We develop a model of tyrosine phosphorylation and activation of the T-cell receptor (TCR) by localization to regions of close membrane-membrane proximity (close contact) that physically exclude tyrosine phosphatases such as CD45. Phosphatase exclusion generates regions of low phosphatase and high kinase activity and thus our model provides a framework to examine the kinetic segregation model of TCR activation. We incorporate a sequence of activation steps modeling the construction of the signalosome with a final sequestered, or high-stability, signaling state. The residence time of unbound TCRs in tyrosine kinase-rich domains is shown to be too short for accumulation of activation steps, whereas binding to an agonist lengthens the localization time and leads to generation of fully active TCRs. Agonist detection depends only on this localization, and therefore kinetic segregation represents a viable ligand detection mechanism, or signal transduction mechanism across membranes, distinct from receptor oligomerization and conformational change. We examine the degree of discrimination of agonists from a background of null (self) peptides, and from weak agonists achievable by this mechanism.