Canalization and competition: the cornerstone of genetic network's dynamic stability and evolution

Grasping the fundamental dynamic property is a crucial approach for understanding living systems. Here we conduct a comprehensive study into the relationship between regulatory modes and dynamic features of gene networks. Our findings indicate that conditional constraints and competition, corresponding to canalizing and threshold regulating modes respectively, play pivotal roles in driving gene networks towards criticality. Particularly, they effectively rescue biosystems from disordered area as source of evolutionary driving force. By employing variant Kauffman models, order parameters, and stability analysis, we provide sufficient numerical evidence demonstrating the diverse and distinctive capabilities of regulatory modes in stabilizing systems. Our findings give the most systematic analysis to date on the dynamic atlas of regulatory modes, offering a framework-independent proof of genetic networks operating at the edge of chaos with evolutionary implications. Furthermore, we discus the bridge between criticality and canalizing/threshold regulating modes and propose a reasonable scheme for generating model.