ABSTRACT

Biological oscillations attracted theoretical work from pioneers such as Arthur Winfree, Albert Goldbeter and John Tyson, and are an active area of research. A delay in biological circuits can be achieved by adding components in the negative feedback loop to make longer paths in the circuit. Negative feedback plus delays and/or noise can provide oscillations. Nonlinearity and similar timescales for the opposing arms help the feedback loop to oscillate. In the frog-egg cell-cycle circuit, the positive feedback loop causes bistability, as experimentally shown by J. R. Pomerening, E. D. Sontag and J. E. Ferrell. The oscillation has an asymmetric pulse shape with slow buildup at first, then accelerated rise as the positive feedback kicks in, and a rapid decline. Tunable frequency is harder to achieve in a simple delay oscillator without positive feedback, because changes to frequency are coupled with changes in amplitude.