Origin of bistability underlying mammalian cell cycle entry

Abstract

Precise control of cell proliferation is fundamental to tissue homeostasis and differentiation. Mammalian cells commit to proliferation at the restriction point (R-point). It has long been recognized that the R-point is tightly regulated by the Rb-E2F signaling pathway. Our recent work has further demonstrated that this regulation is mediated by a bistable switch mechanism. Nevertheless, the essential regulatory features in the Rb-E2F pathway that create this switching property have not been defined. Here we analyzed a library of gene circuits comprising all possible link combinations in a simplified Rb-E2F network. We identified a minimal circuit that is able to generate robust, resettable bistability. This minimal circuit contains a feed-forward loop coupled with a mutual-inhibition feedback loop, which forms an AND-gate control of the E2F activation. Underscoring its importance, experimental disruption of this circuit abolishes maintenance of the activated E2F state, supporting its importance for the bistability of the Rb-E2F system. Our findings suggested basic design principles for the robust control of the bistable cell cycle entry at the R-point.

Figure 1

The Rb–E2F network. (A) A detailed Rb–E2F signaling network (modified from Blagosklonny and Pardee, 2002; Sears and Nevins, 2002) that controls the G1/S transition of mammalian cell cycle. Gray-shaded ovals indicate overlapping or intermediate signaling activities to be lumped. Circled numbers indicate indexes of the regulatory links (Supplementary Table S1). (B) A simplified Rb–E2F network. Positive regulatory links are shown in green and negative regulatory links in red. Link indexes are the same as in (A). (C) The Rb–E2F bistable switch. Once the system at the quiescence state (E2F-OFF state) is stimulated beyond the R-point, it will stay at the proliferation state (E2F-ON state) even in the absence of continuous stimulation.

Figure 2

Robust models for bistability and resettable bistability. (A) Identification of robust models in generating desired switching properties, at each combination of circuit design (C_n) and parameter set (P_n). Inset: constraints to identify switching properties. S, serum input; EE_ss, the steady-state level of EE. Red and green curves indicate EE_ss dose–responses simulated from initial conditions of quiescence and proliferation, respectively. See Materials and methods for details. (B) Matrix presentation of model robustness. Shown is the two-way clustering result of 768 gene circuits by 20 000 random parameter sets. Red and blue colors indicate positive and negative for bistability, respectively. (C) The most robust model for bistability, 2–3–5–6–7–9b. (D) Minimal models for bistability. (Left) Ranked distribution of the robustness of minimal models in generating bistability. (Right) The top 5 minimal models for bistability. The type of logic gate and the correspondingly regulated node are indicated under each circuit. See text for details. (E) Minimal models for resettable bistability. (Left) Ranked distribution of the robustness of minimal models in generating resettable bistability. (Right) The top 2 minimal models for resettable bistability. The type of logic gate, the type of involved positive feedback, and the correspondingly regulated node are indicated under each circuit. See text for details.

Figure 3

Experimental disruption of the gene circuit 3–5–6–7 abolishes the Rb–E2F bistable switch. (A) The Cdk2 inhibitor CVT-313 selectively blocks the mutual-inhibition feedback loop 5–6, but not the other three positive-feedback loops (9, 2–3–6, and 2–7). (B) Experimental protocol of serum-pulse stimulation and Cdk2 inhibition. At time 0, cells were serum-starved and at quiescence. See Materials and methods for details. (C) The influence of Cdk2 inhibition on E2F bistability. Each curve represents the histogram of the E2F–d2GFP distribution from approximately 5000 cells. The Cdk2 inhibitor dose and sample harvest time are as indicated. The dashed lines connecting the high and low E2F–d2GFP modes are for the guide of eyes.

Figure 4

The gene circuit 3–5–6–7 exhibits high structural flexibility. (A) Structural flexibility of the gene circuit 3–5–6–7. Each direct topological neighbor of 3–5–6–7 is shown with its robustness (number in parentheses) in generating resettable bistability. (B) The correlation between structural flexibility (Y axis) and robustness (X axis) of all gene circuits in creating resettable bistability. (C) Top 10 models in structural flexibility. All models were derived from the same circuit 3–5–6–7, with corresponding link additions shown by the arrows. Number in parentheses indicates the structural flexibility of each model. Number above the oval node indicates the rank of structural flexibility. (D) Interconnected gene circuits derived from models 3–5–6–7 and 7–9a. Each node represents one gene circuit. Each edge connects direct topological neighbors (models with one-link variation). Shown in each graph are all gene circuits with up to two-link variations from the red-circled node (circuit 3–5–6–7 or 7–9a). The diameter of each node is proportional to the structural flexibility of the corresponding gene circuit. The layout of the nodes does not have specific meaning.