Predicting Perfect Adaptation Motifs in Reaction Kinetic Networks

Adaptation and compensation mechanisms are important to keep organisms fit in a changing environment. "Perfect adaptation" describes an organism's response to an external stepwise perturbation by resetting some of its variables precisely to their original preperturbation values. Examples of perfect adaptation are found in bacterial chemotaxis, photoreceptor responses, or MAP kinase activities. Two concepts have evolved for how perfect adaptation may be understood. In one approach, so-called "robust perfect adaptation", the adaptation is a network property (due to integral feedback control), which is independent of rate constant values. In the other approach, which we have termed "nonrobust perfect adaptation", a fine-tuning of rate constant values is needed to show perfect adaptation. Although integral feedback describes robust perfect adaptation in general terms, it does not directly show where in a network perfect adaptation may be observed. Using control theoretic methods, we are able to predict robust perfect adaptation sites within reaction kinetic networks and show that a prerequisite for robust perfect adaptation is that the network is open and irreversible. We applied the method on various reaction schemes and found that new (robust) perfect adaptation motifs emerge when considering suggested models of bacterial and eukaryotic chemotaxis.