Excitable dynamics of flares and relapses in autoimmune diseases

Abstract

Many autoimmune diseases show flares in which symptoms erupt and then decline. A prominent example is multiple sclerosis (MS) in its relapsing-remitting phase. Mathematical models attempting to capture the flares in multiple sclerosis have often been oscillatory in nature, assuming a regular pattern of symptom flare-ups and remissions. However, this fails to account for the non-periodic nature of flares, which can appear at seemingly random intervals. Here we propose that flares resemble excitable dynamics triggered by stochastic events and show that a minimal mathematical model of autoimmune cells and inhibitory regulatory cells can provide such excitability. In our model, autoimmune response releases antigens that cause autoimmune cells to expand in a positive feedback loop, while regulatory cells inhibit the autoimmune cells in a negative feedback loop. The model can quantitatively explain the decline of MS relapses during pregnancy and their postpartum surge based on lymphocyte dynamics, as well as the decline in MS relapses with age. The model also points to potential therapeutic targets and predicts that even small modulation of regulatory T cell production, removal or activity can have a large effect on relapse rate. Excitable dynamics may underlie flares and relapses found across autoimmune diseases, thus providing an understanding that may help improve treatment strategies.