TY - JOUR

T1 - Chaos and Its Degradation-Promoting-Based Control in an Antithetic Integral Feedback Circuit

AU - Zand, Armin M.

AU - Tavazoei, Mohammad Saleh

AU - Kuznetsov, Nikolay V.

N1 - Publisher Copyright: © 2017 IEEE.

PY - 2022

Y1 - 2022

N2 - This letter deals with a novel variant of antithetic integral feedback controller (AIFC) motifs which can feature robust perfect adaptation, a pervasive (desired) ability in natural (synthetic) biomolecular circuits, when coupled with a wide class of process networks to be regulated. Using the separation of time-scales in the proposed kind of AIFC, here we find a reduced-order controller that captures the governing slow part of the original solutions under suitable assumptions. Inspired by Rössler systems, we then make use of such a simpler controller to show that the antithetic circuit can exhibit chaotic behaviors with strange attractors, where the bifurcation from a homeostatic state to chaotic orbits can happen, e.g., when considering saturated Hill-type reactions for the actuation. Addition of degradation terms to the controller species, whether naturally due to dilution or exogenously using protein tags, is showcased by simulation results to be an effective solution in suppressing deterministic chaos and aperiodic oscillations. In the same vein, we recapitulate the recently introduced antithetic rein IFC motif and confirm that the promotion of degradation by a rein mechanism also can control chaos and improve the stability of closed-loop circuit.

AB - This letter deals with a novel variant of antithetic integral feedback controller (AIFC) motifs which can feature robust perfect adaptation, a pervasive (desired) ability in natural (synthetic) biomolecular circuits, when coupled with a wide class of process networks to be regulated. Using the separation of time-scales in the proposed kind of AIFC, here we find a reduced-order controller that captures the governing slow part of the original solutions under suitable assumptions. Inspired by Rössler systems, we then make use of such a simpler controller to show that the antithetic circuit can exhibit chaotic behaviors with strange attractors, where the bifurcation from a homeostatic state to chaotic orbits can happen, e.g., when considering saturated Hill-type reactions for the actuation. Addition of degradation terms to the controller species, whether naturally due to dilution or exogenously using protein tags, is showcased by simulation results to be an effective solution in suppressing deterministic chaos and aperiodic oscillations. In the same vein, we recapitulate the recently introduced antithetic rein IFC motif and confirm that the promotion of degradation by a rein mechanism also can control chaos and improve the stability of closed-loop circuit.

KW - adaptation

KW - bifurcation analysis

KW - Oscillatory reaction networks

KW - singular perturbation theory

KW - synthetic biology

UR - http://www.scopus.com/inward/record.url?scp=85120038368&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2021.3129320

DO - 10.1109/LCSYS.2021.3129320

M3 - Article

AN - SCOPUS:85120038368

VL - 6

SP - 1622

EP - 1627

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

ER -