Balancing reaction-diffusion network for cell polarization pattern with stability and asymmetry*

Cell polarization is a critical process that separates molecules into two distinct regions in prokaryotic and eukaryotic cells, guiding biological events like cell division and cell differentiation. Although some underlying antagonistic reaction-diffusion networks capable of setting up cell polarization have been identified experimentally and theoretically, it is still elusive how the pattern stability and asymmetry can be modulated. Here, we first numerically demonstrate that the polarized pattern generated by an antagonistic 2-node network would collapse into a homogeneous distribution when single-sided self-regulation, single-sided additional regulation, or unequal system parameters are added. Interestingly, the combination of two of those unbalanced modifications can stabilize the polarized pattern. To test if this fundamental rule governs the network programming in the real system, we conduct an elaborate literature search to reconstruct the cell polarization network in the nematode Caenorhabditis elegans zygote, where a 4-node network with full mutual inhibitions between anterior and posterior is modified by a mutual activation in the anterior and an additional mutual inhibition between the anterior and the posterior, constituting a 5-node network. Numerical simulation further reveals the balance between these two modifications, which jointly maintain pattern stability and enhance pattern asymmetry. Our computational framework successfully simulates the simple 2-node network and C. elegans 5-node network in wild-type and perturbed embryos, providing new insight into the design principles of both natural and artificial cell polarization systems. Last but not least, we build user-friendly software, PolarSim, to facilitate the exploration of networks with alternative node numbers, parameter values, and regulation pathways.