Amy E. Nicholson , James A. Mechanisms of B-Myb oncogenicity in ovarian cancer Audra N.
CDK inhibitors: positive and negative regulators of G1-phase progression.
References Publications referenced by this paper. The transcription factor p Not a repressor, solely an activator M. Fischer , Lydia Steiner , Kurt Engeland. Marshall , Michael F Olson. The pRb-related protein p is regulated by phosphorylation-dependent proteolysis via the protein-ubiquitin ligase SCF Skp2. Mirijam Mannefeld , Elena V.
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S2 , and a fixed-point attractor corresponding to quiescent G0 cells H. Using insight from these individual switch-level models, we separated the molecular mediators of restriction point control into our first module, termed the Restriction Switch Fig. We then turned to a minimalistic dynamic modeling framework well suited to capture the switch-like function of regulatory circuits, namely Boolean modeling 22 , 49 Methods MBOL1.
Boolean models use the crudest approximation to describe the activity of their regulatory molecules: ON active or OFF inactive.
This captures an important qualitative feature of interactions as diverse as biochemical reactions, signaling, cooperative binding or genetic regulation, namely that they respond to changes in input concentration via sigmoid functions with a step-like region of steep change 50 , In the past decade, Boolean models have emerged as a powerful framework for modeling complex, context-dependent regulatory phenotypes Supplementary Note 2.
This framework allows us to focus on the logic, rather than the kinetic details, of cell cycle regulation. What are the states it can stably maintain, and what transient paths does it reach them by? To this end we enumerate every trajectory our model can take from all 2 N possible initial states biological or not , and visualize the resulting state transition graph Methods MBOL2.
Figure 2D indicates that the Restrictions Switch has two locally stable attractor states. One stable state corresponds to cells that have yet to pass the restriction point labeled Before Restriction Pt. The Phase Switch , on the other hand, is tri-stable Fig. Its three point-attractors represent i cells that completed cytokinesis daughter cells in G0 or G1 , ii cells in G2 and iii mitotic cells at the spindle assembly checkpoint SAC.
Inside the cell, the two switches are tightly coupled to form the control network of the mammalian cell cycle Fig. These nodes represent regulatory sub-networks rather than molecular species 19 , 52 Methods FullCC.
The resulting full Cell Cycle Model has a limit cycle: the mammalian cell cycle Fig. S2 , and a fixed-point G0 attractor Fig. The rationale for constructing individual models for the two switches, as well as a coupled, modular Cell Cycle Model , is that it allows us to evaluate the dynamics of the system in terms of the behavior of its building blocks, the switches. We begin this with visualizing the attractor landscape of a network of isolated switches Fig.
This landscape is composed of every combination of every attractor phenotype of each switch. Its state transition graph is thus a set of isolated trees, representing attractor basins of individual switch-phenotype combinations. Each switch-phenotype combination is marked with a distinct color. Next, we compare the global attractor landscape of the coupled multi-switch network to its disconnected counterpart Fig.
This landscape is composed of the same ensemble of global network states. The coupled dynamics, however, creates a new set of connections state-transitions between them, giving rise to a different state transition graph. To visualize this change, we preserved the 3D position of each global network state nodes on Fig. This resulted in a color change for all but one basin on the bottom No GF plane of Fig. In contrast, growth factors give rise to a global cycle that toggles through a series of different switch-phenotype combinations. A Decoupled, the Restriction Switch top, blue , Phase Switch top, purple , and Growth Factor switch top, red create a dynamical system with 12 fixed-point attractors, representing all switch-phenotype combinations.
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B Coupled, the three switches give rise to the Cell Cycle Model top graph. This procedure reveals a single basin on the No Growth Factors plane with the fixed-point attractor G0 dark green basin and another basin on the Growth Factors plane with a periodic attractor, the cell cycle red arrows and basin. In addition to visual inference, this process can be automated by matching each global state along an attractor loop to the most similar switch-phenotype combination, and eliminating steps with no switch-phenotype change Supplementary Fig.
Intriguingly, this global cyclic behavior is not a property of a single switch, but it emerges from the connections between the underling multi-stable switches. In summary, comparing the dynamics of decoupled switches to the coupled cell-cycle model Fig. Indeed, direct simulation of mitogen withdrawal by turning OFF the GF node at different time-points along the cell cycle confirms this Fig. Our network commits to a new division the moment Cyclin A is deactivated upon mitotic entry white boxes on Fig.
This behavior is surprising, as the canonical understanding of the restriction point posits that it occurs in late G1 Published models of the full mammalian cell cycle reflect this canonical understanding 15 , 16 , 54 , 55 , 56 ; they describe cells that become mitogen-independent late in G1, complete a division cycle, reset to an uncommitted early G1 state, and again require growth factors for further division. A recent series of experiments by Spencer et al.
The entire G1 phase of this final cycle lacks environmental mitogens. Closer examination of individual cell states following cytokinesis revealed that continuously cycling cell populations stochastically assume two distinct phenotypes. The majority of cells start with slightly elevated Cdk2 activity, which increases immediately after cytokinesis and leads to rapid S-phase entry. The remaining cells, with slightly lower Cdk2 activity following cytokinesis, exit into a temporary G0-like state where Cdk2 activity remains low.
Subsequently, these cells spontaneously reenter the cell cycle after highly variable pause lengths. Based on these results, the authors hypothesized that mammalian cells have two distinct restriction points. Bottom , GF withdrawal in early Metaphase after Cyclin A inhibition leads to commitment to an additional cycle. E Percentage of cells that transiently exit the cell cycle as a function of growth stimulation. Horizontal lines mark experimentally reported percentages in three mammalian cell lines In contrast, our model shows that a single bistable switch is responsible for both commitments.
Depending on the history of each individual cell, the Restriction Switch can either flip its state in late G1 upon mitogen exposure in G0; Supplementary Fig. S3 , or early in Metaphase in continuously dividing cells; Fig. Running our model with a stochastic input where GF is randomly set to ON with probability p GF in every time-step allows us to qualitatively reproduce these experimental observations.
As Fig. Log-linear fitting of these distributions reveals that the G0 escape rate increases roughly as the 3 rd power of p GF ; Fig. The latter fraction declines sharply with growth factor saturation. Experimentally measured values in different cell types are commensurate with low or medium growth stimulation in our model Fig.
Once flipped in late G1, this circuit remains committed even in the absence of active Cyclin D responsible for flipping it by inactivating RB. Thus, the above feedback-loop is unable to commit cells to another division. We expect this to occur abruptly upon Cyclin A deactivation at the start of mitosis. The effect of mitogen removal during G2 depends on whether this loss can lower Myc before the transition occurs. Modular construction of the Cell Cycle Model allows us to examine the behavior of the Restriction Switch as a semi-autonomous circuit highlighted in Fig.
This procedure reveals that the Restriction Switch is only bistable in the absence of growth factors Fig. This monostability guarantees that upon growth factor stimulation the regulatory network deterministically enters the cell cycle. A Restriction Switch embedded in the Cell Cycle network. Middle : dynamics of the full model exposed to a short GF pulse that triggers a single cycle. Middle: deterministic cell cycle dynamics of the full model. More importantly, this method allows us to examine the behavior of the Restriction Switch as the cell cycle unfolds time-trace in Fig.
Its behavior is dominated by Replication which resets it into the Before RP state , and growth factors, which otherwise keep it in the Past RP state. In intracellular environments the Restriction Switch encounters upon abrupt growth-factor removal at various points along the cell cycle Fig.