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Lipniacki, T.; Paszek, P.; Brasier, A.R.; Luxon, B.; Kimmel, M. (2004) Mathematical Model of NF-κB regulatory module. J. Theor. Biol., 228, 195-215. Abstract
NF-κB is a mammalian transcription factor involved in the regulation of many cellular processes including cell cycle, inflammation and immune response. A mathematical model is used to study two regulatory feedback loops involving IκBα and A20. Both proteins are under transcriptional control of NF-κB, with IκBα sequestering NF-κB in the cytosol and thus avoiding activation of gene expression, and A20 controlling the inactivation of IKK(IkB kinase), which phosphorylates IκBα leading to its degradation and release of NF-κB. The authors based their model on a previous one (see Hoffmann et. al, 2002), but amended it in three important points: (1) correct implementation of multi-compartmentation, arising from the existence of two compartments with different volumes (cytosol and nucleus); (2) re-estimation of mRNA transcription rates to plausible values, based on experimental rates of transcription; and (3) re-estimation of the ratio between NF-κB and IκBα to plausible values. Unknown parameters were estimated based on a "manual" fitting to experiments, instead of using a numerical algorithm. This was necessary because the experimental data available was semi-quantitative and from different laboratories. This work constitutes a good example where a careful "manual" fitting based on the biological knowledge of the researcher can be used with advantage over automatic "blind" fittings.
The model simulated well continuous and pulsed TNF-α-dependent NF-κB activation observed in experiments. The influence of A20 on NF-κB activation was modeled by switching off A20 synthesis, simulating experiments in A20-deficient cells. As observed experimentally, the model showed that in absence of A20, IKK activation is higher, which in turn causes cytosolic IκBα to remain low during the course of simulation (and at almost undetectable levels in the experiment) contrary to observations in wild-type cells in which cytosolic IκBα recovers rapidly following its activation by NF-κB.
After comparison with experiments, simulations were performed to study the regulatory dynamics of the model. Upon:
a three-fold increase in A20 mRNA rate of transcription, the period of oscillations became longer;
a three-fold increase in IκBα mRNA rate of transcription, oscillations became less damped;
a three-fold increase in IKK production rate, a three-fold decrease in NF-κB or a decrease in ratio between cytosolic and nuclear volume from 5 to 2, oscillatory dynamics of NF-κB were lost;
a three-fold increase in the levels of NF-κB, or an increase in the ratio between cytosolic and nuclear volume from 5 to 10 lowered the damping and increased the amplitude of oscillations. Among the parameters studied, the concentration of NF-κB was the one that had a higher effect on the transcription rate of target genes. This is an evidence that overexpression of NF-κB, so comnoly used nowdays to study NF-κB dynamics, may introduce artifactual behavior).
In conclusion, this theoretical work clear shows the importance of the A20-dependent regulatory loop, as wells as, the influence of the ratio between the volume of the cytosol and the nucleus for the dynamics of NF-κB activation. 