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Figure 2 | Journal of Systems Chemistry

Figure 2

From: Maximizing output and recognizing autocatalysis in chemical reaction networks is NP-complete

Figure 2

Construction of a CRN from a given instance of 3PART. (A) In the first step, an intermediate network consisting of input nodes, switch nodes (green diamonds), and waste nodes (open circles), and a single output sink (hexagon) is constructed. The input is encoded as capacity constraints on the l.h.s. input nodes (corresponding to the input numbers s i of 3PART) and on the m top nodes (corresponding to 1 / m of the sum of the inputs). A solution of 3PART corresponds to a flow through this network that transport ∑ i s i to the output sink. (B) In the second step, each switch node is replaced by reaction network that which admits a non-zero flow only if s i copies of Q i and Z j are available. The reaction then produces s i copies of the output molecule O. Note that the "drainage reactions" as not shown in panel (B). These channel the Q j and Z j input material directly to the "waste material" sink whenever the reaction networks inside the switch node receives insufficient input to produce both W ij and V ij .

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