  Microtubule asters - radial arrays of microtubules organized by centrosomes -
play a fundamental role in the spatial coordination of animal cells. The
standard model of aster growth assumes a fixed number of microtubules
originating from the centrosomes. However, aster morphology in this model does
not scale with cell size, and we recently found evidence for non-centrosomal
microtubule nucleation. Here, we combine autocatalytic nucleation and
polymerization dynamics to develop a biophysical model of aster growth. Our
model predicts that asters expand as traveling waves and recapitulates all
major aspects of aster growth. As the nucleation rate increases, the model
predicts an explosive transition from stationary to growing asters with a
discontinuous jump of the growth velocity to a nonzero value. Experiments in
frog egg extract confirm the main theoretical predictions. Our results suggest
that asters observed in large frog and amphibian eggs are a meshwork of short,
unstable microtubules maintained by autocatalytic nucleation and provide a
paradigm for the assembly of robust and evolvable polymer networks.
