This cell organelle participates actively in animal apoptosis

The correct option is mitochondria.

Apoptosis is a highly regulated process of programmed cell death that occurs in multicellular organisms. Among the cell organelles listed, mitochondria play a central and active role in initiating and regulating the intrinsic pathway of animal apoptosis.

During cellular stress or damage, the outer mitochondrial membrane becomes permeable. This permeability is controlled by the Bcl-2 family of proteins. Once permeabilized, mitochondria release key pro-apoptotic factors, most notably cytochrome c, from their intermembrane space into the cytosol.

Once in the cytosol, cytochrome c binds to Apaf-1 (apoptotic protease activating factor-1) and dATP to form a wheel-like protein complex called the apoptosome. The apoptosome recruits and activates caspase-9, an initiator caspase, which in turn activates executioner caspases (such as caspase-3 and caspase-7). These executioner caspases systematically degrade the cell's structural proteins and DNA, leading to organized cell death.

Other organelles like chloroplasts (which are found in plants, not animals), the nucleus (which is a target of apoptotic degradation but doesn't actively initiate the process in the same way), and vacuoles (which are primary lysosomal-like structures in plants and fungi) do not play the primary regulatory role in initiating the apoptotic cascade in animals that mitochondria do.