Antithetic Integral Feedback ensures robust perfect adaptation in noisy biomolecular networks

TL;DR

This paper introduces antithetic integral feedback, a novel molecular regulation motif that ensures robust perfect adaptation in noisy biochemical networks, leveraging stochastic noise for improved regulation and minimal molecular resources.

Contribution

It develops a new regulation theory at the molecular level, proposing a simple, noise-exploiting feedback motif that guarantees stability and adaptation with low molecular count.

Findings

Ensures robust perfect adaptation in noisy networks.

Can be implemented with few molecules, reducing metabolic load.

Exploits noise to enhance regulation where deterministic methods fail.

Abstract

Homeostasis is a running theme in biology. Often achieved through feedback regulation strategies, homeostasis allows living cells to control their internal environment as a means for surviving changing and unfavourable environments. While many endogenous homeostatic motifs have been studied in living cells, some other motifs may remain under-explored or even undiscovered. At the same time, known regulatory motifs have been mostly analyzed at the deterministic level, and the effect of noise on their regulatory function has received low attention. Here we lay the foundation for a regulation theory at the molecular level that explicitly takes into account the noisy nature of biochemical reactions and provides novel tools for the analysis and design of robust homeostatic circuits. Using these ideas, we propose a new regulation motif, which we refer to as {\em antithetic integral feedback, and demonstrate its effectiveness as a strategy for generically regulating a wide class of reaction networks. By combining tools from probability and control theory, we show that the proposed motif preserves the stability of the overall network, steers the population of any regulated species to a desired set point, and achieves robust perfect adaptation -- all with low prior knowledge of reaction rates. Moreover, our proposed regulatory motif can be implemented using a very small number of molecules and hence has a negligible metabolic load. Strikingly, the regulatory motif exploits stochastic noise, leading to enhanced regulation in scenarios where noise-free implementations result in dysregulation. Finally, we discuss the possible manifestation of the proposed antithetic integral feedback motif in endogenous biological circuits and its realization in synthetic circuits.