Modeling oscillatory microtubule polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here, simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates, and typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of guanosine triphosphate liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold, oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold, a so-called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.

Microtubule nucleation from stable tubulin oligomers

Microtubule assembly from purified tubulin preparations involves both microtubule nucleation and elongation. Whereas elongation is well documented, microtubule nucleation remains poorly understood because of difficulties in isolating molecular intermediates between tubulin dimers and microtubules. Based on kinetic studies, we have previously proposed that the basic building blocks of microtubule nuclei are persistent tubulin oligomers, present at the onset of tubulin assembly. Here we have tested this model directly by isolating nucleation-competent cross-linked tubulin oligomers. We show that such oligomers are composed of 10-15 laterally associated tubulin dimers. In the presence of added free tubulin dimers, several oligomers combine to form microtubule nuclei competent for elongation. We provide evidence that these nuclei have heterogeneous structures, indicating unexpected flexibility in nucleation pathways. Our results suggest that microtubule nucleation in purified tubulin solution is mechanistically similar to that templated by gamma-tubulin ring complexes with the exception that in the absence of gamma-tubulin complexes the production of productive microtubule seeds from tubulin oligomers involves trial and error and a selection process.

Microtubules: strange polymers inside the cell

This paper provides a consistent approach (within a one-dimensional approximation) to the description of the evolution of the microtubule length at both low- and high-density concentrations. We derive general master-type equations which are based on the key chemical reactions involved in the assembly and disassembly of microtubules. The processes included are: polymerization and depolymerization of a single protein dimer, catastrophic disassembly affecting an a piori arbitrary number of dimers, and a rescue event. Solutions of the derived equations are compared with the existing experimental data. Important conclusions linking the emergence of bell-shaped histograms with the nature of catastrophe and rescue phenomena are drawn. Finally, we briefly discuss the emergence of coherent phenomena in microtubule polymerization, i.e., a transition to collective oscillations in the assembly and disassembly effects.

Low resolution structure of microtubules in solution

The structure of microtubules has been characterized to 3 nm resolution employing time-resolved X-ray scattering. This has revealed detailed structural features of microtubules not observed before in solution. The polymerization of highly purified tubulin, induced by the antitumour drug taxol, has been employed as a microtubule model system. This assembly reaction requires Mg2+, is optimal at a 1:1 taxol to tubulin heterodimer molar ratio, proceeds with GTP or GDP and is intrinsically reversible. The X-ray scattering profiles are consistent with identical non-globular alpha and beta-tubulin monomers ordered within the known helical surface lattice of microtubules. Purified tubulin-taxol microtubules have a smaller mean diameter (approx. 22 nm) than those induced by microtubule associated proteins or glycerol (approx. 24 nm), but nearly identical wall substructure to the resolution of the measurements. This is because the majority of the former consist of only 12 protofilaments instead of the typical 13 protofilaments, as confirmed by electron microscopy of thin-sectioned, negatively stained and ice-embedded taxol microtubules. It may be concluded that taxol induces a slight reduction of the lateral contact curvature between tubulin monomers. The main fringe pattern observed in cryo-electron micrographs is consistent with a simple 12 protofilament 3-start skewed lattice model. Cylindrical closure of this lattice can be achieved by tilting the lattice 0.8 degrees with respect to the microtubule axis. The closure implies a discontinuity in the type of lateral contacts between the tubulin monomers (regardless of whether these are of the -alpha-beta- or the -alpha-alpha-/-beta-beta- type), which indicates that lateral contacts and the subunit specificity of taxol binding are, to a large degree, equivalent.

Characterization of microtubule protofilament numbers. How does the surface lattice accommodate?

Frozen-hydrated specimens of microtubules assembled in vitro were observed by cryoelectron microscopy. Specimens were of both pure tubulin, and of microtubule protein isolated by three cycles of assembly and disassembly. It is shown that the characteristic image contrast of individual microtubules allows the microtubule protofilament number to be determined unambiguously. Microtubules with 13, 14 and 15 protofilaments are observed to coexist in specimens prepared under various assembly conditions. Confirmation of these results is obtained by observations of thin sections of pelleted samples fixed and stained using the glutaraldehyde/tannic acid technique. Images of individual microtubules show both characteristic contrast profiles across their width and typical variations of these profiles along their length. The profiles across the images indicate the protofilament number of the microtubule. The lengthwise variations indicate how the protofilaments are aligned with respect to the microtubule axis giving what has previously been called a supertwist. In 13 protofilament microtubules the protofilaments are paraxial. In 14 and 15 protofilament microtubules, the protofilaments are skewed with respect to the microtubule axis. The skew is greater for the 15 protofilament case than for 14 protofilaments. The skew allows the extra protofilaments to be accommodated by the surface lattice. These results should also be relevant to situations in vivo.