Newton's cradle: Cell cycle regulation by two mutually inhibitory oscillators.

The cell division cycle is a fundamental physiological process displaying a great degree of plasticity during the course of multicellular development. This plasticity is evident in the transition from rapid and stringently-timed divisions of the early embryo to subsequent size-controlled mitotic cycles. Later in development, cells may pause and restart proliferation in response to myriads of internal or external signals, or permanently exit the cell cycle following terminal differentiation or senescence. Beyond this, cells can undergo modified cell division variants, such as endoreplication, which increases their ploidy, or meiosis, which reduces their ploidy. This wealth of behaviours has led to numerous conceptual analogies intended as frameworks for understanding the proliferative program. Here, we aim to unify these mechanisms under one dynamical paradigm. To this end, we take a control theoretical approach to frame the cell cycle as a pair of arrestable and mutually-inhibiting, doubly amplified, negative feedback oscillators controlling chromosome replication and segregation events, respectively. Under appropriate conditions, this framework can reproduce fixed-period oscillations, checkpoint arrests of variable duration, and endocycles. Subsequently, we use phase plane and bifurcation analysis to explain the dynamical basis of these properties. Then, using a physiologically realistic, biochemical model, we show that the very same regulatory structure underpins the diverse functions of the cell cycle control network. We conclude that Newton's cradle may be a suitable mechanical analogy of how the cell cycle is regulated.

The oscillation of mitotic kinase governs cell cycle latches in mammalian cells.

The mammalian cell cycle alternates between two phases - S-G2-M with high levels of A- and B-type cyclins (CycA and CycB, respectively) bound to cyclin-dependent kinases (CDKs), and G1 with persistent degradation of CycA and CycB by an activated anaphase promoting complex/cyclosome (APC/C) bound to Cdh1 (also known as FZR1 in mammals; denoted APC/C:Cdh1). Because CDKs phosphorylate and inactivate Cdh1, these two phases are mutually exclusive. This 'toggle switch' is flipped from G1 to S by cyclin-E bound to a CDK (CycE:CDK), which is not degraded by APC/C:Cdh1, and from M to G1 by Cdc20-bound APC/C (APC/C:Cdc20), which is not inactivated by CycA:CDK or CycB:CDK. After flipping the switch, cyclin E is degraded and APC/C:Cdc20 is inactivated. Combining mathematical modelling with single-cell timelapse imaging, we show that dysregulation of CycB:CDK disrupts strict alternation of the G1-S and M-G1 switches. Inhibition of CycB:CDK results in Cdc20-independent Cdh1 'endocycles', and sustained activity of CycB:CDK drives Cdh1-independent Cdc20 endocycles. Our model provides a mechanistic explanation for how whole-genome doubling can arise, a common event in tumorigenesis that can drive tumour evolution.