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 the synthesis of the branched carbohydrates known as glycans. These molecules play a key role in conveying cellular identity and self/non-self information across all domains of life; for example, the famous A/B blood group antigens are glycans. In eukaryotic cells (including human cells) glycans are synthesized by collections of enzymes in a factory-line system of compartments known as the Golgi apparatus. The Golgi can stochastically convert a single input molecule to a heterogeneous set of possible outputs; yet in living cells the observed diversity of the outputs is very small. Here we resolve this paradox by borrowing from the theory of algorithmic self-assembly. For a large class of stochastic models, given an input and a target output we either prove that the output cannot be algorithmically synthesized from the input, or explicitly construct a succession of Golgi compartments that achieves this synthesis. Our theoretical analysis allows us to infer the causes of heterogeneity in real glycan datasets.
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