Self-replenishment cycles generate a threshold response

Many metabolic cycles, including the tricarboxylic acid cycle, glyoxylate cycle, Calvin cycle, urea cycle, coenzyme recycling, and substrate cycles, are well known to catabolize and anabolize different metabolites for efficient energy and mass conversion. In terms of stoichiometric structure, this study explicitly identifies two types of metabolic cycles. One is the well-known, elementary cycle that converts multiple substrates into different products and recycles one of the products as a substrate, where the recycled substrate is supplied from the outside to run the cycle. The other is the self-replenishment cycle that merges multiple substrates into two or multiple identical products and reuses one of the products as a substrate. The substrates are autonomously supplied within the cycle. This study first defines the self-replenishment cycles that many scientists have overlooked despite its functional importance. Theoretical analysis has revealed the design principle of the self-replenishment cycle that presents a threshold response without any bistability nor cooperativity. To verify the principle, three detailed kinetic models of self-replenishment cycles embedded in an E. coli metabolic system were simulated. They presented the threshold response or digital switch-like function that steeply shift metabolic status.