Microtubules (MTs), a major component of the eukaryotic cytoskeleton, are hollow tubes composed of on average 13 protofilaments. The protofilaments longitudinally assemble from tubulin dimers in the presence of GTP (Guanosine triphosphate). In vivo, MTs self-organize into the spindles and asters essential for mitosis and the parallel arrays and stripes necessary for directing early processes in embryogenesis. Many in vitro studies of MT organization have been performed in order to elucidate the mechanisms underlying the formation of these structures. Of particular relevance here are the striped birefringence patterns that spontaneously form in MT solutions without motors. Hitt et al. attributed these patterns to the formation of nematic liquid crystalline domains. Tabony et al., on the other hand, proposed that a reaction-diffusion based mechanism drives the alignment of individual MTs. More recent investigations imply a starkly different scenario in which the local MT alignment occurs through a more collective process. Quantitative fluorescence and birefringence microscopy revealed that MTs, initially aligned by means of static magnetic field or convective flow, form bundles that spontaneously buckle in coordination with their neighbors. The nesting of the buckled bundles gives rise to MT density and orientation variations that can quantitatively account for the stripes.

We present a mechanical model of the spontaneous buckling process and use measurements of the time evolution of the striped pattern to assert that microtubule polymerization forces drive the buckling. The model considers the instability of a single microtubule bundle under compressive stress, embedded in an elastic network formed by both bundled and unbundled microtubules. The buckling wavelength selected depends upon the elastic properties of the bundle and the network in a manner consistent with scaling arguments presented previously. Time lapse phase contrast and birefringence microscopy indicate that the bundles elongate uniformly along their length nearly linearly in time while maintaining constant radii implying that bundles grow through the polymerization of the individual MTs comprising them. Within the model and known force velocity curves for polymerizing MTs, the measured elongation rate and estimated buckling force are consistent with this polymerization producing the compressional load necessary for the buckling.