Final answer:
PK1 activates PK2 in the signaling pathway, and cells with an inactivating mutation in PK1 and activating mutation in PK2 do not respond since the sequence begins with PK1.
Step-by-step explanation:
The correct answer to the question is Option 1: PK1 activates PK2. The doubly mutant cells would not respond in the presence of the signal. This is because the permanently active mutant form of PK1 can initiate the cellular response even without the extracellular signal, while the inactivated PK2 cannot act downstream to continue the signaling cascade.
The explanation relies on the data provided: when either kinase is completely inactive, the normal response to an extracellular signal is abolished. This indicates that both kinases are essential. Since cells with permanently active PK1 can respond without the extracellular signal, PK1 is upstream of PK2 and activates it. Finally, if both PK1 is inactive and PK2 is permanently active, there would be no response since the upstream activator, PK1, is required to activate PK2.