Fig. 2: The curvature fluctuation around the inter-dimer interfaces of tubulin tetramer in solution.

a Overview of three major conformations of GDP- and GMPCPP-tubulin tetramers. All models are aligned together using β1-tubulin as reference. GDP-tubulin tetramers are colored with coral, plum and khaki, respectively. GMPCPP-tubulin tetramers are colored with steel blue, light sea green and light gray, respectively. b The coordinate system is defined to describe the bending angles of α2, β2-tubulin relative to α1, β1-tubulin. And the quantitative values of the angles are decomposed in the x (radial bending), y (tangential bending) and z (twist) axes. c–h Bending of inter-dimer in radial, tangential and twist directions. The upper heterodimer (α2, β2-tubulin) shown in (a) of GDP-state (c–e) and GMPCPP-state (f–h). The black arrow indicates the direction of bending. A simplified cartoon model and its bending angle range are displayed in the left-bottom corner. H11 and H12 helices are represented as cylinders, the N and I domain are shown as surfaces. i–k Violin plots representing the standard deviation of bending angles are shown for GDP and GMPCPP states, obtained from bootstrapping datasets for a two sample T-test. The circles in each related violin plot indicate the mean value of the standard deviation angle. The vertical axis represents the standard deviation of bending angles, while the horizontal axis corresponds to different nucleotide states. The two sided T-test assumed the standard deviation angles of GDP and GMPCPP are in the same distributions with equal means in 1 dimensional space with the 95% confidence interval. Statistically significant results from the two sided T-tests are denoted as follows: *p-value < 0.05; **p-value < 0.01; ***p-value < 0.001. In all three tests, the hypotheses are rejected. i Violin plot displaying the distribution of standard deviation in radial bending angles. The p-value is 1*10⁻¹¹ and effect size is 5.38. j Violin plot displaying the distribution of standard deviation in tangential bending angles. The p-value is 1*10⁻¹² and effect size is 13.13. k Violin plot displaying the distribution of standard deviation in twist angles. The p-value is 1*10⁻¹² and effect size is 30.07.