Response metrics of T-cell activation models

T-cell activation models describe the way in which antigens and T-cell receptors (TCRs) interact in order to trigger an immune response. A number of mathematical models of TCR-mediated T-cell activation have been proposed in the last decades. Often, the only measurable quantities available for the identification of these models are Emax, the maximum achievable T cell activation level (over the background level), and EC50, that is, the antigen concentration that results in 50% of Emax. In order to analyse model properties such as identifiability, observability, and sensitivity, it is necessary to know how Emax and/or EC50 relate to the model parameters. However, their expressions are only available for a few of the published models of T-cell activation. Here we present a general method to derive the expressions of Emax and/or EC50, and apply it to those models for which they are yet unknown. Our results expand the range of analyses that can be performed on T-cell activation models, contributing to enable their exploitation to understand and control the immune response.