Bifurcation analysis of the regulatory modules of the mammalian G₁/S transition

Abstract

Motivation: Mathematical models of the cell cycle can contribute to an understanding of its basic mechanisms. Modern simulation tools make the analysis of key components and their interactions very effective. This paper focuses on the role of small modules and feedbacks in the gene–protein network governing the G₁/S transition in mammalian cells. Mutations in this network may lead to uncontrolled cell proliferation. Bifurcation analysis helps to identify the key components of this extremely complex interaction network.

Results: We identify various positive and negative feedback loops in the network controlling the G₁/S transition. It is shown that the positive feedback regulation of E2F1 and a double activator–inhibitor module can lead to bistability. Extensions of the core module preserve the essential features such as bistability. The complete model exhibits a transcritical bifurcation in addition to bistability. We relate these bifurcations to the cell cycle checkpoint and the G₁/S phase transition point. Thus, core modules can explain major features of the complex G₁/S network and have a robust decision taking function.

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Author notes

1Institute for Theoretical Biology, Humboldt University Berlin, Invalidenstrasse 43, Berlin, D-10115, Germany, 2BIOBASE, Halchtersche Strasse 33, Wolfenbüttel, D-38304, Germany and 3Institute of Cytology and Genetics SB RAN, 10 Lavrentyev pr., Novosibirsk, 630090, Russia