A systematic survey of the response of a model NF-κB signalling pathway to TNFα stimulation.

White's lab established that strong, continuous stimulation with tumour necrosis factor-α (TNFα) can induce sustained oscillations in the subcellular localisation of the transcription factor nuclear factor κB (NF-κB). But the intensity of the TNFα signal varies substantially, from picomolar in the blood plasma of healthy organisms to nanomolar in diseased states. We report on a systematic survey using computational bifurcation theory to explore the relationship between the intensity of TNFα stimulation and the existence of sustained NF-κB oscillations. Using a deterministic model developed by Ashall et al. in 2009, we find that the system's responses to TNFα are characterised by a supercritical Hopf bifurcation point: above a critical intensity of TNFα the system exhibits sustained oscillations in NF-kB localisation. For TNFα below this critical value, damped oscillations are observed. This picture depends, however, on the values of the model's other parameters. When the values of certain reaction rates are altered the response of the signalling pathway to TNFα stimulation changes: in addition to the sustained oscillations induced by high-dose stimulation, a second oscillatory regime appears at much lower doses. Finally, we define scores to quantify the sensitivity of the dynamics of the system to variation in its parameters and use these scores to establish that the qualitative dynamics are most sensitive to the details of NF-κB mediated gene transcription.

Interactions among oscillatory pathways in NF-kappa B signaling.

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.

Physiological levels of TNFalpha stimulation induce stochastic dynamics of NF-kappaB responses in single living cells.

Nuclear factor kappa B (NF-kappaB) signalling is activated by cellular stress and inflammation and regulates cytokine expression. We applied single-cell imaging to investigate dynamic responses to different doses of tumour necrosis factor alpha (TNFalpha). Lower doses activated fewer cells and those responding showed an increasingly variable delay in the initial NF-kappaB nuclear translocation and associated IkappaBalpha degradation. Robust 100 minute nuclear:cytoplasmic NF-kappaB oscillations were observed over a wide range of TNFalpha concentrations. The result is supported by computational analyses, which identified a limit cycle in the system with a stable 100 minute period over a range of stimuli, and indicated no co-operativity in the pathway activation. These results suggest that a stochastic threshold controls functional all-or-nothing responses in individual cells. Deterministic and stochastic models simulated the experimentally observed activation threshold and gave rise to new predictions about the structure of the system and open the way for better mechanistic understanding of physiological TNFalpha activation of inflammatory responses in cells and tissues.

Pulsatile stimulation determines timing and specificity of NF-kappaB-dependent transcription.

The nuclear factor kappaB (NF-kappaB) transcription factor regulates cellular stress responses and the immune response to infection. NF-kappaB activation results in oscillations in nuclear NF-kappaB abundance. To define the function of these oscillations, we treated cells with repeated short pulses of tumor necrosis factor-alpha at various intervals to mimic pulsatile inflammatory signals. At all pulse intervals that were analyzed, we observed synchronous cycles of NF-kappaB nuclear translocation. Lower frequency stimulations gave repeated full-amplitude translocations, whereas higher frequency pulses gave reduced translocation, indicating a failure to reset. Deterministic and stochastic mathematical models predicted how negative feedback loops regulate both the resetting of the system and cellular heterogeneity. Altering the stimulation intervals gave different patterns of NF-kappaB-dependent gene expression, which supports the idea that oscillation frequency has a functional role.

Single live-cell imaging for systems biology.

Understanding how mammalian cells function requires a dynamic perspective. However, owing to the complexity of signalling networks, these non-linear systems can easily elude human intuition. The central aim of systems biology is to improve our understanding of the temporal complexity of cell signalling pathways, using a combination of experimental and computational approaches. Live-cell imaging and computational modelling are compatible techniques which allow quantitative analysis of cell signalling pathway dynamics. Non-invasive imaging techniques, based on the use of various luciferases and fluorescent proteins, trace cellular events such as gene expression, protein-protein interactions and protein localization in cells. By employing a number of markers in a single assay, multiple parameters can be measured simultaneously in the same cell. Following acquisition using specialized microscopy, analysis of multi-parameter time-lapse images facilitates the identification of important qualitative and quantitative relationships-linking intracellular signalling, gene expression and cell fate.