Role of Fast and Slow Inhibitors in Oscillatory Rhythm Design

Abstract

In biological or abiotic systems, rhythms occur, owing to the coupling between positive and negative feedback loops in a reaction network. Using the Semenov–Whitesides oscillatory network for thioester hydrolysis as a prototype, we experimentally and theoretically analyzed the role of fast and slow inhibitors in oscillatory reaction networks. In the presence of positive feedback, a single fast inhibitor generates a time delay, resulting in two saddle-node bifurcations and bistability in a continuously stirred tank reactor. A slow inhibitor produces a node-focus bifurcation, resulting in damped oscillations. With both fast and slow inhibitors present, the node-focus bifurcation repeatedly modulates the saddle-node bifurcations, producing stable periodic oscillations. These fast and slow inhibitions result in a pair of time delays between steeply ascending and descending dynamics, which originate from the positive and negative feedbacks, respectively. This pattern can be identified in many chemical relaxation oscillators and oscillatory models, e.g., the bromate–sulfite pH oscillatory system, the Belousov–Zhabotinsky reaction, the trypsin oscillatory system, and the Boissonade–De Kepper model. This study provides a novel understanding of chemical and biochemical rhythms and suggests an approach to designing such behavior.

Selenium catalysis enables negative feedback organic oscillators

“…We have recently developed a series of thiol-based oscillators 27 – 29 , which are called Semenov-Whitesides oscillators by Epstein, Gao, and coworkers 30 . All of them have the same topology, which includes quadratic autocatalysis combined with negative feedback based on two inhibitors (Fig.…”

“…Both inhibitors (Michael acceptors or oxidants) directly react with autocatalysts (thiols) according to the mass-action law and do not form a negative feedback loop where autocatalysts should first activate inhibitors from dormant precursors. These direct reactions are neither delayed nor nonlinear; oscillations are achieved by having two inhibitors with drastically different reactivities: one reacting with thiols very quickly, whereas the other reacting slowly 30 . Many non-biological chemical oscillators, including large classes of redox and pH oscillators 31 – 35 and a recently published amine-based oscillator 36 , rely on the direct removal of autocatalysts by inhibitors without a negative feedback loop.…”