First Passage Times to T Cell Activation

Abstract. Effective recognition of foreign antigens by the adaptive immune system relies on the activation of T cells by antigen-presenting cells (APCs) in lymph nodes. Diffusing T cells may encounter and bind to cognate APCs presenting matching antigen fragments or to noncognate APCs that carry an “incorrect” antigen. The T cells may also exit the lymph node before binding any APC. We develop a stochastic model in which T cell–APC interactions proceed through a sequence of recognition steps represented by a multistage Markov chain. Activation occurs only upon reaching the terminal state associated with a cognate APC. We compute activation probabilities and mean first-passage times in the presence of abundant noncognate APCs and show how kinetic proofreading with state resetting enhances specificity. Relevance to Life Sciences. We present a quantitative framework to study T cell activation within the lymph node that integrates diffusion, the presence and abundance of cognate and noncognate APCs, and T cell exit from the lymph node. Relevant spatio-temporal parameters, such as T cell diffusivity and residence time within the lymph node, are estimated from existing literature. Quantification of the activation probability and time to first activation provide fundamental insights into the onset of the adaptive immune response. Mathematical Content. T cell recognition is modeled as a multistage Markov process, coupled with spatial diffusion and exit. All three processes are represented through a system of partial differential equations that are analyzed under Robin and Neumann boundary conditions. Using first-passage time theory, we calculate activation probabilities and mean activation times. We also show how kinetic proofreading through stochastic resetting enhances specificity.