A central goal of synthetic biology is the design of molecular controllers that can manipulate the dynamics of intracellular networks in a stable and accurate manner. To address the fact that detailed knowledge about intracellular networks is unavailable, integral-feedback controllers (IFCs) have been put forward for controlling molecular abundances. These controllers can maintain accuracy in spite of the uncertainties in the controlled networks. However, this desirable feature is achieved only if stability is also maintained. In this paper, we show that molecular IFCs  suffer from a hazardous instability called negative-equilibrium catastrophe (NEC), whereby all nonnegative equilibria vanish under the action of the controllers, and some of the underlying molecular abundances blow up. We show that unimolecular IFCs do not exist due to a NEC. We then derive a family of bimolecular IFCs that are safeguarded against NECs when unimolecular networks are controlled. However, we show that, without a detailed knowledge of the controlled systems, NECs cannot be prevented when IFCs are applied on bimolecular, and hence the vast majority of intracellular, networks .
A central goal of synthetic biology is the design of molecular controllers that can manipulate the dynamics of intracellular networks in a stable and accurate manner. To address the fact that detailed knowledge about intracellular networks is unavailable, integral-feedback controllers (IFCs) have been put forward for controlling molecular abundances. These controllers can maintain accuracy in spite of the uncertainties in the controlled networks. However, this desirable feature is achieved only if stability is also maintained. In this paper, we show that molecular IFCs can suffer from a hazardous instability called negative-equilibrium catastrophe (NEC), whereby all nonnegative equilibria vanish under the action of the controllers, and some of the molecular abundances blow up. We show that unimolecular IFCs do not exist due to a NEC. We then derive a family of bimolecular IFCs that are safeguarded against NECs when uncertain unimolecular networks, with any number of molecular species, are controlled. However, when IFCs are applied on uncertain bimolecular (and hence most intracellular) networks, we show that preventing NECs generally becomes an intractable problem as the number of interacting molecular species increases .
A
can
D
underlying
R
unimolecular networks
uncertain unimolecular networks, with any number of molecular species,
D
we show that, without a detailed knowledge of the controlled systems, NECs cannot be prevented
R
bimolecular, and hence the vast majority of intracellular, networks
uncertain bimolecular (and hence most intracellular) networks, we show that preventing NECs generally becomes an intractable problem as the number of interacting molecular species increases