Mathematical model of NF-κB regulatory module

The two-feedback-loop regulatory module of nuclear factor κB (NF-κB) signaling pathway is modeled by means of ordinary differential equations. The constructed model involves two-compartment kinetics of the activators IκB (IKK) and NF-κB, the inhibitors A20 and IκBα, and their complexes. In resting cells, the unphosphorylated IκBα binds to NF-κB and sequesters it in an inactive form in the cytoplasm. In response to extracellular signals such as tumor necrosis factor or interleukin-1, IKK is transformed from its neutral form (IKKn) into its active form (IKKa), a form capable of phosphorylating IκBα, leading to IκBα degradation. Degradation of IκBα releases the main activator NF-κB, which then enters the nucleus and triggers transcription of the inhibitors and numerous other genes. The newly synthesized IκBα leads NF-κB out of the nucleus and sequesters it in the cytoplasm, while A20 inhibits IKK converting IKKa into the inactive form (IKKi), a form different from IKKn, no longer capable of phosphorylating IκBα. After parameter fitting, the proposed model is able to properly reproduce time behavior of all variables for which the data are available: NF-κB, cytoplasmic IκBα, A20 and IκBα mRNA transcripts, IKK and IKK catalytic activity in both wild-type and A20-deficient cells. The model allows detailed analysis of kinetics of the involved proteins and their complexes and gives the predictions of the possible responses of whole kinetics to the change in the level of a given activator or inhibitor.