Molecular mechanisms creating bistable switches at cell cycle transitions

Abstract

Progression through the eukaryotic cell cycle is characterized by specific transitions, where cells move irreversibly from stage i-1 of the cycle into stage i. These irreversible cell cycle transitions are regulated by underlying bistable switches, which share some common features. An inhibitory protein stalls progression, and an activatory protein promotes progression. The inhibitor and activator are locked in a double-negative feedback loop, creating a one-way toggle switch that guarantees an irreversible commitment to move forward through the cell cycle, and it opposes regression from stage i to stage i-1. In many cases, the activator is an enzyme that modifies the inhibitor in multiple steps, whereas the hypo-modified inhibitor binds strongly to the activator and resists its enzymatic activity. These interactions are the basis of a reaction motif that provides a simple and generic account of many characteristic properties of cell cycle transitions. To demonstrate this assertion, we apply the motif in detail to the G1/S transition in budding yeast and to the mitotic checkpoint in mammalian cells. Variations of the motif might support irreversible cellular decision-making in other contexts.

Figure 1.

Generic picture of a bistable cell cycle switch. (a) Signal–response curve. The activator of stage i of the cell cycle (‘response’) is a bistable function of a ‘signal’ generated by stage i−1, for 0 ≤ signal < threshold. When the signal exceeds the threshold, the activator turns on and the cell proceeds to stage i. Subsequently, even if the signal drops to zero, the activator stays on and the cell remains in stage i. (b) An activator–inhibitor pair involved in a double-negative feedback loop can generate the sort of bistable response postulated in (a). (c,d) Phase planes for an activator–inhibitor system for (c) signal < threshold and for (d) signal > threshold.

Figure 2.

The SIMM motif. (a) Wiring diagram. Enzyme A binds to substrate I to form an enzyme–substrate complex, A:I, which then reacts to form a modified substrate IM plus free enzyme. Then, the same sequence of steps occurs a second time to form the doubly modified form of I. (b) Signal–response curve. For a fixed value of total enzyme concentration, A_T = 1, the steady-state concentration of free enzyme, A_ss, is plotted as a function of total substrate concentration, I_T. Path b is explained in (d). (c) Signal–response curve. For a fixed value of total substrate concentration, I_T = 4, the steady-state concentration of free enzyme, A_ss, is plotted as a function of total enzyme concentration, A_T. Path c is explained in (d). (d) Control plane. As a function of A_T and I_T, the reaction network is bistable only within the V-shaped region. Below the V, the checkpoint is engaged (A inhibited), and above the V, the checkpoint is disengaged (A active). The black circle represents the neutral state of the checkpoint before the cell cycle transition: the reaction system is in the bistable region, in the checkpoint-engaged stable steady state. Paths b and c are possible paths for disengaging the checkpoint and triggering an irreversible cell cycle transition, as shown in (b,c). Indeed, any path that carries the control system across the upper boundary of the V and back to the neutral state will trigger an irreversible cell cycle transition. Eventually, the checkpoint must be reset to the ‘engaged’ state, which requires the system to follow a path r that crosses the lower boundary of the V and then returns to the neutral state.

Figure 3.

The SIMM* motif. (a) Wiring diagram. For the second modification of I, we replace the Michaelis–Menten mechanism by a simple mass-action rate law. (b) Control plane, A_T versus I_T. The V-shaped bistability zone for the SIMM* motif (solid line) is almost identical to the zone for the full SIMM motif (dashed line, from figure 2d). (c) Phase plane, I_MM versus , in the bistable zone (A_T = 2 and I_T = 6). There are two stable steady states—checkpoint engaged (1) and checkpoint disengaged (3)—separated by an unstable steady state (2). (d) Phase plane in the monostable zone (A_T = 3 and I_T = 6). There is now a single steady state: the stable checkpoint-disengaged state (3). In (c,d), the arrows indicate the direction of change of the state variables, I_MM and , as predicted by the dynamical system, equations (3.8) and (3.9).

Figure 4.

The Sic1-cyclin switch in budding yeast. (a) Wiring diagram for Sic1 and Clb (B-type cyclins). Sic1 is a substrate and inhibitor of Clb-dependent kinase. The second phosphorylation of Sic1 leads to its rapid degradation. (b) Signal–response curve. The total concentration of Sic1 in the cell (a variable) depends, in a bistable manner, on the total concentration of Clb cyclins in the cell (a parameter, in this model). The black dashed line indicates how the switch flips from the Clb-inactive state to the Clb-active state as [ClbT] increases. (c) Wiring diagram for Sic1, Clb and Cln (G1-type cyclins). Sic1 is a substrate—but not an effective inhibitor—of Cln-dependent kinase. (d) Control plane, [ClnT] versus [ClbT]. The V-shaped bistable zone is coloured red. The ‘cell cycle trajectory’ (path a–b–c–d–e) is explained in the text. (e) Simulation of the G1b/S transition in budding yeast, and resetting the checkpoint at cell division. Equations (3.13)–(3.16) are solved numerically for the parameter values in table 2d, and with additional differential equations for the synthesis and degradation of ClnT and ClbT. The synthesis terms for ClnT and ClbT are turned on at t = 0 (the Start transition); at t = 30 min, synthesis of ClnT is turned off and degradation is turned on; at t = 50 min (cell division), synthesis of ClbT is turned off and degradation is turned up. The G1/S transition takes place at t ≈ 20 min, when the cell cycle trajectory passes point b in (d), and there is enough active Clb-kinase to trigger DNA replication. About 50 min after Start, the cell divides and the G1 phase is re-established.

Figure 5.

The mitotic checkpoint. (a) Wiring diagram. The mitotic checkpoint complex (MCC) binds to and inhibits the anaphase-promoting complex (APC). APC ubiquitinates MCC, and the ubiquitin moiety is removed by a de-ubiquitinase. Poly-ubiquitination of MCC leads to degradation of some of its components (notably Cdc20) and release of inactive checkpoint proteins (labelled by Mad2 only). Checkpoint proteins (Mad2, etc.), are reactivated by tensionless centromeres, N₀ = N_T(1 − X_tens), leading to reassembly of MCC. Securin degradation by active APC leads to dissolution of cohesin complexes and separation of sister chromatids in early anaphase. (b) Signal–response curve: [MCCT], the total concentration of active MCC, versus X_tens, the fraction of centromeric regions that are in tension on the mitotic spindle. The black dashed curve indicates that the mitotic checkpoint is engaged (i.e. [MCCT] large) until the last chromosome aligns on the mitotic spindle. When X_tens increases above approximately 0.97, the checkpoint disengages and APC is activated. As the cell enters anaphase, X_tens drops back to zero. (c) Simulation of in vitro release of the mitotic checkpoint. Compare with fig. 1 of Reddy et al. [23]. Note that when X_tens drops below approximately 0.89 the checkpoint re-engages, as predicted by the signal-response curve in (b). (d) Wiring diagram of the CycB–MCC–APC network. Cycin B-dependent kinase is required for activation of tensionless centromeres, X_0A. (e) Signal–response curve: [MCCT] versus X_tens. Now the threshold for re-engaging the checkpoint has moved to negative values of X_tens, and the checkpoint remains disengaged when X_tens drops to zero in anaphase (black dashed line). (f) Simulation of in vivo release of the mitotic checkpoint. The checkpoint mechanism does not re-engage as X_tens decreases.

Figure 6.

Wiring diagrams for other cell cycle transitions. (a) The G2/M transition. Wee1 is a protein kinase that phosphorylates and inactivates Cdk1 (i). Simultaneously, active Cdk1 (complexed with cyclin B) phosphorylates Wee1 on multiple sites in a typical SIMM motif (ii), where Wee1 functions as a stoichiometric inhibitor of Cdk1 as well as a substrate. Cdc25, the phosphatase that dephosphorylates P-Cdk1, is activated by multi-site phosphorylation catalysed by active Cdk1. (b) Mitotic exit. Cdh1 (in combination with the APC) stabilizes G1 phase of the cell cycle by poly-ubiquitinating cyclin B (i). Simultaneously, active Cdk1:CycB phosphorylates Cdh1 on multiple sites (ii). Both sides of the interaction have SIMM topology, but it is not known if either of the ‘substrates’ serves also as a ‘stoichiometric inhibitor’ of the enzyme.