Optimal Compartmentalization Strategies for Metabolic Microcompartments

Intracellular compartmentalization of cooperating enzymes is a strategy that is frequently used by cells. Segregation of enzymes that catalyze sequential reactions can alleviate challenges such as toxic pathway intermediates, competing metabolic reactions, and slow reaction rates. Inspired by nature, synthetic biologists also seek to encapsulate engineered metabolic pathways within vesicles or proteinaceous shells to enhance the yield of industrially and pharmaceutically useful products. Although enzymatic compartments have been extensively studied experimentally, a quantitative understanding of the underlying design principles is still lacking. Here, we study theoretically how the size and enzymatic composition of compartments should be chosen so as to maximize the productivity of a model metabolic pathway. We find that maximizing productivity requires compartments larger than a certain critical size. The enzyme density within each compartment should be tuned according to a power-law scaling in the compartment size. We explain these observations using an analytically solvable, well-mixed approximation. We also investigate the qualitatively different compartmentalization strategies that emerge in parameter regimes where this approximation breaks down. Our results suggest that the different sizes and enzyme packings of α- and β-carboxysomes each constitute an optimal compartmentalization strategy given the properties of their respective protein shells.