On the dephasing of genetic oscillators

Abstract

The digital nature of genes combined with the associated low copy numbers of proteins regulating them is a significant source of stochasticity, which affects the phase of biochemical oscillations. We show that unlike ordinary chemical oscillators, the dichotomic molecular noise of gene state switching in gene oscillators affects the stochastic dephasing in a way that may not always be captured by phenomenological limit cycle-based models. Through simulations of a realistic model of the NFκB/IκB network, we also illustrate the dephasing phenomena that are important for reconciling single-cell and population-based experiments on gene oscillators. C yclic rhythms are a common feature of many self-organized systems (1) manifesting themselves in myriad forms in biology, ranging from subcellular biochemical oscillations to cell division and on to the familiar predator-prey cycles of ecology. An oscillatory response of a gene regulatory circuit, whether transient or self-sustained, can provide several advantages over a temporally monotonic response (2, 3). The ability of copies of a system to synchronize may lead to dramatic noise reduction and greater precision for timing in assemblies. On the subcellular level, rhythmic dynamics span time scales from a few seconds, as in the calcium oscillations, to days, as in the circadian rhythms, or years for cicada cycles (1, 4-6). Ultradian genetic oscillations, which take place on an intermediate scale from minutes to a few hours, are medically important. A singularly important case is the Nuclear Factor Kappa B (NFκB) gene network, which organizes the mammalian cell's response to various types of external stress and plays a role in regulating inflammation levels in populations of cells. The response of the NFκB circuit to continuous external stimulation has been studied by Hoffmann et al. (7) who observed damped oscillatory dynamics for NFκB, which has been linked to the presence or absence of particular isoforms of the inhibitor IκB. On the other hand, experiments carried out on individual cells have detected more sustained NFκB/IκB oscillations that either are completely self-sustained (8, 9) or damp at a much slower rate (9) than found for the population, depending on the duration of external stimulation. It follows that some type of averaging takes place, but the physical mechanisms and the stochastic aspects of this population averaging are not fully understood. Many aspects of the NFκB oscillatory dynamics may be rationalized using deterministic mass action rate equations (10, 11), but how stochastic self-sustained oscillations average out at a cell population level remains unclear.In this work, we provide a conceptual framework for understanding stochastic averaging as a result of "dephasing" of genetic oscillators. By dephasing, one essentially means the loss of common phase or coherence of oscillations in populations of mRNA or protein by-products of gene activation, caused by the stochastic molecular events in the course of an oscillator's operation that occur at di...

Molecular dynamics simulations demonstrate the regulation of DNA‐DNA attraction by H4 histone tail acetylations and mutations

“…[34][35][36][37] Formation of a-helix and increase of helical content with acetylation was reported. [34][35][36][37] Formation of a-helix and increase of helical content with acetylation was reported.…”

“…[34][35][36][37] Our earlier molecular dynamics simulations studied three B-form DNA 22-mers and 14 identical oligopeptides with sequence KGGKGLGK, which model a.a. 5 to 12 of the H4 histone tail carrying a positive charge 13. [34][35][36][37] Our earlier molecular dynamics simulations studied three B-form DNA 22-mers and 14 identical oligopeptides with sequence KGGKGLGK, which model a.a. 5 to 12 of the H4 histone tail carrying a positive charge 13.…”

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators

“…This binary gene regulation noise manifests itself as a stochastic temporal pattern of all-or-none gene activity depending on whether the promoter is bound by the regulatory protein. Recent work shows that slow DNA binding-unbinding kinetics (also called the nonadiabatic limit) can exacerbate the binary noise and have profound consequences on gene expression [7], epigenetic switching [8], and oscillation [3,4,9,10]. Faster kinetic rates and complex gene promoter architectures have been proposed as a way to suppress the effect of this binary noise.…”

Dichotomous noise models of gene switches

“…Most conventional approximations for treating stochastic chemical reactions, such as size expansion methods, 32,33 are not applicable when there is sufficient dichotomous noise since these approximations usually rely on the uniform scaling with size of the entire population of species to the near deterministic limit. 34 Time averaging can play a role, however, in reducing the influence of the single molecule dichotomous noise. In the limit of infinitely fast switching of the gene, one can again obtain the strictly deterministic result if the molecular populations of all the other components are sufficiently large.…”