Leveraging mathematical models to predict and control T-cell activation

Abstract T-cell receptor (TCR)-mediated T-cell activation is a key process in adaptive immune responses. The complexity of this process has led to the development of different mathematical models that seek to describe and predict the conditions of antigen-TCR interactions required for TCR triggering and T-cell activation. These models are characterized by describing different sets of sequential molecular interactions and their kinetics, positing the generation of a final product as a necessary and sufficient condition for T-cell activation. Such modeling could provide an effective tool for simulating antigen recognition by T cells and, consequently, aid in the design of effective therapeutic strategies. However, it is necessary to previously assess the predictive capabilities of the proposed models when fitted to experimental data. To achieve this goal, in this work we examine the parameter identifiability and sensitivity of the published models of TCR-based T-cell activation. For each model, we consider different, often experimentally measured, output quantities and show how their availability affects the results. These analyses allow us to determine the ability of each model to correctly describe different experimental situations, and to establish to what extent these models can be applied to reliably predict and control T-cell activation by specific therapeutic targets. Author summary The adaptive immune system is a highly specialized defense mechanism present in vertebrates. It produces a response that results from a complex set of interrelated cellular and molecular mechanisms. A key process is antigen-dependent activation of T lymphocytes, for which several mechanisms have been postulated. The corresponding mathematical models allow us to explore competing hypotheses, make quantitative predictions, and eventually aid in the design of strategies to control the immune response. To achieve these goals, it is essential that the models be identifiable and observable, that is, it must be possible to infer their parameters and state from output measurements. Furthermore, their response should exhibit an adequate level of sensitivity to certain key parameters. In this work, we evaluate the degree to which currently existing models possess these qualities. Our findings provide minimum requirements for the design of system identification experiments, allowing us to discard those models that cannot be successfully calibrated with a given experimental setup.