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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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Nonlinear resonances to sinusoidal forcing. A heat map showing the power spectral density of the response of Horton's model to forcing of the form (2) with ε = η = 0.5 and frequencies in the range 0 ≤ ν ≤ 4.5 × ν0.
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Figure 7: Nonlinear resonances to sinusoidal forcing. A heat map showing the power spectral density of the response of Horton's model to forcing of the form (2) with ε = η = 0.5 and frequencies in the range 0 ≤ ν ≤ 4.5 × ν0.

Mentions: Figure 7 which is a heat map of the power spectral density of the response generated by relatively strong sinusoidal forcing of the from (2), illustrates many of the behaviours described above. Consider first the vertical strip with ν/ν0 ≈ 1. In this region the sinusoidal modulation entrains the NF-κB system essentially completely and so the heat map resembles the corresponding region in the left panel Figure 4: the power in the response is concentrated along lines corresponding to harmonics of the forcing frequency. Away from the region ν/ν0 ≈ 1 the power spectrum of the response is considerably more complex: the strong horizontal bands in Figure 7 which occur at integer multiples of ν0, show that there is substantial power at the NF-κB system's natural frequency and its harmonics. Additionally, the nonlinearity of the system means that the response has power at frequencies given by


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)

Nonlinear resonances to sinusoidal forcing. A heat map showing the power spectral density of the response of Horton's model to forcing of the form (2) with ε = η = 0.5 and frequencies in the range 0 ≤ ν ≤ 4.5 × ν0.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Nonlinear resonances to sinusoidal forcing. A heat map showing the power spectral density of the response of Horton's model to forcing of the form (2) with ε = η = 0.5 and frequencies in the range 0 ≤ ν ≤ 4.5 × ν0.
Mentions: Figure 7 which is a heat map of the power spectral density of the response generated by relatively strong sinusoidal forcing of the from (2), illustrates many of the behaviours described above. Consider first the vertical strip with ν/ν0 ≈ 1. In this region the sinusoidal modulation entrains the NF-κB system essentially completely and so the heat map resembles the corresponding region in the left panel Figure 4: the power in the response is concentrated along lines corresponding to harmonics of the forcing frequency. Away from the region ν/ν0 ≈ 1 the power spectrum of the response is considerably more complex: the strong horizontal bands in Figure 7 which occur at integer multiples of ν0, show that there is substantial power at the NF-κB system's natural frequency and its harmonics. Additionally, the nonlinearity of the system means that the response has power at frequencies given by

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