As the basic unit of life, cells are compartmentalized microreactors with molecularly crowded microenvironments. The quest to understand the cell origin inspires the design of synthetic analogs to mimic their functionality and structural complexity. In this work, we integrate membraneless coacervate microdroplets, a prototype of artificial organelles, into a proteinosome to build hierarchical protocells that may serve as a more realistic model of cellular organization. The protocell subcompartments can sense extracellular signals, take actions in response to these stimuli, and adapt their physicochemical behaviors. The tiered protocells are also capable of enriching biomolecular reactants within the confined organelles, thereby accelerating enzymatic reactions. The ability of signal processing inside protocells allows us to design the Boolean logic gates (NOR and NAND) using biochemical inputs. Our results highlight possible exploration of protocell-community signaling and render a flexible synthetic platform to study complex metabolic reaction networks and embodied chemical computation.