Atomistic molecular dynamics simulations of tubulin heterodimers explain the motion of a microtubule

Abstract

Microtubules are essential parts of the cytoskeleton that are built by polymerization of tubulin heterodimers into a hollow tube. Regardless that their structures and functions have been comprehensively investigated in a modern soft matter, it is unclear how properties of tubulin heterodimer influence and promote the self-assembly. A detailed knowledge of such structural mechanisms would be helpful in drug design against neurodegenerative diseases, cancer, diabetes etc. In this work atomistic molecular dynamics simulations were used to investigate the fundamental dynamics of tubulin heterodimers in a sheet and a short microtubule utilizing well-equilibrated structures. The breathing motions of the tubulin heterodimers during assembly show that the movement at the lateral interface between heterodimers (wobbling) dominates in the lattice. The simulations of the protofilament curvature agrees well with recently published experimental data, showing curved protofilaments at polymerization of the microtubule plus end. The tubulin heterodimers exposed at the microtubule minus end were less curved and displayed altered interactions at the site of sheet closure around the outmost heterodimers, which may slow heterodimer binding and polymerization, providing a potential explanation for the limited dynamics observed at the minus end.

Keywords: Alzheimer’s disease; Diabetes; Equilibrium dynamics; Microtubules; Molecular dynamics; Protofilament; Small drugs.

Fig. 1

Guanosine-5’-triphosphate (GTP) and guanosine-5’-diphosphate (GDP)

Fig. 2

Systems simulated in this work to scale. a A protofilament (PF) sheet of nine heterodimers as viewed from three sides. Red ball-and stick representation shows residues constrained in their movements during simulations. b A microtubule consisting of 78 heterodimers (12 monomeric layers) as viewed from the side and from the plus-end

Fig. 3

Average root mean square deviation (RMSD) of the heterodimer in simulated systems for C${}_{\alpha }$ atoms. Top —PF sheet, middle—GDP microtubule, bottom—GTP microtubule. The shaded area depicts standard deviation of RMSD values

Fig. 4

Scree plot of the first 20 principal modes. Large arrow ($\downarrow$) indicates the first kink in the scree plot and small arrows ($\downarrow$) point to the second and the third kink in the plot. The inset shows accumulated dynamics as a ratio between a sum of all modes up to the current mode and a sum of all modes

Fig. 5

The top row shows the first three modes of $\alpha \beta$-tubulin heterodimers as seen in the microtubule lattice. Modes derived in MD-simulations from left to right: wobbling toward the microtubule axis, rotation around common monomer axis and compression along the common axis of monomers. Arrows in the compression mode qualitatively indicate the amplitude of compression for various parts of tubulin heterodimer. The middle and the bottom rows show motions of the tubulin heterodimer for the GDP and GTP-bound microtubules respectively. Two images for every mode show the tubulin heterodimer and motions as to see the largest displacement

Fig. 6

Projection of the concatenated $\alpha \beta$-tubulin heterodimer trajectory from PF-sheet simulations of the first three PC-modes. Subplots are depicting projections for various rows of heterodimers (colored in red): a plus-end heterodimers ($▽$), b central heterodimers ($◯$), c minus-end heterodimers ($△$). Colorbar is given in a logarithm of the number of points in every bin of the surface. Projections are measured as an RMSD between trajectory structure and corresponding eigenvector of the PC-mode, all axes are in nm. Black solid circle ($\bullet$) is an average projection of PC-modes in the beginning of the simulation

Fig. 7

Projection of the concatenated tubulin heterodimer trajectory from microtubule simulations of GDP-bound microtubule (top panel) and GTP-bound microtubule (bottom panel) of the first three PC-modes, namely axial rotation, intradimer bending and axial compression. The map is produced by taking logarithm of population in every bin of the plot. Here “n” is over all considered steps in the bin. The colorbar on the right is a logarithm of the number of points in the bin of the surface. Red crosses and black triangles depict minus- and plus-end corner heterodimers respectively. The data for corner heterodimers is downsampled by block-averaging to increase visibility. Black solid circle is an average projection of PC-modes in the beginning of the simulation. All axes are in nm. Bottom right panel depicts microtubule and two corner heterodimers

Fig. 8

PCA on the trajectory combining GDP-MT and GTP-MT. Projections of the outmost heterodimers for every system are also shown. Here “n” is over all considered steps in the bin