Multistability in biological systems is seen as a mechanism of cellular decision making. Biological systems are known in which several different kinases phosphorylate a single substrate and others where a single kinase phosphorylate several different substrates. Furthermore, phosphorylation in more than one site can be carried out by a unique kinase or, as in the case of priming kinases, different ones (and similarly for phosphatases) . In this paper we determine  the emergence of multistationarity in small motifs  that repeatedly occur in signaling pathways. 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  .
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multistationarity are of particular interest to determine as well as the stability properties of the steady states . In this paper we determine conditions for the emergence of multistationarity in small motifs without feedback that repeatedly occur in signaling pathways. We derive an explicit mathematical relationship between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that the relation determines 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 drawn in full generality without resorting to simulations or random generation of parameters . The approach is extensible to other systems .
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Multistability
Multistationarity
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seen as
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Biological systems are known in which several different kinases phosphorylate a single substrate and others where a single kinase phosphorylate several different substrates. Furthermore, phosphorylation in more than one site can be carried out by a unique kinase or, as in the case of priming kinases, different ones (and similarly for phosphatases)
In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multistationarity are of particular interest to determine as well as the stability properties of the steady states
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conditions for
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without feedback
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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
We derive an explicit mathematical relationship between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that the relation determines the
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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
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
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derived
drawn
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restoring
resorting
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. The approach is extensible to other systems