Growth rate-dependent flexural rigidity of microtubules influences pattern formation in collective motion

Abstract

Background Microtubules (MTs) are highly dynamic tubular cytoskeleton filaments that are essential for cellular morphology and intracellular transport. In vivo, the flexural rigidity of MTs can be dynamically regulated depending on their intracellular function. In the in vitro reconstructed MT-motor system, flexural rigidity affects MT gliding behaviors and trajectories. Despite the importance of flexural rigidity for both biological functions and in vitro applications, there is no clear interpretation of the regulation of MT flexural rigidity, and the results of many studies are contradictory. These discrepancies impede our understanding of the regulation of MT flexural rigidity, thereby challenging its precise manipulation. Results Here, plausible explanations for these discrepancies are provided and a new method to evaluate the MT rigidity is developed. Moreover, a new relationship of the dynamic and mechanic of MTs is revealed that MT flexural rigidity decreases through three phases with the growth rate increases, which offers a method of designing MT flexural rigidity by regulating its growth rate. To test the validity of this method, the gliding performances of MTs with different flexural rigidities polymerized at different growth rates are examined. The growth rate-dependent flexural rigidity of MTs is experimentally found to influence the pattern formation in collective motion using gliding motility assay, which is further validated using machine learning. Conclusion Our study establishes a robust quantitative method for measurement and design of MT flexural rigidity to study its influences on MT gliding assays, collective motion, and other biological activities in vitro. The new relationship about the growth rate and rigidity of MTs updates current concepts on the dynamics and mechanics of MTs and provides comparable data for investigating the regulation mechanism of MT rigidity in vivo in the future. Graphic Abstract

Durability of Aligned Microtubules Dependent on Persistence Length Determines Phase Transition and Pattern Formation in Collective Motion

“…The growth rates of the MTs were modified by adjusting the tubulin concentration (i.e., at 30 or 100 μM). The three groups of MTs, that is, softer GTP-MTs , stiffer GTP-MTs , and GMPCPP-MTs , had a L p of 0.65 ± 0.24, 1.93 ± 0.82, and 3.54 ± 0.99 mm, respectively, as measured using our previous method …”

“…The L p of MTs is affected by their polymerization conditions, including the types of nucleotides and their growth rate . A faster growth rate of MTs induces more lattice defects and, thus, softens the MTs. , On the basis of this mechanism, a method for controlling the L p of MTs by altering tubulin concentrations has been presented in our previous work . Herein, three types of MTs with different L p were engineered using two types of nucleotides (GTP or GMPCPP) and two different growth rates of the MTs (Figure a and Supplementary Table S1).…”

“…Furthermore, the three types of MTs were classified with an accuracy of 97.7% on the basis of their different features using our previously reported method of deep-learning-based image recognition (see Supplementary Text, Model for Classifying Images and Supplementary Figure S2). The pattern differences between the three MT groups were visualized using the technique of class activation mapping (see Supplementary Text, Visualization of the Classification Strategy and Supplementary Figure S3), which corresponds well with our observed results.…”

“…However, the polymerization conditions of the MTs were different (tubulin concentration of 55.6 μM by Inoue et al, and 45 μM by Farhadi et al). Although the L p of MTs in the two groups was not reported, on the basis of the theory that a faster growth rate induced by a higher tubulin concentration softens MTs, − the MTs used in Inoue et al should be softer than those used in Farhadi et al A different L p of the MTs is probably the reason for the formation of different patterns in the two studies.…”

“…All MTs were polymerized from TAMRA-labeled tubulin at 37 °C for 30 min and then stabilized with 20 μM paclitaxel after elongation. The L p of MTs was measured with our previous method . The measured MTs were partially immobilized on a gold stripe via biotin–streptavidin binding.…”