Synthesizing a Clock Signal with Reactions---Part I: Duty Cycle Implementation Based on Gears

TL;DR

This paper introduces a gear-inspired method to synthesize tunable clock signals with specific duty cycles using chemical reaction networks, providing a new approach to timing in biological systems.

Contribution

It presents a novel gear-based framework for implementing clock signals with various duty cycles in CRNs, focusing on the design and quantitative description of these signals.

Findings

Successfully implemented clock signals with duty cycles 1/2, 1/N, and M/N.

Provides a gear theory-based quantitative description of CRN clock signals.

Lays groundwork for physical realization using DNA strand displacement reactions.

Abstract

Timing is of fundamental importance in biology and our life. Borrowing ideas from mechanism, we map our clock signals onto a gear system, in pursuit of better depiction of a clock signal implemented with chemical reaction networks (CRNs). On a chassis of gear theory, more quantitative descriptions are offered for our method. Inspired by gears, our work to synthesize a tunable clock signal could be divided into two parts. Part I, this paper, mainly focuses on the implementation of clock signals with three types of duty cycles, namely $1/2$, $1/N$ ($N > 2$), and $M/N$. Part II devotes itself in addressing frequency alteration issues of clock signals. \textcolor{black}{Guaranteed by existing literature, the experimental chassis can be taken care of by DNA strand displacement reactions, which lay a solid foundation for the physical implementation of nearly arbitrary CRNs.