Novak–Tyson model
The Novak–Tyson Model is a non-linear dynamics framework developed in the context of cell-cycle control by Bela Novak and John J. Tyson. It is a prevalent theoretical model that describes a hysteretic, bistable bifurcation of which many biological systems have been shown to express.
Historical background
Bela Novak and John Tyson came from the Department of Biology at the Virginia Polytechnic Institute and State University in Blacksburg, Virginia, when this model was first published in the Journal of Cell Science in 1993.In 1990, two key papers were published that identified and characterized important dynamic relationships between cyclin and MPF in interphase-arrested frog egg extracts. The first was Solomon's 1990 Cell paper, titled "Cyclin activation of p34cdc2" and the second was Felix's 1990 Nature paper, titled "Triggering of cyclin degradation in interphase extracts of amphibian eggs of cdc2 kinase". Solomon's paper showed a distinct cyclin concentration threshold for the activation of MPF. Felix's paper looked at cyclin B degradation in these extracts and found that MPF degrades cyclin B in a concentration dependent and time-delayed manner.
In response to these observations, three competing models were published in the next year, 1991, by Norel and Agur, Goldbeter, and Tyson. These competing theories all attempted to model the experimental observations seen in the 1990 papers regarding the cyclin-MPF network.
The Norel and Agur model
Norel and Agur's model proposes a mechanism where cyclin catalytically drives the production of MPF, which in turn autocatalyzes. This model assumes that MPF activates cyclin degradation via APC activation, and it decouples cyclin degradation from MPF destruction. However, this model is unable to recreate the observed cyclin dependent MPF activity relationship seen in Solomon's 1990 paper, as it shows no upper steady-state level of MPF activity.Goldbeter model
Goldbeter proposed a model where cyclin also catalytically activates MPF, but without an autocatalytic, positive feedback loop. The model describes a two-step process, where MPF first activates the APC, and then the APC drives cyclin degradation. When graphing the MPF activity with respect to cyclin concentration, the model shows a sigmoidal shape, with a hypersensitive, threshold region similar to what was observed by Solomon. However, this model depicts an effectively asymptotic plateau behavior at cyclin concentrations above the threshold, whereas the observed curve shows a steady increase in MPF activity at cyclin concentrations above the threshold.Tyson model
In Tyson's 1991 model, cyclin is a stoichiometric activator of Cdc2, as cyclin binds with phosphorylated Cdc2 to form preMPF, which is activated by Cdc25 to generate MPF. Because Cdc25 itself is also activated by MPF, the conversion of preMPF to active MPF is a self-amplifying process in this model. Tyson neglected the role of MPF in activating the APC, assuming that only a phosphorylated form of cyclin was rapidly degraded. Tyson's model predicts an S-shaped curve, which is phenotypically consistent with Solomon's experimental results. However, this model generates additional lower turning point behavior on the S-curve that implies hysteresis when interpreted as a threshold.The Novak–Tyson model, first published in the paper titled "Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos", builds on the Goldbeter and Tyson 1991 models in order to generate a unifying theory, encapsulating the observed dynamics of the cyclin-MPF relationship.