Quantitative modelers of the molecular circadian oscillator have long recognized

Here we have highlighted a few important positive feedback interactions in the mammalian circadian clock, but the state-of-the art network of interactions is very 6-Acetamidohexanoic acid complex encompassing additional positive and negative feedback motifs. Quantitative modelers of the molecular circadian oscillator have long recognized the need for ��modifications�� to the core Goodwin motif model to have more plausible cooperativity requirements. MM degradation kinetics for one or more components representing proteins is the most common approach used in these models to reduce the cooperativity to at least 4. In fact, Tyson et al. reduced the cooperativity of the feedback to 2 by introducing dimerization and Michealis-Menten-like degradation of the proteins motivated by biological observations. Some features identified as positive feedback-like mechanisms, such as nuclear transport and heterodimerization, were also suggested as mechanisms that promote oscillations in clock models based on the core Goodwin motif. In fact, Kurosawa et al. compared four different model architectures also using cooperativity in the feedback as a measure of ��ease�� of obtaining oscillations. Protein sequestration has been shown to be capable of generating highly cooperative signaling responses, such as those needed for sustained oscillations with no other nonlinearity. Kim and Forger showed using their model that sequestration of the repressor by the activator EED226 enable oscillations in the molecular circadian clock by requiring a stoichiometric balance between activators and repressors in the system. Griffith first showed that cooperativity of at least 8 was necessary to produce oscillations in the core Goodwin motif. Subsequently, Tyson and Othmer presented the exact relationship between the cooperativity in the negative feedback and length of the enzymatic chain. Thus, they confirmed generally that cooperativity could be reduced by increasing the length of the feedback loop, i.e., adding more steps. Similarly, Bliss et al. showed that the required cooperativity could be reduced by explicit time-delay in the loop and saturable end-product removal.