The Mathematics of Life’s Robustness: Internal Models and Perfect Adaptation in Biological Control

Venue: Stellenbosch University

Abstract: Biological systems achieve remarkable robustness: cells maintain homeostasis and adapt precisely to environmental changes despite stochasticity, delays, and parametric uncertainty. How do they accomplish this, and how can we replicate such capabilities in synthetic systems? In this lecture, I will present a theoretical framework for robust perfect adaptation (RPA) in biomolecular networks, revealing deep structural parallels between biological regulation and classical control theory. I will introduce a universal internal model principle (IMP) for living systems, showing how integral feedback and its generalizations emerge naturally as the only architectures capable of achieving kinetics-independent robust perfect adaptation. Using a linear-algebraic characterization of network stoichiometry, I will identify the necessary and sufficient structural conditions for maximal adaptation in both deterministic and stochastic settings. Beyond theory, I will discuss synthetic implementations of these principles in living cells, where engineered integral feedback controllers achieve robust regulation of protein expression and growth. Together, these results demonstrate that the logic of control—long the foundation of engineered systems—is also the mathematics of life’s stability, offering a blueprint for designing adaptive, intelligent biological systems.

Co-hosted by SACAC and NITheCS