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Interactions among oscillatory pathways in NF-kappa B signaling.

Wang Y, Paszek P, Horton CA, Kell DB, White MR, Broomhead DS, Muldoon MR - BMC Syst Biol (2011)

Bottom Line: Power spectra of the ratio of nuclear-to-cytoplasmic concentration of NF-kappa B suggest that the cells' responses are entrained by the pulsing frequency.Our results show that, at least in simulation, frequencies other than those of the forcing and the main NF-kappa B oscillator can be excited via sub- and superharmonic resonance, producing quasiperiodic and even chaotic dynamics.Further simulations suggest that the nonlinearities of the NF-kappa B feedback oscillator mean that even sinusoidally modulated forcing can induce a rich variety of nonlinear interactions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Mathematical Biosciences Institute, The Ohio State University, Jennings Hall, Columbus, Ohio 43210, USA. ywang@mbi.osu.edu

ABSTRACT

Background: Sustained stimulation with tumour necrosis factor alpha (TNF-alpha) induces substantial oscillations--observed at both the single cell and population levels--in the nuclear factor kappa B (NF-kappa B) system. Although the mechanism has not yet been elucidated fully, a core system has been identified consisting of a negative feedback loop involving NF-kappa B (RelA:p50 hetero-dimer) and its inhibitor I-kappa B-alpha. Many authors have suggested that this core oscillator should couple to other oscillatory pathways.

Results: First we analyse single-cell data from experiments in which the NF-kappa B system is forced by short trains of strong pulses of TNF-alpha. Power spectra of the ratio of nuclear-to-cytoplasmic concentration of NF-kappa B suggest that the cells' responses are entrained by the pulsing frequency. Using a recent model of the NF-kappa B system due to Caroline Horton, we carried out extensive numerical simulations to analyze the response frequencies induced by trains of pulses of TNF-alpha stimulation having a wide range of frequencies and amplitudes. These studies suggest that for sufficiently weak stimulation, various nonlinear resonances should be observable. To explore further the possibility of probing alternative feedback mechanisms, we also coupled the model to sinusoidal signals with a wide range of strengths and frequencies. Our results show that, at least in simulation, frequencies other than those of the forcing and the main NF-kappa B oscillator can be excited via sub- and superharmonic resonance, producing quasiperiodic and even chaotic dynamics.

Conclusions: Our numerical results suggest that the entrainment phenomena observed in pulse-stimulated experiments is a consequence of the high intensity of the stimulation. Computational studies based on current models suggest that resonant interactions between periodic pulsatile forcing and the system's natural frequencies may become evident for sufficiently weak stimulation. Further simulations suggest that the nonlinearities of the NF-kappa B feedback oscillator mean that even sinusoidally modulated forcing can induce a rich variety of nonlinear interactions.

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Weak and strong modulations. Heat maps showing the power spectral density of the responses to forcing of the form (2) with ε = 0.5 and η = 1 (left) or η = 0.1 (right).
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Figure 8: Weak and strong modulations. Heat maps showing the power spectral density of the responses to forcing of the form (2) with ε = 0.5 and η = 1 (left) or η = 0.1 (right).

Mentions: The two panels of Figure 8 are analogues of Figure 7 but with especially strong (η = 1, left panel) or weak (η = 0.1, right panel) modulation. The qualitative features are much the same, though it is interesting to note that in the limit of very strong modulation—when η = 1 and so TR (t) vanishes once per forcing period—the system is very strongly entrained by the forcing and does not show much power at its natural frequency ν0 or its harmonics until the forcing frequency ν > 1.5 ν0. By contrast, when the modulation is weak evidence of modal interaction is also weak, with very narrow mode-locking regions near forcing frequencies of the form ν ≈ mν0.


Interactions among oscillatory pathways in NF-kappa B signaling.

Wang Y, Paszek P, Horton CA, Kell DB, White MR, Broomhead DS, Muldoon MR - BMC Syst Biol (2011)

Weak and strong modulations. Heat maps showing the power spectral density of the responses to forcing of the form (2) with ε = 0.5 and η = 1 (left) or η = 0.1 (right).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3050740&req=5

Figure 8: Weak and strong modulations. Heat maps showing the power spectral density of the responses to forcing of the form (2) with ε = 0.5 and η = 1 (left) or η = 0.1 (right).
Mentions: The two panels of Figure 8 are analogues of Figure 7 but with especially strong (η = 1, left panel) or weak (η = 0.1, right panel) modulation. The qualitative features are much the same, though it is interesting to note that in the limit of very strong modulation—when η = 1 and so TR (t) vanishes once per forcing period—the system is very strongly entrained by the forcing and does not show much power at its natural frequency ν0 or its harmonics until the forcing frequency ν > 1.5 ν0. By contrast, when the modulation is weak evidence of modal interaction is also weak, with very narrow mode-locking regions near forcing frequencies of the form ν ≈ mν0.

Bottom Line: Power spectra of the ratio of nuclear-to-cytoplasmic concentration of NF-kappa B suggest that the cells' responses are entrained by the pulsing frequency.Our results show that, at least in simulation, frequencies other than those of the forcing and the main NF-kappa B oscillator can be excited via sub- and superharmonic resonance, producing quasiperiodic and even chaotic dynamics.Further simulations suggest that the nonlinearities of the NF-kappa B feedback oscillator mean that even sinusoidally modulated forcing can induce a rich variety of nonlinear interactions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Mathematical Biosciences Institute, The Ohio State University, Jennings Hall, Columbus, Ohio 43210, USA. ywang@mbi.osu.edu

ABSTRACT

Background: Sustained stimulation with tumour necrosis factor alpha (TNF-alpha) induces substantial oscillations--observed at both the single cell and population levels--in the nuclear factor kappa B (NF-kappa B) system. Although the mechanism has not yet been elucidated fully, a core system has been identified consisting of a negative feedback loop involving NF-kappa B (RelA:p50 hetero-dimer) and its inhibitor I-kappa B-alpha. Many authors have suggested that this core oscillator should couple to other oscillatory pathways.

Results: First we analyse single-cell data from experiments in which the NF-kappa B system is forced by short trains of strong pulses of TNF-alpha. Power spectra of the ratio of nuclear-to-cytoplasmic concentration of NF-kappa B suggest that the cells' responses are entrained by the pulsing frequency. Using a recent model of the NF-kappa B system due to Caroline Horton, we carried out extensive numerical simulations to analyze the response frequencies induced by trains of pulses of TNF-alpha stimulation having a wide range of frequencies and amplitudes. These studies suggest that for sufficiently weak stimulation, various nonlinear resonances should be observable. To explore further the possibility of probing alternative feedback mechanisms, we also coupled the model to sinusoidal signals with a wide range of strengths and frequencies. Our results show that, at least in simulation, frequencies other than those of the forcing and the main NF-kappa B oscillator can be excited via sub- and superharmonic resonance, producing quasiperiodic and even chaotic dynamics.

Conclusions: Our numerical results suggest that the entrainment phenomena observed in pulse-stimulated experiments is a consequence of the high intensity of the stimulation. Computational studies based on current models suggest that resonant interactions between periodic pulsatile forcing and the system's natural frequencies may become evident for sufficiently weak stimulation. Further simulations suggest that the nonlinearities of the NF-kappa B feedback oscillator mean that even sinusoidally modulated forcing can induce a rich variety of nonlinear interactions.

Show MeSH
Related in: MedlinePlus