Frustrated bistability as a means to engineer oscillations in biological systems

Abstract

Oscillations play an important physiological role in a variety of biological systems. For example, respiration and carbohydrate synthesis are coupled to the circadian clock in cyanobacteria (Ishiura et al 1998 Science 281 1519) and ultradian oscillations with time periods of a few hours have been observed in immune response (NF-κB, Hoffmann et al 2002 Science 298 1241, Neson et al 2004 Science 306 704), apoptosis (p53, Lahav et al 2004 Nat. Genet. 36 53), development (Hes, Hirata et al 2002 Science 298 840) and growth hormone secretion (Plotsky and Vale 1985 Science 230 461, Zeitler et al 1991 Proc. Natl. Acad. Sci. USA 88 8920). Here we discuss how any bistable system can be ‘frustrated’ to produce oscillations of a desired nature—we use the term frustration, in analogy to frustrated spins in antiferromagnets, to refer to the addition of a negative feedback loop that destabilizes the bistable system. We show that the molecular implementation can use a wide variety of methods ranging from translation regulation, using small non-coding RNAs, to targeted protein modification to transcriptional regulation. We also introduce a simple graphical method for determining whether a particular implementation will produce oscillations. The shape of the resulting oscillations can be readily tuned to produce spiky and asymmetric oscillations—quite different from the shapes produced by synthetic oscillators (Elowitz and Leibler 2000 Nature 403 335, Fung et al 2005 Nature 435 118). The time period and amplitude can also be manipulated and these oscillators are easy to reset or switch on and off using a tunable external input. The mechanism of frustrated bistability could thus prove to be an easily implementable way to synthesize flexible, designable oscillators.