Editing G2 phase (section)

=== Positive feedback and switch-like activation ===
[[File:G2-M Bistability.png|thumb|This graph illustrates the stable equilibria for cyclin-B1/CDK1 activity at varying cyclin B1 concentrations, with the threshold of cyclin B concentration for entering mitosis higher than the threshold for exiting mitosis.]]

These positive feedback loops encode a [[Hysteresis|hysteretic]] [[Bistability|bistable]] switch in CDK1 activity relative to cyclin B1 levels (see figure). This switch is characterized by two distinct stable equilibria over a bistable region of cyclin B1 concentrations. One equilibrium corresponds to interphase and is characterized by inactivity of Cyclin-B1/CDK1 and Cdc25, and a high level of Wee1 and Myt1 activity. The other equilibrium corresponds to M-phase and is characterized by high activity of Cyclin-B1/CDK1 and Cdc25, and low Wee1 and Myt1 activity. Within the range of bistability, a cell’s state depends upon whether it was previously in interphase or M-phase: the threshold concentration for entering M-phase is higher than the minimum concentration that will sustain M-phase activity once a cell has already exited interphase.

Scientists have both theoretically and empirically validated the bistable nature of the G2/M transition. The [[Novak-Tyson model]] shows that the differential equations modelling the cyclin-B/CDK1-cdc25-Wee1-Myt1 feedback loop admit two stable equilibria over a range of cyclin-B concentrations.<ref>{{cite journal | vauthors = Novak B, Tyson JJ | title = Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos | journal = Journal of Cell Science | volume = 106 | pages = 1153–68 | date = December 1993 | pmid = 8126097 | issue = 4 | doi = 10.1242/jcs.106.4.1153 }}</ref> Experimentally, bistability has been validated by blocking endogenous cyclin B1 synthesis and titrating interphase and M-phase cells with varying concentrations of non-degradable cyclin B1. These experiments show that the threshold concentration for entering M-phase is higher than the threshold for exiting M-phase: nuclear envelope break-down occurs between 32-40&nbsp;nm cyclin-B1 for cells exiting interphase, while the nucleus remains disintegrated at concentrations above 16-24&nbsp;nm in cells already in M-phase.<ref>{{cite journal | vauthors = Sha W, Moore J, Chen K, Lassaletta AD, Yi CS, Tyson JJ, Sible JC | title = Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 100 | issue = 3 | pages = 975–80 | date = February 2003 | pmid = 12509509 | pmc = 298711 | doi = 10.1073/pnas.0235349100 | bibcode = 2003PNAS..100..975S | doi-access = free }}</ref>

This bistable, hysteretic switch is physiologically necessary for at least three reasons.<ref>{{cite journal | vauthors = Pomerening JR, Sontag ED, Ferrell JE | title = Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2 | journal = Nature Cell Biology | volume = 5 | issue = 4 | pages = 346–51 | date = April 2003 | pmid = 12629549 | doi = 10.1038/ncb954 | s2cid = 11047458 }}</ref> First, the G2/M transition signals the initiation of several events, such as chromosome condensation and nuclear envelope breakdown, that markedly change the morphology of the cell and are only viable in dividing cells. It is therefore essential that cyclin-B1/CDK1 activation occurs in a switch-like manner; that is, cells should rapidly settle into a discrete M-phase state after the transition, and should not persist in a continuum of intermediate states (e.g., with a partially decomposed nuclear envelope). This requirement is satisfied by the sharp [[Discontinuity (mathematics)|discontinuity]] separating the interphase and M-phase equilibrium levels of CDK1 activity; as the cyclin-B concentration increases beyond the activation threshold, the cell rapidly switches to the M-phase equilibrium.

Secondly, it is also vital that the G2/M transition occur unidirectionally, or only once per cell cycle  Biological systems are inherently [[Noise (signal processing)|noisy]], and small fluctuations in cyclin B1 concentrations near the threshold for the G2/M transition should not cause the cell to switch back and forth between interphase and M-phase states. This is ensured by the bistable nature of the switch: after the cell transitions to the M-phase state, small decreases in the concentration of cyclin B do not cause the cell to switch back to interphase.

Finally, the continuation of the cell cycle requires persisting oscillations in cyclin-B/CDK1 activity as the cell and its descendants transition in and out of M-phase. Negative feedback provides one essential element of this long-term oscillation: cyclin-B/CDK activates APC/C, which causes degradation of cyclin-B from metaphase onwards, restoring CDK1 to its inactive state. However, simple negative feedback loops lead to [[Damping ratio|damped oscillations]] that eventually settle on a steady state. Kinetic models show that negative feedback loops coupled with bistable positive feedback motifs can lead to persistent, non-damped oscillations (see [[relaxation oscillator]]) of the kind required for long-term cell cycling.