Actomyosin Regulation and Symmetry Breaking in a Model of Polarization in the Early Caenorhabditis elegans Embryo

Abstract

Polarization, whereby a cell defines a spatial axis by segregating specific determinants to distinct regions, is an essential and highly conserved biological process. The process of polarization is initiated by a cue that breaks an initially symmetric distribution of determinants, allowing for a spatially asymmetric redistribution. The nature of this cue is currently not well understood. Utilizing the conservation of polarization process and its determinants, we theoretically investigate the nature of the cue and the regulation of contractility that enables the establishment of polarity in early embryos of the nematode worm Caenorhabditis elegans (C. elegans). Our biologically based model, which consists of coupled partial differential equations, suggests that a biochemical but not mechanical cue is sufficient for symmetry breaking, and inhibition of contractile elements by specific determinants is needed for sustained spatial redistribution.

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

“…A third limitation is that there are many feedback loops between PAR-3 clustering and other proteins which we have ignored. During the polarization of the embryo, PAR-3 proteins promote local association of PAR-6/PKC-3 with active CDC-42 GTPase (Kravtsova and Dawes, 2014; Lang and Munro, 2017; Sailer et al, 2015; Seirin-Lee et al, 2020). This process may alter the transport of PAR-3 clusters as it binds and unbinds with other proteins or modulates the local flow of the cortex through GTPase signaling (which affects the cytoskeleton).…”

“…A number of models have been developed to understand properties of the PAR signaling network. These models are typically partial differential equation models that capture the diffusion, biochemical reactions, and transport due to flow in the system (Aras et al, 2018; Dawes and Iron, 2013; Geßele et al, 2020; Goehring et al, 2011; Gross et al, 2018; Kravtsova and Dawes, 2014; Seirin-Lee et al, 2020; Wigbers et al, 2020). Goehring et al (2011) for example found that a wave-pinning like mechanism (Holmes and Edelstein-Keshet, 2016; Holmes et al, 2012a,b, 2017; Jilkine and Edelstein-Keshet, 2011; Jilkine et al, 2007; Lin et al, 2012; Marée et al, 2006; Mata et al, 2013; Mori et al, 2008; Zmurchok and Holmes, 2020) may be responsible for stabilization of the anterior-posterior border.…”

Efficient parameter generation for constrained models using MCMC

“…We demonstrate the high speed property (1) of the proposed MCMC on a number of models with varying type of constraints, including bistability (models from 4 , 9 along with two newly constructed models), emergence of oscillations (model from 22 ), and the ability to reproduce a given cell pattern (model from 20 ) (Fig. 1 B).…”

“…Some of these systems are known to exhibit specific types of behavior, attracting interest from both natural and mathematical sciences. For instance, consider bistability, a key feature of many natural processes studied in physics 1 , chemistry 2 , material science 3 , and biology, over a range of spatial and temporal scales [4][5][6][7][8][9] . Any mathematical model of a bistable system is constrained by its ability to reproduce a bistable behavior upon simulations, the minimal requirement that such a model needs to satisfy to meaningfully reflect the underlying natural process.…”

Delineating the mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

“…Using a combination of computational and experimental techniques, Goehring et al (2011) demonstrated that the advective flow of actomyosin in the cortex of C. elegans zygote is a critical trigger and facilitator of the robust segregation of PAR proteins and established a mechanochemical scheme for cell polarization [176] , [177] . In other research, Kravtsova et al (2014) provided theoretical evidence that actomyosin contractility is required to stabilize the polarity pattern and that this mechanical cue can only break cell symmetry in the presence of certain chemical interactions [178] . Seirin-Lee et al (2015) examined the morphometric features of the polarity distribution and found that polarity proteins’ advective transport in the membrane and cytosol and their mass concentrations in these regions regulate the width of the posterior domain [179] .…”