Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

Order from chaos: cellular asymmetries explained with modelling

Molecules inside cells are subject to physical forces and undergo biochemical interactions, continuously changing their physical properties and dynamics. Despite this, cells achieve highly ordered molecular patterns that are crucial to regulate various cellular functions and to specify cell fate. In the Caenorhabditis elegans one-cell embryo, protein asymmetries are established in the narrow time window of a cell division. What are the mechanisms that allow molecules to establish asymmetries, defying the randomness imposed by Brownian motion? Mathematical and computational models have paved the way to the understanding of protein dynamics up to the 'single-molecule level' when resolution represents an issue for precise experimental measurements. Here we review the models that interpret cortical and cytoplasmic asymmetries in the one-cell C. elegans embryo.

Design principles for selective polarization of PAR proteins by cortical flows

Clustering of membrane-associated molecules is thought to promote interactions with the actomyosin cortex, enabling size-dependent transport by actin flows. Consistent with this model, in the Caenorhabditis elegans zygote, efficient anterior segregation of the polarity protein PAR-3 requires oligomerization. However, through direct assessment of local coupling between motion of PAR proteins and the underlying cortex, we find no links between PAR-3 oligomer size and the degree of coupling. Indeed, both anterior and posterior PAR proteins experience similar advection velocities, at least over short distances. Consequently, differential cortex engagement cannot account for selectivity of PAR protein segregation by cortical flows. Combining experiment and theory, we demonstrate that a key determinant of differential segregation of PAR proteins by cortical flow is the stability of membrane association, which is enhanced by clustering and enables transport across cellular length scales. Thus, modulation of membrane binding dynamics allows cells to achieve selective transport by cortical flows despite widespread coupling between membrane-associated molecules and the cell cortex.