Design Principles for Biological Adaptation: A Systems and Control-Theoretic Treatment

Establishing a mapping between (from and to) the functionality of interest and the underlying network structure (design principles) remains a crucial step toward understanding and design of bio-systems. Perfect adaptation is one such crucial functionality that enables every living organism to regulate its essential activities in the presence of external disturbances. Previous approaches to deducing the design principles for adaptation have either relied on computationally burdensome brute-force methods or rule-based design strategies detecting only a subset of all possible adaptive network structures. This chapter outlines a scalable and generalizable method inspired by systems theory that unravels an exhaustive set of adaptation-capable structures. We first use the well-known performance parameters to characterize perfect adaptation. These performance parameters are then mapped back to a few parameters (poles, zeros, gain) characteristic of the underlying dynamical system constituted by the rate equations. Therefore, the performance parameters evaluated for the scenario of perfect adaptation can be expressed as a set of precise mathematical conditions involving the system parameters. Finally, we use algebraic graph theory to translate these abstract mathematical conditions to certain structural requirements for adaptation. The proposed algorithm does not assume any particular dynamics and is applicable to networks of any size. Moreover, the results offer a significant advancement in the realm of understanding and designing complex biochemical networks.