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 corneal allograft rejection, a simple mathematical model is developed for the regulation of TNF-alpha, which incorporates both negative feedback and amplification pathways. Mathematical analysis reveals a surprisingly rich behavioural repertoire for this simple cytokine pathway, including excitability, threshold behaviour, hysteresis, oscillations and bistability. This suggests new possibilities for experimental demonstration, and reveals the potential contributions of nonlinear dynamics to understanding cytokine regulation.