Designing biochemical networks with adaptation

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Steffen Waldherr, Stefan Streif, Frank Allgwer

Free University Berlin, Germany

A biomolecular network is called adaptive if a specific output concentration returns to the original value after a transient response even under a persisting stimulus. Adaptation is an important mechanism to reset cellular sensing systems to a basal level, and serves to have cells react to changes in a stimulus only, but not to specific constant stimulus values. Biochemical networks with adaptation have for example been studied in eukaryotic gradient sensing, bacterial chemotaxis, yeast osmo regulation, and cellular signal transduction via the MAP kinase pathway. From a systems perspective, the conditions for a biochemical network to be adaptive are well known and straightforward to check on a mathematical model of the considered network. These conditions typically imply the existence of an internal feedback or feedforward circuit structure in the network. In this contribution, we look at the design problem for adaptation in biochemical networks. In contrast to the problem of checking whether a given network is adaptive, designing a network for adaptation is more challenging, especially for medium and large-scale networks. We present a systematic approach, based on a linear network approximation and the notion of kinetic perturbations, to design reaction rate modifications that make a biochemical reaction network adaptive. The approach indicates all interactions in the network where a modification can yield adaptation, and provides specific values for such modifications. An advantage of our approach in the context of synthetic biology is that both the stoichiometry as well as the steady state in the unstimulated system are not perturbed by these modifications. Thus, a predesigned network can be tuned to be adaptive without interfering with other core properties of the network. Furthermore, the method covers both parameter and network structure modifications and can be applied to any reaction rate formalism and even to medium-scale or partially unknown models.