Papers by A. Rendall and E.D. Sontag

This paper analizes a model for the initial stage of T cell activation. The state variables in the model are the concentrations of phosphorylation states of the T cell receptor complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero, and that there is more than one positive steady state for certain values of the parameters; in addition, damped oscillations are possible. It is also shown that the chemical concentration which represents the degree of activation of the cell, represented by the maximally phosphorylated form of the T cell receptor complex, is in general a non-monotone function of the activating signal. In particular there are cases where there is a value of the dissociation constant of the ligand from the receptor which produces an optimal activation of the T cell. In this way the results of certain simulations in the literature have been confirmed rigorously and new features are discovered.