The kinetic space of multistationarity in dual phosphorylation. (English) Zbl 1496.92028

In biology and biochemistry, phosphorylation (as well as its inverse, dephosphorylation) is a fundamental modification process consisting in the attachment (or removal, resp.) of a phosphate group. It is important in cell signaling and is a special case of post-translational modification (PTM) in that it, e.g., changes the behavior of a compound w.r.t. a membrane. It is managed by an enzyme reaction open to quantitative description by the ODE system of a mass action reaction network. The standard machinery is applied to the enzyme reaction of a dual phosphorylation, involving a substrate with two phosphorylation sites and two enzymes, resulting in a polynomial ODE system with nine species concentrations and 12 rate constants (parameters). The objective is to study the parameter space w.r.t. points of multistationarity. In the situation investigated here, real algebraic geometry allows rather precise statements on the parameter areas of monostationarity and multistationarity, their boundaries and their connectedness. Suitable polynomials, their signs, Newton polytopes and cylindrical algebraic decompositions play a decisive role, as well as application of symbolic algorithms. The approach explored here is relevant not only for the system itself, but lends itself also to test the examination of similar models.


92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C42 Systems biology, networks
92C40 Biochemistry, molecular biology
92C37 Cell biology
14P10 Semialgebraic sets and related spaces
37N25 Dynamical systems in biology
92E20 Classical flows, reactions, etc. in chemistry
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
34A34 Nonlinear ordinary differential equations and systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations


CoNtRol; crntwin; MESSI
Full Text: DOI arXiv


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