  At the one-cell stage, the C. elegans embryo becomes polarized along the
anterior-posterior axis. The PAR proteins form complementary anterior and
posterior domains in a dynamic process driven by cytoskeletal rearrangement.
Initially, the PAR proteins are uniformly distributed throughout the embryo.
Following a cue from fertilization, cortical actomyosin contracts towards the
anterior pole. PAR-3/PAR-6/PKC-3 (the anterior PAR proteins) become restricted
to the anterior cortex. PAR-1 and PAR-2 (the posterior PAR proteins) become
enriched in the posterior cortical region. We present a mathematical model of
this polarity establishment process, in which we take a novel approach to
combine reaction-diffusion dynamics of the PAR proteins coupled to a simple
model of actomyosin contraction. We show that known interactions between the
PAR proteins are sufficient to explain many aspects of the observed cortical
PAR dynamics in both wild-type and mutant embryos. However, cytoplasmic PAR
protein polarity, which is vital for generating daughter cells with distinct
molecular components, cannot be properly explained within such a framework. We
therefore consider additional mechanisms that can reproduce the proper
cytoplasmic polarity. In particular we predict that cytoskeletal asymmetry in
the cytoplasm, in addition to the cortical actomyosin asymmetry, is a critical
determinant of PAR protein localization.
