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 ß-carboxysomes each constitute an optimal compartmentalization strategy given the properties of their respective protein shells.

Optimization of collective enzyme activity via spatial localization.

The spatial organization of enzymes often plays a crucial role in the functionality and efficiency of enzymatic pathways. To fully understand the design and operation of enzymatic pathways, it is therefore crucial to understand how the relative arrangement of enzymes affects pathway function. Here we investigate the effect of enzyme localization on the flux of a minimal two-enzyme pathway within a reaction-diffusion model. We consider different reaction kinetics, spatial dimensions, and loss mechanisms for intermediate substrate molecules. Our systematic analysis of the different regimes of this model reveals both universal features and distinct characteristics in the phenomenology of these different systems. In particular, the distribution of the second pathway enzyme that maximizes the reaction flux undergoes a generic transition from co-localization with the first enzyme when the catalytic efficiency of the second enzyme is low, to an extended profile when the catalytic efficiency is high. However, the critical transition point and the shape of the extended optimal profile is significantly affected by specific features of the model. We explain the behavior of these different systems in terms of the underlying stochastic reaction and diffusion processes of single substrate molecules.

Regulation of reaction fluxes via enzyme sequestration and co-clustering.

Experimental observations suggest that cells change the intracellular localization of key enzymes to regulate the reaction fluxes in enzymatic networks. In particular, cells appear to use sequestration and co-clustering of enzymes as spatial regulation strategies. These strategies should be equally useful to achieve rapid flux regulation in synthetic biomolecular systems. Here, we leverage a theoretical model to analyse the capacity of enzyme sequestration and co-clustering to control the reaction flux in a branch of a reaction-diffusion network. We find that in both cases, the response of the system is determined by two dimensionless parameters, the ratio of total activities of the competing enzymes and the ratio of diffusion to reaction timescales. Using these dependencies, we determine the parameter range for which sequestration and co-clustering can yield a biologically significant regulatory effect. Based on the known kinetic parameters of enzymes, we conclude that sequestration and co-clustering represent a viable regulation strategy for a large fraction of metabolic enzymes, and suggest design principles for reaction flux regulation in natural or synthetic systems.