Modelling the Establishment of PAR Protein Polarity in the One-Cell C. elegans Embryo

TL;DR

This paper presents a mathematical model of PAR protein polarity establishment in C. elegans embryos, highlighting the roles of cortical actomyosin contraction and cytoskeletal asymmetry in polarization.

Contribution

The authors develop a novel reaction-diffusion model coupling PAR protein dynamics with actomyosin contraction, providing insights into cortical and cytoplasmic polarity mechanisms.

Findings

Model explains cortical PAR dynamics in wild-type and mutant embryos.

Cytoplasmic PAR polarity requires additional mechanisms beyond cortical interactions.

Cytoskeletal asymmetry in the cytoplasm is predicted to be crucial for proper PAR localization.

Abstract

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.