Universal structures for embedded integral control in biological adaptation

Abstract

At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. While adaptation is known to require some form of embedded integral control, current approaches can only identify an internal integral structure in simple special cases. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. We present a universal method to test for adaptation capacity, and for detecting the adaptation-conferring integrals, in any CRN. Using this new approach, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signalling networks across all domains of life, and for the design of synthetic biosystems.

Protein-protein complexes can undermine ultrasensitivity-dependent biological adaptation

“…Unlike Balancer nodes, which are relatively easy to construct [40], opposer nodes are now acknowledged to be notoriously difficult to create at the level of intermolecular interactions, in the form of chemical reaction networks (CRNs) [39]. The Ma et al study [8] used the commonly-employed simplification of Michaelis-Menten kinetics to model three-node networks of interlinked covalent-modification cycles, and used this modelling approximation to suggest that an ultrasensitivity-generating mechanism suffices as an opposer node (or a ‘buffer node’ in the language of that early study).…”

“…We call this maximum possible value its conversion potential [45] (see Fig 3). It is now well-established that all RPA-capable networks have at least one 'non-RPA' variable, which acts as an 'actuator' node [40].…”

“…On closer examination of parameter sets associated with RPA, we found that the Michaelis constants, K A1 and K A2 , as well as the catalytic constants, k A1 and k A2 , for the input/output cycle, had a significant impact on the ability of the network to exhibit RPA and on the RPA range. Unlike Balancer nodes, which are relatively easy to construct [40], opposer nodes are now acknowledged to be notoriously difficult to create at the level of intermolecular interactions, in the form of chemical reaction networks (CRNs) [39]. The Ma et al study [8] used the commonly-employed simplification of Michaelis-Menten kinetics to model three-node networks of interlinked covalent-modification cycles, and used this modelling approximation to suggest that an ultrasensitivity-generating mechanism suffices as an opposer node (or a 'buffer node' in the language of that early study).…”

“…Antithetic integral control is a universal ‘opposer node’ that confers an exact (i.e. ‘perfect’) form of RPA, which has been identified in endogenous cellular networks in the form of sigma/anti-sigma factors [40], for instance. Antithetic integral control has also been implemented successfully in a variety of synthetic bionetworks [2, 44, 43, 21].…”

“…A central question in biochemical network theory remains how complex organisms incorporate these well-defined RPA-conferring network structures into their signalling networks [4, 39]. Until now, most known Balancer modules have been identified in very small signalling networks such as two-component regulatory systems in bacteria [29, 40], and two- or three-node transcription networks across a variety of cell types [41, 42]. By contrast, RPA in large and highly complex signalling networks such as mammalian signal transduction networks is thought to depend on feedback structures, and hence, Opposer modules [1, 4, 39].…”