A comparative mathematical modeling study of phenotypic approaches to T cell activation.

T cells use their T cell antigen receptors (TCRs) to recognize peptides presented by major histocompatibility complex molecules (pMHC). These peptides may be low-affinity self-peptides or high-affinity foreign peptides from pathogens. Despite recognizing a broad range of affinities, TCRs trigger significant immune responses only to strongly binding foreign peptides. The mechanisms enabling T cells to distinguish diverse antigens with high sensitivity remain a key focus of research. Our goal is to analyze mathematical models of T-cell activation for their ability to replicate key experimental features like optimal response, specificity, sensitivity, and antigen discrimination. We analyzed nine models using mathematical and numerical methods to examine their solutions, responses, and parameter sensitivity. We found that in all models, except kinetic proofreading with negative feedback, solutions converged to a unique steady state. Most response functions defined by ligand concentration and dissociation time showed an optimum value, except for the Occupancy, KPR, and stabilizing activation chain models. Models like KPR with negative feedback, limited/sustained signaling, and incoherent feedforward loops effectively reproduced the key features of specificity, sensitivity, and antigen discrimination. Our sensitivity analysis identified phosphorylation rate as a key parameter influencing most model outcomes. This study highlights the strengths and limitations of current T-cell activation models, suggests directions for improving to enhance their predictive accuracy in future research.