Synthesising periodic triggering signals with genetic oscillators

The potential of the clock lies in its role of triggering logic reaction for sequential biological circuits. This research introduces an idea of designing a genetic clock generator by Fourier series based on the genetic oscillators. The authors generalise the design idea using a combination of fundamental sinusoidal signals. Since biochemical reaction of the biological system is extremely slow, however, transition between minimal and maximal levels is instantaneous for an ideal clock signal; it is thus not directly realisable in biological systems. That means it would be hard to directly synthesize a square wave generator for use as a genetic clock. They apply Fourier series to represent a square wave as a finite summation of sinusoidal waves generated by some genetic oscillators with different harmonic oscillating frequencies, in which the amplitude alternates at a constant frequency between the fixed minimal and maximal levels with the same duration of time.