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. 2012 Mar 21;297(2-12):137-47.
doi: 10.1016/j.jtbi.2011.12.014. Epub 2011 Dec 23.

A Systematic Survey of the Response of a Model NF-κB Signalling Pathway to TNFα Stimulation

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Free PMC article

A Systematic Survey of the Response of a Model NF-κB Signalling Pathway to TNFα Stimulation

Yunjiao Wang et al. J Theor Biol. .
Free PMC article

Abstract

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.

Figures

Fig. B1
Fig. B1
A typical experiment tracks single cells for 600 min, which is long enough to distinguish the low-dose oscillatory regime (blue curve) from the exponentially damped oscillations that occur at slightly higher (black curve) and lower (green curve) levels of stimulation. The model here is the same as that depicted in Fig. 4 and has totalNFkB=0.15μM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. C1
Fig. C1
The two-parameter bifurcation diagrams for TR and kv, kd1, h and k, in which the curves trace out the locations of Hopf bifurcation points. These curves divide the parameter space into two types of regions: limit cycle region is marked by 1 and steady-state region marked by 2.
Fig. C2
Fig. C2
The two-parameter bifurcation diagrams for TR and ka1, ki1, kitria and ktria, in which the curves trace out the locations of Hopf bifurcation points. These curves divide the parameter space into two types of regions: limit cycle region is marked by 1 and steady-state region marked by 2.
Fig. C3
Fig. C3
The two-parameter bifurcation diagrams for TR and kdegf, kdegta, kc3 and kdegc, in which the curves trace out the locations of Hopf bifurcation points. These curves divide the parameter space into two types of regions: limit cycle region is marked by 1 and steady-state region marked by 2.
Fig. C4
Fig. C4
The two-parameter bifurcation diagrams for TR and ke1c, ke2, ki2 and kp, in which the curves trace out the locations of Hopf bifurcation points. These curves divide the parameter space into two types of regions: limit cycle region is marked by 1 and steady-state region marked by 2.
Fig. C5
Fig. C5
The two-parameter bifurcation diagrams for TR and ktra, kitra, kbA20 and kda, in which the curves trace out the locations of Hopf bifurcation points. These curves divide the parameter space into two types of regions: limit cycle region is marked by 1 and steady-state region marked by 2.
Fig. C6
Fig. C6
The two-parameter bifurcation diagrams for TR and kc3, kdegpin, kdegtia, ka and ki, in which the curves trace out the locations of Hopf bifurcation points. These curves divide the parameter space into two types of regions: limit cycle region is marked by 1 and steady-state region marked by 2.
Fig. 1
Fig. 1
A graphical representation of the model NF-κB signalling network detailed in Appendix A. Here ovals represent proteins and the two rounded rectangles represent messenger RNAs whose production is regulated by NF-κB.
Fig. 2
Fig. 2
Left panel: bifurcation diagram for TR, where the thick black curve represents a branch of steady states, the thin black curve represents a branch of unstable steady states and the red curve represents a branch of limit cycles. The upper part of the red curve shows the peak values of the oscillations while the lower part shows the troughs. Right panel: period of the limit cycle as a function of TR.
Fig. 3
Fig. 3
The two-parameter bifurcation diagrams for TR and totalIKK (left panel) and TR and totalNFkB (right panel). Here each point on the curves represents a HB-point and the curves divide the parameter spaces into two types of region: there is a limit cycle for each pair of the parameters in Region 1, in which and there is a non-oscillatory steady-state for each pair of parameters in Region 2.
Fig. 4
Fig. 4
The bifurcation diagram for TR when totalNFkB=0.15μM: there are three HB-points at TR=0.002, 0.01 and 0.366, respectively. Sustained oscillations occur for values of TR in either of the intervals (0.002, 0.01) and (0.366, 1]. The right panel shows the period of these oscillations.
Fig. 5
Fig. 5
Sensitivity scores for the 26 reaction rates and the two concentration parameters (totalNFkB and totalIKK) constructed using Eq. (4) with θ=0.1: (left) absolute value of the sensitivity score against parameter number (see Table 1) and (right) sensitivity score against the index of parameters.
Fig. 6
Fig. 6
Scores measuring the sensitivity of the period of the NF-κB oscillations to the changes in parameters: (left) absolute value of sensitivity and (right) sensitivity score against parameter index.

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