  Many cells contain non-centrosomal arrays of microtubules (MT), but the
assembly, organisation and function of these arrays are poorly understood. We
present the first theoretical model for the non-centrosomal MT cytoskeleton in
$Drosophila$ oocytes, in which $bicoid$ and $oskar$ mRNAs become localised to
establish the anterior-posterior body axis. Constrained by experimental
measurements, the model shows that a simple gradient of cortical MT nucleation
is sufficient to reproduce the observed MT distribution, cytoplasmic flow
patterns and localisation of $oskar$ and naive $bicoid$ mRNAs. Our simulations
exclude a major role for cytoplasmic flows in localisation and reveal an
organisation of the MT cytoskeleton that is more ordered than previously
thought. Furthermore, modulating cortical MT nucleation induces a bifurcation
in cytoskeletal organisation that accounts for the phenotypes of polarity
mutants. Thus, our three-dimensional model explains many features of the MT
network and highlights the importance of differential cortical MT nucleation
for axis formation.
