In biological systems, chemical activity takes place in micrometer- and nanometer-sized compartments that constantly change in shape and volume. These ever-changing cellular compartments embed chemical reactions, and we demonstrate that the rates of such incorporated reactions are directly affected by the ongoing shape reconfigurations. First, we show that the rate of product formation in an enzymatic reaction can be regulated by simple volume contraction-dilation transitions. The results suggest that mitochondria may regulate the dynamics of interior reaction pathways (e.g., the Krebs cycle) by volume changes. We then show the effect of shape changes on reactions occurring in more complex and structured systems by using biomimetic networks composed of micrometer-sized compartments joined together by nanotubes. Chemical activity was measured by implementing an enzymatic reaction-diffusion system. During ongoing reactions, the network connectivity is changed suddenly (similar to the dynamic tube formations found inside Golgi stacks, for example), and the effect on the reaction is registered. We show that spatiotemporal properties of the reaction-diffusion system are extremely sensitive to sudden changes in network topology and that chemical reactions can be initiated, or boosted, in certain nodes as a function of connectivity.