Analysis of a Generic Model of Eukaryotic Cell-Cycle Regulation

Abstract

We propose a protein interaction network for the regulation of DNA synthesis and mitosis that emphasizes the universality of the regulatory system among eukaryotic cells. The idiosyncrasies of cell cycle regulation in particular organisms can be attributed, we claim, to specific settings of rate constants in the dynamic network of chemical reactions. The values of these rate constants are determined ultimately by the genetic makeup of an organism. To support these claims, we convert the reaction mechanism into a set of governing kinetic equations and provide parameter values (specific to budding yeast, fission yeast, frog eggs, and mammalian cells) that account for many curious features of cell cycle regulation in these organisms. Using one-parameter bifurcation diagrams, we show how overall cell growth drives progression through the cell cycle, how cell-size homeostasis can be achieved by two different strategies, and how mutations remodel bifurcation diagrams and create unusual cell-division phenotypes. The relation between gene dosage and phenotype can be summarized compactly in two-parameter bifurcation diagrams. Our approach provides a theoretical framework in which to understand both the universality and particularity of cell cycle regulation, and to construct, in modular fashion, increasingly complex models of the networks controlling cell growth and division.

Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle

“…Oscillatory circuits 1 and 2 produce Cdk1-independent Cdk2 oscillations and are therefore associated with endoreplication, whereas circuits 3 and 4 involve Cdk1 oscillations and are associated with periodic cell division. The possibility of endoreplication was previously reported in a model for the yeast cell cycle (48) and in a generic model for the eukaryotic cell cycle (22). Oscillatory circuit 4 is in fact closely related to the mitotic oscillator driving the early cell cycles in amphibian embryos (10)(11)(12)(13)(14)(15).…”

“…Of intermediate complexity, the model contains 39 variables, or 44 when including the ATR/Chk1 checkpoint. It is more comprehensive than partial or global models previously proposed for the mammalian cell cycle (17)(18)(19)(20)(21)(22). It includes additional variables and more biochemical details about the regulation of the various cyclin/Cdk complexes, incorporates the role of a key checkpoint, and does not rely on control by cell mass.…”

“…Theoretical models were subsequently proposed for portions of the mammalian cell cycle, particularly the G 1 /S transition and the restriction point (17)(18)(19)(20)(21). A generic model for the eukaryotic cell cycle has also been presented (22). We still lack a detailed, integrative model coupling the different cyclin/Cdk complexes that control the successive phases of the mammalian cell cycle, which would be capable of describing their repetitive, sequential activation.…”

“…Building on previous work that showed the occurrence of oscillations in models for the cell cycle in embryos (10)(11)(12)(13)(14) and yeast (16), and in less detailed or partial models for the mammalian cell cycle (17)(18)(19)(20)(21)(22), we focus on the conditions in which the cyclin/Cdk network may function as a self-sustained biochemical oscillator solely as a result of its regulatory structure. To this end we disregard the control by cell mass, which appears less stringent in mammalian cells than in yeast (23).…”

Biological switches and clocks

“…Although the experimentalists paid little attention to modellers during this time, in recent years there have appeared many influential papers that self-consciously test (and confirm) predictions of the models (Cross et al 2002(Cross et al , 2005Cross 2003;Pomerening et al 2003;Sha et al 2003) or bring modelling to bear on experimental design and interpretation (Pomerening et al 2005;Queralt et al 2006). All eukaryotes use the same basic mechanism, based on cyclin-dependent kinases, to regulate the progression of DNA synthesis, mitosis and cell division (Csikasz-Nagy et al 2006), but the idiosyncrasies of specific cell types require specifically tailored mathematical models (Chen et al 2004;Calzone et al 2007). The cell cycles of bacteria are regulated by a completely different set of genes and proteins, unrelated to the eukaryotic control system, and modellers have focused on specific details of the gene-protein interaction network in a-proteobacteria (Shen et al 2007;Li et al 2008), as well as convergent evolution of the dynamical properties of the two distinct control systems (Brazhnik & Tyson 2006).…”