Speaker
Description
Boolean networks, first introduced by Kauffman as models for gene regulatory networks, have gained widespread popularity for their ability to capture complex biological behaviors through simple logical rules. A systematic investigation of these biological models suggests that they are incredibly robust. In particular, they are resilient to perturbations and tend to reach the same phenotype despite small disturbance. An explanation of this phenomenon was first given by Kauffman, who showed empirically that a network's connectivity determines the stability of the Boolean network. This was further expanded on by Derrida, who provided a theoretical explanation for the effect of connectivity. This was succeeded by many empirical studies that explored the relationship between a network's structural parameters and its stability.
Building upon this foundation, our work delves into the intrinsic trade-off between phenotypic complexity and network stability. We extend a conjecture proposed by Willadsen, Triesch, and Wiles, proving that entropy—acting as a proxy for complexity—provides a tight asymptotic upper bound for coherence, our measure of stability. By deriving this Pareto frontier between complexity and stability, we show that natural gene regulatory networks are not merely stable—they are highly optimized, consistently residing on or near this theoretical limit.
