Mechanisms of microtubule dynamics and force generation examined with computational modeling and electron cryotomography

Abstract

Microtubules are dynamic tubulin polymers responsible for many cellular processes, including the capture and segregation of chromosomes during mitosis. In contrast to textbook models of tubulin self-assembly, we have recently demonstrated that microtubules elongate by addition of bent guanosine triphosphate tubulin to the tips of curving protofilaments. Here we explore this mechanism of microtubule growth using Brownian dynamics modeling and electron cryotomography. The previously described flaring shapes of growing microtubule tips are remarkably consistent under various assembly conditions, including different tubulin concentrations, the presence or absence of a polymerization catalyst or tubulin-binding drugs. Simulations indicate that development of substantial forces during microtubule growth and shortening requires a high activation energy barrier in lateral tubulin-tubulin interactions. Modeling offers a mechanism to explain kinetochore coupling to growing microtubule tips under assisting force, and it predicts a load-dependent acceleration of microtubule assembly, providing a role for the flared morphology of growing microtubule ends.

Fig. 1. Brownian dynamics analysis of the properties of isolated tubulin PFs.

a Visualization of a single PF. Darker and lighter spheres depict β- and α-tubulins, respectively. For illustration, tubulins in other PFs of the MT, which were not part of this simulation, are shown as semi-transparent spheres. The bottom tubulin dimer of the simulated PF is fixed in place, while the other tubulins experience Brownian fluctuations. b Potential energy of PF bending, described with the formula above the graph. c Predicted dependence of the frequency of PF straightening by thermal fluctuations on the PF bending stiffness. Straightening frequency is calculated as the number of passages per second from curved (θ > 0.15 rad) to straight (θ ≤ 0.05 rad) configurations at the lowest nonrestrained tubulin monomer in the PF (black arrow in a). Data represent mean ± s.d. from three repeats of each simulation. Source data are provided as a Source Data file. d Predicted dependence of the frequency of PF straightening by thermal fluctuations on the length of the PF. The frequency is scored as in panel c. Simulations were carried out with PF bending stiffness of 174 kcal mol⁻¹ rad⁻². Data represent mean ± s.d. from three repeats of each simulation. Source data are provided as a Source Data file. e A single PF experiencing an extensive force. In this case, the PF cannot withstand force, F, with which the purple sphere is dragged upwards. f Dependence of the force a PF can withstand, as a function of the PF bending stiffness, expressed in two ways on the two X-axes.

Fig. 2. Role of lateral tubulin activation energy for MT dynamics and force generation.

a Visualization of an MT, β- and α-tubulins depicted as in Fig. 1. Each tubulin monomer has two lateral and two longitudinal interaction sites (black dots). b Energy of longitudinal interaction between tubulin monomers as a function of distance between the interaction sites. Formula below describes the shape of longitudinal tubulin energy potentials. c A set of energy curves, describing lateral tubulin−tubulin interactions as a function of distance with different lateral activation energies (a_lat). Strength of the lateral bond, b_lat, equals 6 kcal mol⁻¹ in this example. d Dependence of MT growth or shortening rate on the lateral bond strength, b_lat, for different lateral barrier parameters, a_lat. Numbers less than zero imply shortening. e Dependence of PF curl length on the strength of the lateral bond, b_lat, graphed for several lateral activation energies, a_lat. f Dependence of MT shortening rate on opposing force in simulations. The strength of the lateral bonds between the tubulins (b_lat) was set to be weak, representing tubulins in the GDP state. Specifically, with each activation barrier height (a_lat), b_lat was selected to enable shortening at ~400 nm s⁻¹. See Source Data file for a full list of parameter values in all simulations. g Dependence of MT growth rate on opposing force in simulation and experiment. Tubulins were configured to have strong lateral bonds, b_lat = 8 kcal mol⁻¹, to represent the GTP-state of tubulins. No GTP hydrolysis was allowed. Data points, describing simulation results in all graphs in this figure, represent mean ± s.d. based on 3–6 repeats of each simulation. Source data are provided as a Source Data file.

Fig. 3. Possible mechanisms of MT lattice destabilization by GTP hydrolysis.

a Visualization of the starting configuration of an MT in the tubulin dilution simulations. GDP-bound tubulin dimers are shown with light and dark green spheres. GTP-bound dimers are shown with yellow and orange spheres. b Dependence of MT length on time in three independent repeats of the tubulin dilution simulation: PF bending stiffness is identical for GTP- and GDP-bound PFs and equal to 174 kcal mol⁻¹ rad⁻²; lateral bond strength, b_lat equals 8 and 4.7 kcal mol⁻¹ for GTP- and GDP-bound tubulins, respectively. Blue arrow indicates a brief pause of rapid GDP-MT lattice disassembly at a random GTP-tubulin remnant, which happened occasionally in some simulation runs (also see Supplementary Movie 3). c Dependence of the total number of remaining GTP-tubulin subunits on time in three independent repeats of tubulin dilution simulation from panel b. d Dependence of MT length on time in two independent repeats of tubulin dilution simulation: the lateral bond strength is set to 4.7 kcal mol⁻¹, regardless of the bound nucleotide; PF bending stiffnesses are 78 and 174 kcal mol⁻¹ rad⁻² for GTP- and GDP-bound PFs, respectively. e Dependence of the total number of remaining GTP-tubulin subunits on time in two independent repeats of tubulin dilution simulation from panel d.

Fig. 4. Dependence of MT assembly and disassembly on free tubulin concentration.

a MT growth rate vs. tubulin concentration in experiments and in the simulation. GTP hydrolysis constant was set to zero. GTP-tubulins were assumed to have strong lateral bonds: b_lat = 8 kcal mol⁻¹. Full list of model parameters is given in Supplementary Table 1 and Source Data file. b Dependence of MT shortening rates on free GTP-tubulin concentration in published experiments and in simulation. At the onset of the simulation MTs were composed entirely of GDP-tubulins. They depolymerized in spite of transient additions of GTP-tubulins at the tips of curved PFs. Full list of model parameters is given in Supplementary Table 1 and Source Data file. c Shapes of growing GTP-MT tips in simulations at three tubulin concentrations. d, e GTP-PF curl lengths and average PF curl curvatures as functions of tubulin concentration in simulations. Data points, describing simulation results in all graphs in this figure, represent mean ± s.d. based on 3–6 repeats of each simulation. Source data are provided as a Source Data file.

Fig. 5. Quantitative analysis of PF tip shapes on MTs grown at three tubulin concentrations.

a–c Tomographic slices and models of representative MTs elongating from axonemal doublet MTs at three concentrations of free tubulin. Red crosses mark the origins of the coordinate systems used. Bars, 25 nm. d–f LOESS-smoothed traces of PFs from 136 growing MTs (49 MTs at 10 μM, 37 MTs at 20 μM, and 50 MTs at 40 μM). Ns numbers of PFs traced. Raw tracing coordinates are provided as a Source Data file. g Average curvatures of PFs as a function of free tubulin concentration. Means ± s.d. h Average curled PF lengths as a function of free tubulin concentration. Means ± s.d. Source data, describing PF curvatures and lengths, are provided as a Source Data file.

Fig. 6. Effects of an MT polymerase and assembly-inhibiting drugs on PF tips.

a, b Tomographic slices and models of representative MTs elongating from axonemal doublet MTs in presence of 20 μM free tubulin and two concentrations of TOG12 protein. Bars, 50 nm. c, d LOESS-smoothed traces of PFs from 16 MTs growing in the presence of 1 μM TOG12 protein and 12 MTs growing in the presence of 3 μM TOG12 protein, respectively. N numbers of PFs traced. e, f Tomographic slices and models of representative MTs elongating from axonemal doublet MTs in the presence of 20 μM free tubulin and 10 nM paclitaxel or 10 nM epothilone. g, h LOESS-smoothed traces of PFs from 22 MTs growing in the presence of 10 nM paclitaxel and 47 MTs growing in the presence of 10 nM epothilone, respectively. N numbers of PFs traced. i Tomographic slices and models of representative MTs elongating from axonemal doublet MTs in the presence of 20 μM free tubulin and 1 μM paclitaxel. j LOESS-smoothed traces of PFs from 36 MTs growing in the presence of 1 μM paclitaxel. N numbers of PFs traced. See Supplementary Table 3 for mean curvatures and PF lengths in each condition. Raw tracing coordinates for all conditions are provided as a Source Data file.

Fig. 7. Raggedness of MT tips grown in different conditions.

a Schematic explaining the MT end raggedness parameter. Dashed lines mark the origins of PF curls. Double-ended arrows show distance from a fixed arbitrary point to the start of each PF curl. Raggedness is defined as the standard deviation of positions of PF curve starts. b Series of snapshots, demonstrating growing GTP-MT end shapes in simulations with high and low lateral activation energies for lateral bonding potentials. More ragged ends tend to form when the activation barrier is high. c Dependence of model GTP-MT end raggedness on tubulin concentration. Data points represent mean ± s.d. from thee repeats of each simulation; source data are provided as a Source Data file. d Experimental data on MT raggedness under various experimental conditions. Black points show dependence of MT end raggedness on tubulin concentration. Black line is a linear fit to these data. Zero tubulin concentration (cross) corresponds to isothermal dilution experiments. Open circle shows data for MT growth in the presence of GMPCPP, blue triangle is growth in α1B/βI+βIVb tubulin. All data points show mean ± s.e.m. based on measurements for 15–97 MTs; source data are provided as a Source Data file. All data points show mean ± s.e.m. e Tomographic slices and models of representative MTs elongating from axonemal doublet MTs in the presence of 20 μM free α1B/βI+βIVb tubulin.

Fig. 8. MT growth with flared PFs can sustain assisting load and be accelerated by it.

a Snapshots from a simulation of GTP-MT growth with long PF curls in the presence of a Dam1 ring. GTP hydrolysis is turned off. b Snapshots from a simulation of GTP-MT growth with ring and short PF curls. GTP hydrolysis is turned off. c Dependence of GTP-MT growth on assisting force in the model (10 µM tubulin, 37 °C) and experimental data (15 µM tubulin, 23 °C). The difference in MT growth rates between the simulation and experiments is likely due to the distinct temperature conditions. Simulation data points represent mean ± s.e.m. based on three repeats of each simulation; source data are provided as a Source Data file. d Schematic illustrating the proposed principle of synchronization of growing and shortening MTs during chromosome oscillations in mitosis.