Mathematical modelling of T cell activation: from phenotypic approaches to mechanochemical models

Abstract

T cell activation is a central process in adaptive immunity, initiated when T cell receptors recognise peptide--MHC complexes. A key question is how T cells achieve high sensitivity and specificity despite weak receptor--ligand binding and the presence of abundant self-peptides. This thesis studies this problem using mathematical models, moving from phenotypic descriptions of T cell signalling to mechanochemical models of force-dependent TCR--pMHC binding.

The first part of the thesis presents a comparative mathematical analysis of phenotypic models of T cell activation. Models based on receptor occupancy, kinetic proofreading, feedback, limited and sustained signalling, activation-chain stabilization, and incoherent feedforward motifs are analysed with respect to steady states, response functions, antigen discrimination, sensitivity, specificity, and parameter dependence. The KPR model with an incoherent feedforward loop and limited signalling captured the broadest range of experimentally observed features, because it balances activation by high-affinity ligands with restricted responses to low-affinity ligands. Sensitivity analysis further identifies phosphorylation-related parameters and phosphatase activity as major determinants of model behaviour.

The second part develops a mechanochemical energy-landscape model for TCR--pMHC binding under force. The model combines receptor extension, binding-site separation, hinge elasticity, ligand-dependent binding strength, and applied mechanical force. Mathematical analysis gives a cutoff force above which no bound state exists, while numerical calculations show how force reshapes energy barriers and bond lifetimes. Within this framework, agonist and weak agonist ligands can display catch--slip behaviour, whereas antagonist-like ligands exhibit slip-bond behaviour.

Together, the thesis shows how mathematical modelling can connect biochemical signalling architectures with force-dependent mechanisms of receptor--ligand recognition in T cell activation.