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Yao et al., (2008). A bistable Rb-E2F switch underlies the restriction point.

June 2012, model of the month by Maciej Swat
Original model: BIOMD0000000318

This model addresses the vital question of the origin and mechanism behind the restriction point within the mammalian cell cycle [1]. The achieved results demonstrate in the experimental and theoretical fashion the bistable character of the G1/S transition.

With the help of single cell measurements the authors provided the proof of the bistable Rb-E2F pathway behaviour, i.e. it functions as a switch converting graded serum inputs into all-or-none E2F responses. Once switched ON by sufficient serum stimulation, E2F stays in this state independently of continuous serum stimulation. They also have demonstrated that, at critical parameter values of serum stimulation such as concentrations and durations, the bistable E2F activation corresponds with the ability of a cell to traverse the restriction point.

The mathematical model constructed for the purpose of this work is a simplified one (Figure 1a). It reduces the vast complexity of the mammalian G1/S transition to a minimum while capturing the most important qualitative properties of the system. It is important to keep in mind that in the theoretical model E2F stands for all activating members of the E2F family, namely E2F1, E2F2 and E2F3a,b but only E2F1 was measured [2].

The model hypothesises the presence of bistability in the Rb-E2F pathway when stimulated by growth factors. However only E2F activation performs the bistability but not the upstream located cyclin D/cdk4,6 complex, CycD. According to it, there is a critical serum concentration necessary to activate E2F from its previous OFF state (Figure 1b).

After E2F is turned in the ON state, it can maintain this state even when the serum concentration falls below the initial threshold. When serum concentration is within a certain range the steady-state E2F level is bistable and can be either ON or OFF, depending on its previous state. In contrast, model components which are not regulated by positive-feedback, such as CycD, show monostable behaviour, and their steady-state levels depend on the serum concentration only (Figure 1c).

Figure 2

Figure 2 E2F and CycD expression in cultured mammalian cells. Each histogram represents distribution of approximately 10,000 cells (figure taken from [1]).

Additionally to the bistability, the relationship between the growth factor exposure and E2F activation has been investigated. The interesting question was whether a short serum pulse can trigger the phase transition. In fact, a relatively short (5h) and strong (30%) serum pulse was sufficient to permanently activate the bistable Rb-E2F switch (Figure 3a), even thought the following serum signal was significantly reduced. Again, in contrast to E2F, CycD will remain at the same level regardless pulse strength and duration (Figures 3b and 3c). Unfortunately, other stimulus scenarios are not discussed which makes comprehensive analysis of serum stimulation shape and strength impossible.

Figure 1

Figure 1 A simplified model of the Rb-E2F switch (a). Bifurcation diagrams for E2F and CycD with serum concentration as the bifurcation parameter, (b) and (c) respectively (figure taken from [1]).

One of the theoretical results is that the E2F accumulation has a bimodal distribution in a cell population, which is a hallmark of a bistable system [3]. To test this steady-state prediction of E2F activation, the quiescent cells have been stimulated with different levels of serum concentration while measuring E2F endpoint levels. As shown in Figure 2a (here for four different independent cell clones) the transition from uni- to bimodality is dependent on the serum concentration, varying from 0.02-5%. Within an certain concentration range (0.5-1%) one can observe the hypothesised ultrasensitive E2F activation response. However, outside of this range, the cultures behave in a unimodal fashion. In contrast, the expression of CycD is always unimodal under identical test conditions (Figure 2b). In Figure 2c an empty vector control at different serum concentration is shown.

Figure 3

Figure 3 History dependence of E2F (figure taken from [1]).

Bibliographic References

  1. Yao et al. A bistable Rb-E2F switch underlies the restriction point. Nat Cell Biol 2008 Apr;10(4):476-82. [CiteXplore]
  2. Chen et al. Emerging roles of E2Fs in cancer: an exit from cell cycle control. Nat Rev Cancer. 2009 Nov;9(11):785-97. [CiteXplore]
  3. Gardner et al. Construction of a genetic toggle switch in Escherichia coli. Nature. 2000 Jan 20;403(6767):339-42. [CiteXplore]