Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero‐order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.

Copper (Cu) is a micronutrient essential for the biochemical functioning of numerous processes in vertebrates but is also often present in the aquatic environment at concentrations able to cause adverse health effects in aquatic organisms. This study investigated the signaling pathways mediating the effects of exposure to Cu using a toxicogenomic approach in a fish model, the stickleback ( Gasterosteus aculeatus ). Freshwater-acclimated male fish were exposed via the water to Cu, including at environmentally relevant concentrations (3.2-128 microg of Cu/L for 4 days), and the biological responses explored through analyses of the hepatic transcriptome and metabolome and phenotypic end points, including assessment of DNA damage in blood cells. The Cu exposures resulted in DNA strand breaks in blood cells at all exposure concentrations and alterations in hepatic gene expression and metabolite concentrations in a concentration-dependent manner (from 10 microg of Cu/L). Genes associated with the cholesterol biosynthesis pathway were significantly over-represented and consistently down-regulated (at 128 microg of Cu/L), similar to that occurring in a mouse model for Wilson's disease. Additionally, inductions in metallothionein and catalase were also observed. The concentrations of NAD(+) and lactate increased significantly with the Cu exposure, consistent with a shift toward anaerobic metabolism, and these aligned closely with changes observed in gene expression. The pathways of Cu toxicity identified in our study support the conserved mechanisms of Cu toxicity from lower vertebrates to mammals, provide novel insights into the deleterious effects of Cu in fish, and further demonstrate the utility of fish as environmental sentinels for chemical impacts on both environmental and human health.