Oscillation, cooperativity, and intermediates in the self-repressing gene

Abstract

a b s t r a c tBiological oscillators are vital to living organisms, which use them as clocks for time-sensitive processes. However, much is unknown about mechanisms which can give rise to coherent oscillatory behavior, with few exceptions (e.g., explicitly delayed self-repressors and simple models of specific organisms' circadian clocks). We present what may be the simplest possible reliable gene network oscillator, a self-repressing gene. We show that binding cooperativity, which has not been considered in detail in this context, can combine with small numbers of intermediate steps to create coherent oscillation. We also note that noise blurs the line between oscillatory and non-oscillatory behavior.

Landscape and Global Stability of Nonadiabatic and Adiabatic Oscillations in a Gene Network

“…The potential landscapes for more parameters are given in the Supporting Material. It was shown that with multiple intermediate steps such as transcription, translation, monomers to dimers, dimers to tetramers, and tetramers binding on promoters, oscillations can be generated (14,15). Here we found that with the slow binding/unbinding, robust oscillations can be generated by a two-step, single-loop negative feedback.…”

“…It is also helpful to study the deterministic moment equations for understanding the qualitative behavior in an approximate way (13,15,36). The m th moment is defined as hn m i g ¼ X n n m P g ðnÞ;…”

“…Such rhythms exist at many levels in living organisms, from the cell proliferation cycle to the circadian sleep-wake cycle of higher organisms (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11). Recently, many timing mechanisms accompanied with periodic behaviors were studied, including three-gene repressilators (3,12,13), self-repressors with explicit time delays (14,15), cell cycles (1,9,(16)(17)(18), circadian clock networks (2,6,7,19,20), and engineered two-component motifs from synthetic biology with the interplay of positive feedback and negative feedback (activated repression) (14,17,21,22). These studies shed light on the underlying mechanisms.…”

Stochastic Oscillations Induced by Intrinsic Fluctuations in a Self-Repressing Gene

“…This approach can be used to estimate the amplitude of fluctuations (34) but also to determine their spectrum. In the latter case, the LNA has been useful to characterize the appearance of stochastic oscillations in parameter regions where the mean-field equations predict stable steady behavior (35,36) or to verify that oscillations predicted by a deterministic modeling persist in presence of fluctuations (37), two problems which has been much studied (38)(39)(40)(41). To overcome the fact that this method does not allow one to determine precisely when the steady state loses stability, Scott, Ingalls and Hwa proposed an extension of the LNA which takes into account how fluctuations modify the linearized dynamics around steady state and allows one to study how bifurcation diagrams are modified by noise (42).…”