Fig. 1: Classification tasks performed by biochemical networks.

A The push-pull circuit of enzyme activation. The input here is the activity of activating enzyme, shown in cyan, which affects the colored transition rates in the corresponding Markov network. B Schematic graph of the binary (active vs. inactive) classification task, which computes a soft threshold on the activity of the activating enzyme. Colored points represent desired outputs, which are approximated by the learned function shown in black. C Schematized representation of the process of protein glycosylation in the Golgi apparatus, adapted from the model in ref. ¹⁶. Proteins shown as gray ellipses traverse through many cisternae, and the state of the cell dictates the set of glycosyltransferase enzymes found in each cisternae and, in turn, the sugars attached to the proteins. A decorated protein ends up in one of many distinct glycan forms on the plasma membrane, where it serves as an encoding of the cell state. D Schematic graph of how protein glycosylation yields many output states, which cluster based on the set of enzymes in the Golgi cisternae. The colors of data points represent the output glycan identities at a given point in enzyme space, and the colored ellipsoids represent decision boundaries that approximately achieve this desired classification. E Drawing of a random Markov graph with 15 nodes and 25 edges. The output nodes are labeled, and the input forces (with positive orientation) are drawn labeled with arrows. In classification tasks using this network, the solid arrows are always used as inputs, and the dashed arrows are used when M = 2. Input edge driving, input multiplicity, and Arrhenius-like parameterization of the edge rates are illustrated.