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

Feng, Haidong; Han, Bo; Wang, Jin

doi:10.1016/j.bpj.2012.02.002

Cited by 20 publications

(28 citation statements)

References 35 publications

(64 reference statements)

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“…This leads to the corresponding projections to the protein concentration variable at ξ = − 1 and ξ = 1 giving the different results at the two different locations. Therefore, two peaks for the distribution at the protein concentration space are expected when ω is small in the nonadiabatic regime, which is the possibility ignored in the conventional view of gene switches (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Fig.…”

Section: Theory For Nonequilibrium Eddy Currentmentioning

confidence: 99%

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Zhang

Sasai

Wang

2013

Proc. Natl. Acad. Sci. U.S.A.

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Physical and biological systems are often involved with coupled processes of different time scales. In the system with electronic and atomic motions, for example, the interplay between the atomic motion along the same energy landscape and the electronic hopping between different landscapes is critical: the system behavior largely depends on whether the intralandscape motion is slower (adiabatic) or faster (nonadiabatic) than the interlandscape hopping. For general nonequilibrium dynamics where Hamiltonian or energy function is unknown a priori, the challenge is how to extend the concepts of the intra-and interlandscape dynamics. In this paper we establish a theoretical framework for describing global nonequilibrium and nonadiabatic complex system dynamics by transforming the coupled landscapes into a single landscape but with additional dimensions. On this single landscape, dynamics is driven by gradient of the potential landscape, which is closely related to the steadystate probability distribution of the enlarged dimensions, and the probability flux, which has a curl nature. Through an example of a self-regulating gene circuit, we show that the curl flux has dramatic effects on gene regulatory dynamics. The curl flux and landscape framework developed here are easy to visualize and can be used to guide further investigation of physical and biological nonequilibrium systems.nonequilibrium landscape | adiabaticity | nonadiabaticity H eterogeneity among coupled processes is a hallmark of complex behaviors of physical and biological systems. A photoexcited molecule, for example, may relax into different low-energy states depending on the difference among time scales of electronic and atomic motions. Molecular motors are fueled by ATP hydrolysis and move into the different structural states, where the heterogeneous distribution of time scales of reactions and structural changes should characterize the motor performance. Dynamical complexity owing to the interplay of heterogeneous processes with multiple time scales can give rise to rich phenomena.In a system having multiple time scales, some dynamical quantities may take discrete values whereas others are continuous. An example of such heterogeneity is found in the electron-transfer reaction, in which the electronic state is discrete and atomic motions are continuous (1). Then, the system can be represented by multiple electronic energy surfaces and the change in atomic positions is motion along individual surfaces. Complex behaviors of the system are explained by the combined process of intrasurface motion along the same and intersurface hopping between different electronic energy surface(s). If the intrasurface motion is slower (faster) than the intersurface hopping, the process is called adiabatic (nonadiabatic). We here extend this notion, the significance of adiabatic and nonadiabatic effects, beyond the Hamiltonian systems to general nonequilibrium problems. Indeed, important complex systems such as reaction networks, gene switches, and molecular motors are co...

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Section: Theory For Nonequilibrium Eddy Currentmentioning

confidence: 99%

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Zhang

Sasai

Wang

2013

Proc. Natl. Acad. Sci. U.S.A.

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“…5) for the cases of fast (adiabatic) and slow (nonadiabatic) gene binding/unbinding (28) and also in the absence of dichotomic gene noise (nondichotomic). The latter regime is achieved simply by scaling the gene number with Ω together with the rest of the protein and mRNA populations.…”

Section: Stochastic Simulations Of Genetic Oscillator Modelsmentioning

confidence: 99%

On the dephasing of genetic oscillators

Potoyan

Wolynes

2014

Proc. Natl. Acad. Sci. U.S.A.

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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...

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Karapetyan¹,

Buchler²

2015

Phys. Rev. E

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Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.

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

Cited by 20 publications

References 35 publications

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

On the dephasing of genetic oscillators

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

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