Integral feedback in synthetic biology: negative-equilibrium catastrophe
File(s)
Published version
Author(s)
Plesa, Tomislav
Dack, Alexander
Ouldridge, Thomas
Type
Journal Article
Abstract
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. NECs
therefore place a fundamental limit to design and control of molecular networks.
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. NECs
therefore place a fundamental limit to design and control of molecular networks.
Date Issued
2023-10
Date Acceptance
2023-07-05
Citation
Journal of Mathematical Chemistry, 2023, 61 (9), pp.1980-2018
ISSN
0259-9791
Publisher
Springer
Start Page
1980
End Page
2018
Journal / Book Title
Journal of Mathematical Chemistry
Volume
61
Issue
9
Copyright Statement
© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://link.springer.com/article/10.1007/s10910-023-01495-3
Publication Status
Published
Date Publish Online
2023-08-08