Mathematical models of TCR initial triggering.

T cell receptors (TCRs) play crucial roles in regulating T cell response by rapidly and accurately recognizing foreign and non-self antigens. The process involves multiple molecules and regulatory mechanisms, forming a complex network to achieve effective antigen recognition. Mathematical modeling techniques can help unravel the intricate network of TCR signaling and identify key regulators that govern it. In this review, we introduce and briefly discuss relevant mathematical models of TCR initial triggering, with a focus on kinetic proofreading (KPR) models with different modified structures. We compare the topology structures, biological hypotheses, parameter choices, and simulation performance of each model, and summarize the advantages and limitations of them. Further studies on TCR modeling design, aiming for an optimized balance of specificity and sensitivity, are expected to contribute to the development of new therapeutic strategies.