Algorithmic biosynthesis of eukaryotic glycans

An algorithm converts inputs to corresponding unique outputs through a sequence of actions. Algorithms are used as metaphors for complex biological processes such as organismal development. Here we make this metaphor rigorous for glycan biosynthesis. Glycans are branched sugar oligomers that are attached to cell-surface proteins and convey cellular identity. Eukaryotic O-glycans are synthesized by collections of enzymes in Golgi compartments. A compartment can stochastically convert a single input oligomer to a heterogeneous set of possible output oligomers; yet a given type of protein is invariably associated with a narrow and reproducible glycan oligomer profile. Here we resolve this paradox by borrowing from the theory of algorithmic self-assembly. We rigorously enumerate the sources of glycan microheterogeneity: incomplete oligomers via early exit from the reaction compartment; tandem repeat oligomers via runaway reactions; and competing oligomer fates via divergent reactions. We demonstrate how to diagnose and eliminate each of these, thereby obtaining "algorithmic compartments" that convert inputs to corresponding unique outputs. Given an input and a target output we either prove that the output cannot be algorithmically synthesized from the input, or explicitly construct an ordered series of algorithmic compartments that achieves this synthesis. Our theoretical analysis allows us to infer the causes of non-algorithmic microheterogeneity and species-specific diversity in real glycan datasets.