule shown in b plotted versus time calculated using 0.4-s time windows. (d) The time-weighted velocity histogram of the same example microtubule. The example microtubule had a time-weighted mean gliding velocity of ${\mu }_t=2.68\mu \text{m}/\text{s}$ and an unsteadiness of ${\sigma }_t=1.69\mu \text{m}/\text{s}$ (22 instantaneous velocity measurements). (e) The displacement-weighted velocity histogram of the same example microtubule. The example microtubule had a displacement-weighted mean gliding velocity of ${\mu }_x=3.69\mu \text{m}/\text{s}$ and an unsteadiness of ${\sigma }_x=1.35\mu \text{m}/\text{s}$ (23 μm of total gliding displacement).

Figure 2

Displacement-weighted velocity characterizes unsteady gliding in an unbiased and systematic way. (a) Time-weighted velocity histogram $\left(p_t\left(v\right)\right)$ of all of the analyzed Chlamydomonas microtubules. The mean velocity is ${\mu }_t=2.80\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_t=2.96\mu \text{m}/\text{s}$ for 1183 microtubules and 25,706 instantaneous velocities. (b) Time-weighted velocity histogram $\left(p_t\left(v\right)\right)$ of all of the analyzed porcine microtubules. The mean velocity is ${\mu }_t=2.17\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_t=2.79\mu \text{m}/\text{s}$ for 799 microtubules and 26,551 instantaneous velocities. (c) Displacement-weighted velocity histogram $\left(p_x\left(v\right)\right)$ of all of the analyzed Chlamydomonas microtubules. The mean velocity is ${\mu }_x=5.76\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_x=2.88\mu \text{m}/\text{s}$ for 1183 microtubules and 29.6 mm of total gliding displacement. (d) Displacement-weighted velocity histogram $\left(p_x\left(v\right)\right)$ of all of the analyzed porcine microtubules. The mean velocity is ${\mu }_x=5.48\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_x=2.89\mu \text{m}/\text{s}$ for 799 microtubules and 24.2 mm of total gliding displacement.

Figure 3

Short Chlamydomonas microtubules move faster than short porcine microtubules. (a) Mean velocity $\left({\mu }_x\right)$ as a function of microtubule length (L) for Chlamydomonas microtubules (solid circles) and porcine microtubules (open circles). The lines are best fits to Eq. 7. For Chlamydomonas microtubules, the microtubule length corresponding to half-maximum velocity was $L_0=3.8\pm 0.3\mu \text{m}$ (fit parameter ± standard error), and for porcine microtubules it was $L_0=6.7\pm 0.5\mu \text{m}$ (fit parameter ± standard error). Data points were calculated from pools of microtubules in 2-μm bins. The error bars represent the standard error of the mean $\left(\sigma /\sqrt{N}\right)$ of each microtubule pool. (b) Displacement-weighted velocity histogram $\left(p_x\left(v\right)\right)$ of short Chlamydomonas microtubules $\left(L<6\mu \text{m}\right)$. The mean velocity is ${\mu }_x=4.42\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_x=2.48\mu \text{m}/\text{s}$ for 345 microtubules and 9.8 mm of total gliding displacement. (c) Displacement-weighted velocity histogram $\left(p_x\left(v\right)\right)$ of short porcine microtubules $\left(L<6\mu \text{m}\right)$. The mean velocity is ${\mu }_x=3.36\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_x=2.24\mu \text{m}/\text{s}$ for $N=152$ microtubules and $d=5.3$ mm of total gliding displacement. (d) Displacement-weighted velocity histogram $\left(p_x\left(v\right)\right)$ of long Chlamydomonas microtubules $\left(L>20\mu \text{m}\right)$. The mean velocity is ${\mu }_x=7.61\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_x=2.86\mu \text{m}/\text{s}$ for 110 microtubules and 2.0 mm of total gliding displacement. (e) Displacement-weighted velocity histogram $\left(p_x\left(v\right)\right)$ of long porcine microtubules $\left(L>20\mu \text{m}\right)$. The mean velocity is ${\mu }_x=7.31\mu \text{m}/\text{s}$ and the unsteadiness is ${\sigma }_x=2.64\mu \text{m}/\text{s}$ for 157 microtubules and 3.4 mm of total gliding displacement.