Biological rhythms—what sets their amplitude? (Vol. 49, No. 2)

Analytical amplitude bounds constrain the oscillation minima and maxima for different types of biochemical oscillator systems

Living organisms rely on internal biological timers to ensure their proper development and functioning during adult life; examples are the formation of repetitive embryonic patterns or the entrainment of activity cycles to the day-night cycle. Such timers are typically embodied as biochemical oscillators, i.e., genetic regulatory networks that generate oscillations in the concentration of gene products within cells via a delayed negative feedback. Theoretical descriptions of these oscillators often rely on nonlinear rate equations that describe how the interactions between different gene products can give rise to stable limit-cycle oscillations. For a large class of such models, we here derive a method to construct analytical bounds for the minima and maxima of the oscillations, one of their functional key features besides their period. Numerical simulations of different example systems show that the oscillations saturate the bounds as the feedback delay becomes large. The results shed light on which details of the nonlinear feedback are responsible for constraining the oscillation amplitude and can be readily generalised to similar oscillator systems.

D. J. Jörg, Amplitude bounds for for biochemical oscillators, EPL 119, 58004 (2017)