Negative feedback enables structurally signed steady-state influences in artificial biomolecular networks

We examine the capacity of artificial biomolecular networks to respond to perturbations with structurally signed steady-state changes. We consider network architectures designed to balance their output production as a function of downstream demand: the species producing the output, called a source, up- or down-regulates its production rate as a function of the demand. Using an exact algorithm we show that, in certain negative feedback architectures, changes in the total source concentration cause structurally signed variations of the steady-state output concentration, regardless of reaction rate parameters. Conversely, positive feedback schemes can exhibit the same signed behaviour for reasonable (but not for arbitrary) values of the parameters. Numerical simulations demonstrate how the steady-state concentrations of different network architectures vary, responding to perturbations in total source amounts, consistently with our structural previsions.