Multistationarity in Double Phosphorylation Networks with Protein Synthesis and Degradation

Extended Abstract. Bistability is a prominent and often desired feature in biological networks, for example in signal transduction, cell cycle control and cellular information processing, [1]. Multisite phosphorylation can be found in many intracellular processes, for example as double phosphorylation in the MAPK cascade, [2], or six-fold phosphorylation of Sic1, an essential part of the check point controlling G1/S transition in the cell cycle in budding yeast, [3]. Though bistability is a known feature for certain networks, for example a single layer of the MAPK cascade, providing a parameter region for bistability is not a trivial task. In [4] and [5], two of the authors describe an approach – based on a transformation of the multistationarity equation – that establishes multistationarity, a prerequisite of bistability, for a generic double phosphorylation network via a linear inequality system. Note that, in general, establishing multistationarity for mass action networks requires solving polynomial equations. Using the approach of [4] one can also obtain a parametrization of the multistationarity region in parameter space. This approach is so far only applicable to double phosphorylation networks neglecting synthesis and/or degradation of proteins. We provide the extension to double phosphorylation networks including different network configurations describing protein synthesis and degradation. The extended approach also allows to decide about multistationarity by analysis of linear inequality systems. Multistationarity is established for all but two of the investigated networks. The new approach again yields a parametrization of the multistationarity region – wherever it exists.