Mathematical models for T cell activation through kinetic proofreading

Abstract

An intact antigen discrimination mechanism in T cells is crucial for the body’s immune response. Failure of this mechanism can lead to immune deficiency or autoimmunity. A basic model for antigen discrimination is given by the kinetic proofreading model, which can be represented as a system of ordinary differential equations. This work extends the basic model by incorporating enzyme-substrate reactions which explicitly model the kinase Lck, fundamentally altering its characteristics. Whereas the basic model is known to have a unique steady state, it is shown that including Lck enables the system to support multiple positive steady states, provided it exhibits at least two phosphorylation steps. This capacity to support multiple positive steady states, which can be associated with the digital behavior of T cells, persists when incorporating ZAP-70. Furthermore, conditions are identified under which the minimal kinetic proofreading system with Lck and a single phosphorylation step has a globally asymptotically stable steady state.