Dynamical model and geometric insights in the discontinuity theory of immunity.

The immune system's most basic task is to decide what is "self" and "non-self", but a precise definition of self versus non-self remains challenging. According to the discontinuity theory of immunity, effector responses depend on how quickly an antigenic stimulus changes: rapid change triggers an immune response, whereas gradual change fosters tolerance. We present a model of adaptive immune dynamics including T cells, Tregs and cytokines that reproduces the hallmarks of the discontinuity theory. The model allows for sharp discrimination between acute and chronic infections based on the growth rate of the immune challenge, and vaccination-like acute dynamics upon presentation of a bolus of immune challenge. We further show that the model behavior only depends on a handful of testable assumptions that we map to geometric constraints in phase space. This suggests that the model properties are generic and robust across alternative mechanistic details. We also examine the impact of multiple concurrent immune challenges in this model, and demonstrate the occurrence of dynamical antagonism, wherein, in some parameter regimes, slow-growing challenges hinder acute responses to fast-growing ones, with further counter-intuitive behaviors for sequential co-infections. Together, these results place the discontinuity theory on firm mathematical footing and encourage further investigation of interferences of multi-agent immune challenges, from chronic viral co-infections to cancer immunoediting.