Algorithmic asymptotic analysis of the NF-κ B signaling system

The results of a detailed, step-by-step, asymptotic analysis of the NF-κB signaling system are reported, in the case where the system exhibits limit cycle behavior. The analysis is based on the dimensional form of the model and exploits the various fast/slow time scale gaps that develop as the solution evolves along the limit cycle. It is shown that under the action of fast time scales of dissipative character, the limit cycle is confined on a low-dimensional surface in the phase space. The cycle can be divided in three parts, each one related to a different characteristic time scale. The first part refers to the slow rate of NF-κB release in the cytoplasm. The second part refers to the even slower rate by which the free NF-κB enters into the nucleus. The last part refers to the fast rate by which the nuclear NF-κB is first produced and then depleted. It is demonstrated that these and many other findings (regarding the fast variables, the equilibrated fast processes, the rate limiting and/or driving steps, etc.) can be acquired by simple algorithmic tools.