Mathematical model of NF-kappaB regulatory module.

The two-feedback-loop regulatory module of nuclear factor kappaB (NF-kappaB) signaling pathway is modeled by means of ordinary differential equations. The constructed model involves two-compartment kinetics of the activators IkappaB (IKK) and NF-kappaB, the inhibitors A20 and IkappaBalpha, and their complexes. In resting cells, the unphosphorylated IkappaBalpha binds to NF-kappaB 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 IkappaBalpha, leading to IkappaBalpha degradation. Degradation of IkappaBalpha releases the main activator NF-kappaB, which then enters the nucleus and triggers transcription of the inhibitors and numerous other genes. The newly synthesized IkappaBalpha leads NF-kappaB 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 IkappaBalpha. After parameter fitting, the proposed model is able to properly reproduce time behavior of all variables for which the data are available: NF-kappaB, cytoplasmic IkappaBalpha, A20 and IkappaBalpha 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.