Final answer:
The cause of cells synthesizing proteins during apoptosis is alternative translation initiation pathways that can bypass the degradation of translation initiation factor eIF4.
Step-by-step explanation:
During apoptosis, activated caspases degrade several intracellular proteins, including translation initiation factors such as eIF4, which plays a role in recognizing and binding the 5' cap of mRNA. Despite the cells undergoing apoptosis, they continue to synthesize proteins required for the process. This is possible due to alternative translation initiation pathways that can bypass the degradation of eIF4, allowing the cells to continue protein synthesis. Therefore, the cause of the cells synthesizing proteins during apoptosis is alternative translation initiation pathways.