Pareto-optimal synthesis of multiple glycans in Golgi compartments

Proteins and lipids of eukaryotes are decorated with glycans: branched chains of sugars that affect their folding, stability, recognition, and therapeutic function. Unlike DNA or proteins that are synthesized from a template, glycans are assembled through enzyme-catalyzed monomer addition reactions as they transit through the compartments of the Golgi apparatus. Thus, glycan production can be viewed as a control problem: the enzyme localization and residence times in compartments must be chosen to produce the desired glycans efficiently. A key complication is the promiscuous nature of enzymes: longer compartment residence times can lead to off-target products even as they allow more complex glycans to be made, creating a trade-off. Here, we formulate glycan synthesis as an abstract chemical kinetic manufacturing problem and ask how enzyme allocations and compartment residence times should be chosen in the presence of this trade-off. We show that nonoverlapping enzyme distributions are optimal for single-glycan manufacture of the trees considered; however, overlapping enzyme distributions attain their maximum yield faster. We then consider simultaneous manufacture of multiple glycans, where optimizing the manufacture of one glycan might reduce the yield of another. Pareto-optimal solutions are a class of solutions that reconcile this trade-off. We explore Pareto-optimal solutions for multiple glycan manufacture and show that small changes in residence times can change the optimal enzyme distribution. Even though overlapping enzyme distributions are suboptimal for all the considered cases of single-glycan manufacture, the Pareto set for multiple glycan manufacture contains overlapping distributions. Together, these results show that Pareto optimality provides a useful framework for interpreting trade-offs in Golgi organization and for controlling glycan outputs in industrial settings such as manufacture of biotherapeutics, many of which are glycosylated.