Mathematical modeling of bistable transitions in a simple and direct way

What is it about?

To multiply, a cell goes through a sequence of phases in the cell division cycle. Transitions between different phases can be built on a so-called bistable switch. These switches ensure fast, robust and irreversible activation of proteins, which lead the cell into the new phase. Mathematical modeling of these systems has mostly been based on relatively detailed sets of equations that describe concentrations and activities of the proteins involved in these transitions. However, often these interactions, and the many reaction rates involved, are not completely known. In our paper, we propose a method to model bistable switches without the detailed chemical reactions, only based on the shape of the response function that describes the transition. In this way, bistable transitions can be easily included in larger models.

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Photo by Luca Bravo on Unsplash

Photo by Luca Bravo on Unsplash

Why is it important?

The mathematical method proposed is flexible, and allows bistable switches to be included as smaller modules into larger models. Its applicability is not limited to the cell cycle or even biological systems. Bistable switches also appear in climate models, for example.