Analysis of cytokine dynamics in corneal allograft rejection

Motivated by the discovery of oscillations in tumour necrosis factor-alpha (TNF-alpha) concentration in the aqueous humour of rabbits undergoing corne al allograft rejection, a simple mathematical model is developed for the re gulation of TNF-alpha, which incorporates both negative feedback and amplif ication pathways. Mathematical analysis reveals a surprisingly rich behavio ural repertoire for this simple cytokine pathway, including excitability, t hreshold behaviour, hysteresis, oscillations and bistability. This suggests new possibilities for experimental demonstration, and reveals the potentia l contributions of nonlinear dynamics to understanding cytokine regulation.