Final answer:
ZAP-70 is the protein tyrosine kinase responsible for initiating the phosphorylation cascade leading to T-cell activation, followed by proliferation and differentiation after T-cell receptor engagement.
Step-by-step explanation:
The protein tyrosine kinase involved in T-cell activation, which ultimately leads to T-cell proliferation and differentiation, is ZAP-70. None of the other options listed function as a protein tyrosine kinase in this context.
The enzyme ZAP-70 (zeta-chain-associated protein kinase 70) becomes activated after T-cell receptor (TCR) engagement and is a crucial component in the signal transduction pathway leading to T-cell activation. The activation of ZAP-70 initiates a phosphorylation cascade that includes various steps such as the MAP kinase pathway, eventually resulting in transcriptional changes promoting T-cell proliferation and differentiation. Moreover, options such as AP-1, NF-κB, NFAT, and MyD88 have different functions within the immune response, but they do not serve as the initial protein tyrosine kinase triggered by TCR activation.