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

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.