Before revision:  Our modules are built on a one-site modification cycle and contain one or two cycles combined in all possible ways with the above features regarding the number of modification sites, and competition and non-specificity of enzymes, incorporated. We conclude that multistationarity arises whenever a single enzyme is responsible for catalyzing the modification of two different but linked substrates and that the presence of multiple steady states requires two opposing dynamics (e. g. phosphatase and kinase) acting on the same substrate. The mathematical modeling is based on mass-action kinetics and the conclusions are derived in full generality without restoring to simulations or random generation of parameters  .
After revision:  Our modules are built on a one-site modification cycle and contain one or two cycles combined in all possible ways with the above features regarding the number of steady states and provides a necessary condition for a steady state to be stable, that is, to be biologically attainable. Further, we identify characteristics of the motifs that lead to multistationarity, and extend the view that multistationarity in signaling pathways arises from multisite phosphorylation. Our approach relies on mass-action kinetics and the conclusions are derived in full generality without restoring to simulations or random generation of parameters .