Growth factor stimulation of G₀ quiescent cells drives them into the growth factor-dependent early G₁ phase of the cell cycle, followed by transition into the growth factor-independent late G₁ phase and progression into S phase (Ho and Dowdy, 2002; Ortega et al, 2002; Sherr, 2004). This irreversible commitment point, termed the restriction point (Pardee, 1974), is correlated with inactivation of the retinoblastoma tumor suppressor protein (pRb) by hyperphosphorylation. pRb, a negative regulator of G₁-phase cell-cycle progression, binds E2F transcription factors and chromatin remodeling proteins (HDAC, Suv39, BRG1) to repress E2F target gene expression (Ho and Dowdy, 2002; Ortega et al, 2002; Sherr, 2004). pRb is unphosphorylated and not bound to E2Fs in G₀ quiescent cells. Growth factor stimulation of cells and transition into early G₁ results in hypophosphorylation of pRb by cyclin:Cdk complexes that promote its assembly with E2Fs (Ezhevsky et al, 2001). At the restriction point, cyclin:Cdk complexes inactivate pRb by hyperphosphorylation resulting in E2F release and target gene induction. In both cycling normal and tumor cells, pRb oscillates between an active, hypophosphorylated form in early G₁ and an inactive, hyperphosphorylated form in late G₁, S and G₂/M phases (Fang et al, 1996; Ezhevsky et al, 1997, 2001; Brugarolas et al, 1999; Nagahara et al, 1999; Stevaux and Dyson, 2002). Thus, pRb is differentially regulated by two opposing cyclin:Cdk complexes.

The current paradigm of G₁ cell-cycle progression argues that growth factor stimulation of quiescent cells results in the gradual accumulation of active cyclin D:Cdk4/6 complexes that perform at least two critical functions for cell-cycle progression: (1) partial inactivation of pRb at the restriction point, resulting in release of E2F transcription factors that drive cyclin E expression, and (2) sequestration of the p27^Kip1 Cdk inhibitor (CKI), resulting in activation of cyclin E:Cdk2 complexes that complete pRb inactivation. However, recent targeted gene deletions of G₁-phase cyclins and Cdks in mice have raised several concerns about the validity of this paradigm (Pagano and Jackson, 2004; Sherr and Roberts, 2004). Moreover, similar to tumor cells growing in vivo, the current paradigm remains largely untested in proliferating cells exposed to continuous growth factors. Here, using experimental data derived from highly synchronized cells exposed to continuous growth factors, we developed a mathematical model of G₁ cell-cycle progression that accurately simulates the observed physiological data, kinetics and transitions. The model points to the presence of an unknown activating ‘modifier' element that responds to metabolic input to activate Cdk2 and potentially serves as a functional analogue of the yeast G₁-phase activator Bck2 (Newcomb et al, 2003; Costanzo et al, 2004; de Bruin et al, 2004).

To dissect regulation of G₁ cell-cycle progression, we analyzed human HCT116 colon carcinoma cells (RB^WT, p53^WT, p16^MUT) grown under conditions of constant growth factor exposure. HCT116 cells were synchronized in early G₁ phase by density arrest (contact inhibition) for 48 h in the presence of serum and released from arrest by low-density replating. Synchronized cells consistently entered S phase at 10 h and G₂/M phase by 18 h (Figure 1A). This highly reproducible cell-cycle synchronization method served as the basis for all subsequent experiments.

Figure 1 Physiological expression and activity profiles of cell-cycle regulators during transition from early G1, across the restriction point, into late G1 and S phase. Density-arrested (contact-inhibited) and released HCT116 cells were assayed for (A) kinase (more ...)

We examined the expression and activity profiles of cell-cycle regulatory proteins at various time points in the synchronized HCT116 cells, which yielded several important observations: (1) cyclin D1 and D2 were constitutively expressed and cyclin D:Cdk4/6 complexes were constitutively active from start to finish (0–27 h) (Figure 1B). We did not detect cyclin D3. (2) In contrast, cyclin E:Cdk2 complexes were present throughout the cell cycle, but oscillated between inactive complexes in early G1 and active complexes in late G₁, correlating with the inactivating, hyperphosphorylation of pRb and p130 (Figure 1B). (3) pRb and p130 pocket proteins were present in their active, hypophosphorylated forms in early G₁ phase (0–4 h) and the inactive, hyperphosphorylated forms first appeared at 6 h (Figure 1B). We did not detect p107. (4) Consistent with hyperphosphorylated pRb/p130 being functionally inactive, the switch from hypo- to hyperphosphorylation of pRb/p130 correlated with expression of bona fide E2F target genes, cyclin A2 and DHFR (Figure 1C), in late G₁. Similar profiles were obtained from S-phase-synchronized arrested/released HCT116 cells (data not shown). (5) Lastly, similar to G₁-induced arrest by metabolic starvation of glucose (Singh et al, 1999), deprivation of glutamine amino acids results in an early G1 cell-cycle arrest typified by continued cyclin D:Cdk4/6 activity, the presence of active hypophosphorylated pRb and inactive cyclin E:Cdk2 complexes (Figure 1D).

Thus, under constant growth factor conditions, we find constitutive cyclin D:Cdk4/6 activity, whereas cyclin E:Cdk2 and pRb activity oscillates during transition from early to late G₁ phase. These observations are consistent with results from cycling human T cells and cycling human primary fibroblasts (Ezhevsky et al, 2001). These observations combined with the triple cyclin D and double Cdk4/6 genetic ablation studies (Kozar et al, 2004; Malumbres et al, 2004) suggest that cyclin D:Cdk4/6 activity is neither necessary nor sufficient for activation of cyclin E:Cdk2 complexes. Thus, the rate-limiting activator of Cdk2 complexes at the restriction point remains undefined.

Several mathematical models have been developed that provide insights into dynamical mechanisms of the cell cycle under specific conditions (Aguda and Tang, 1999; Qu et al, 2003; Novak and Tyson, 2004). Novak and Tyson's (2004) model of the restriction point reproduces earlier experimental results of cell-cycle progression in cycloheximide-treated cells performed by Zetterberg and Larsson (1995). That model as well as a model developed by Qu et al (2003) reflect the current paradigm, which ultimately requires cyclin E:Cdk2 complexes to oscillate in phase with inactivated pRb. In both models, cyclin E:Cdk2 also acts as part of a negative feedback loop promoting the degradation of its inhibitor p27. Although these models reproduce central features of G₁ progression in mammalian cells, they do not account for our experimental results of constitutively active cyclin D and/or constitutive cyclin E expression throughout G₁ phase. Modification of the Tyson model to constitutively express cyclin E resulted in continued activation of cyclin E:Cdk2 complexes and constant nonphysiological inactivation of pRb. A similar effect on pRb hyperphosphorylation was observed when p27 was eliminated from this model. In contrast, p27 genetic deletions have no effect on the timing of pRb inactivation (Pagano and Jackson, 2004; Sherr and Roberts, 2004). Therefore, we surmised that the rate-limiting mechanism governing Cdk2 activation requires mechanisms distinct from those of positive feedback loops and antagonistic interactions represented in these mathematical models.

To quantitatively describe experimentally observed dynamics of restriction point progression, we developed a mathematical model of G₁ progression that incorporates additional regulation of Cdk2. For ease of interpretation, the mathematical model is presented in diagrammatic cell language (DCL) (Figure 2A) and in systems biology markup language (see Supplementary information). The model diagram includes interactions between some of the relevant players in G₁ cell-cycle progression, including cyclins, Cdks, CKIs, pRb, E2F transcription factors, APC/C and Emi1 (Ezhevsky et al, 2001; Ho and Dowdy, 2002). Cdk4 represents both Cdk4 and Cdk6, as both proteins have been shown to have homologous functions in G₁ progression and they are activated when bound to cyclin D (D1, D2 or D3). Cyclin D:Cdk4/6 complexes are inhibited by p16-INK4a family (not present in HCT116 cells) and p27 family of proteins. Cyclin E and cyclin A complexed with Cdk2 are also inhibited by p27 binding.

Figure 2 Dynamical model of the mammalian G1 cell-cycle progression. (A) The mathematical model is represented in the DCL. Cdks and pRb are boxes, with circles inside denoting possible states. As an example we show the various Cdk2 states as vectors of integers (more ...)

In formulating the model, we made select simplifications to reduce the number of model parameters and focus on modeling the biology relevant for ascertaining the potential rate-limiting mechanism governing Cdk2 activation. Cdk2 and Cdk1 are present in an inhibited phosphorylated (Thr¹⁴ and Tyr¹⁵) state and require dephosphorylation by Cdc25A, followed by Thr¹⁶⁰ or Thr¹⁶¹ activating phosphorylation, respectively, by CAK. We did not explicitly include these kinases and phosphatases in our mathematical model because, beyond the requirement for Cdk activation, their role in regulating G₁ transition is not yet well defined. As this model concentrates on G₁ progression, interactions involving APC/C were also simplified (Vodermaier and Peters, 2002; Murray, 2004).

Parameter values of processes described in the model are generally unknown in vivo, are cell-type-specific and can vary over large ranges. Physiologically correct model output is fairly robust to variations of parameters within those ranges. Most parameter values are determined by fitting to quantitative data. To add additional constraints to the possible solutions in parameter space that are consistent with the quantitative data, we fixed some parameter values to physiological ranges found in the literature. Protein unbinding rates were set to 0.1 min⁻¹, which is of the same order of magnitude as in other models of protein interaction. Turnover for cyclins is rapid and was fixed to 0.05 min⁻¹ (half-life of 14 min) (Maity et al, 1997; Carlson et al, 1999; Kahl and Means, 2004). Concentrations of proteins in ‘ground' states were set to physiologically reasonable rates found in the literature. Cdk levels were 100 000 molecules/cell (Arooz et al, 2000). Components such as pRb and APC/C have concentrations lower than Cdks.

Cycling cells (normal and tumor) represent an oscillating system in a constant environment that periodically resets itself, requiring doubling of cellular mass and genome before cytokinesis (Jorgensen and Tyers, 2004). Recent evidence suggests that achieving an autonomous critical cell mass is a prerequisite for cells to progress from G₁ into S phase and complete cell division (Dolznig et al, 2004; Jorgensen and Tyers, 2004). Also, treatment of cells with cell-cycle inhibitors does not slow down cellular growth, whereas inhibitors of cellular growth induce cell-cycle arrest, suggesting that growth directly or indirectly regulates cell-cycle progression (Fingar et al, 2002; Kim et al, 2002; Dutcher, 2004). In addition, metabolic restriction experiments result in an early G₁ cell-cycle arrest containing active cyclin D:Cdk4/6 complexes, active hypophosphorylated pRb and inactive cyclin E:Cdk2 complexes (Figure 1D; Singh et al, 1999). Moreover, the analogous G₁ regulatory pathway in yeast (START) contains a metabolically regulated activator of G₁ cell-cycle progression, termed Bck2 (Newcomb et al, 2003; Costanzo et al, 2004; de Bruin et al, 2004). Taken together, these observations led us to introduce into our G₁ progression model a ‘cell growth' variable as an unspecified activating ‘modifier' of Cdk2 (Figure 2A).

The activating ‘modifier' is implemented as a switch, turned on at the end of early G₁ phase inducing a change in Cdk2 required for its activation, which is the simplest functional interaction. Genetic ablation studies of cyclin E or Cdk2 demonstrate that primary and tumor cells fail to arrest (Berthet et al, 2003; Ortega et al, 2003; Tetsu and McCormick, 2003). In contrast to previously published models of G₁ progression in mammalian cells, our mathematical model also incorporates mechanisms to account for cyclin E or Cdk2 deletion. Consistent with appropriate kinetic activation of cyclin A:Cdk2/1 activation in cyclin E1/E2-deficient cells (Kozar et al, 2004), cyclin A:Cdk2 or cyclin A:Cdk1 complexes are also activated by the ‘modifier', providing compensatory inactivating hyperphosphorylation of pRb.

Global parameter optimization techniques yielded an ensemble of parameter sets that enabled our model to quantitatively reproduce the data in Figure 1 (Figure 2B–E). The result of an optimization run is an ensemble of 100 parameter sets that give the lowest cost function. To account for cyclin E and Cdk2 genetic deletion experiments, we examined each parameter set of the ensemble under the cyclin E or Cdk2 deletion condition by setting the respective protein synthesis rates to zero. The network is robust to variation in most of the parameters under the deletion condition. However, owing to variations in the parameters for interactions where cyclin A is involved, there are model solutions that do not satisfy the deletion condition. Solutions were accepted for the parameter sets for which cyclin A at 16 h rose to at least 20% of the activation level of the unperturbed simulation for each deletion. Out of the 100 parameter sets, six fulfilled the requirement of required cyclin A levels for these parameter sets under the unperturbed condition, cyclin E deletion and Cdk2 deletion (see Supplementary Figure 2). In addition, all of these solutions showed no effect on pRb inactivation when p27 was eliminated from the model (data not shown). This is consistent with the activating ‘modifier' as an essential regulator of Cdk2/1 activation in our model.

To test the ability of the model to predict the outcome of an intervention, we examined the effect of Cdk2/1 inactivation. Prediction of Cdk2/1 inhibition was accomplished by reducing the association rates of Cdks to its substrates by a specified percent fraction. The binding constant of the active Cdk complexes with the substrate pRb, kb_–E2_—pRB, kb_–A2_—pRB and kb_–A1_—pRB, were simultaneously reduced by different amounts of inhibition. The model predicts that at greater than 80% inhibition of Cdk2/1, the fraction of active hypophosphorylated pRb at 16 h increases, whereas inactive hyperphosphorylated pRb decreases (Figure 2E). These results were consistent with validation experiments by acute Cdk2/1 inactivation with Roscovitine (Senderowicz, 2003; Figure 1E). Roscovitine treatment of cells abolished Cdk2/1 activity and pRb remained in its active, hypophosphorylated form. In contrast, control cells contained active Cdk2/1 and inactive, hyperphosphorylated pRb. At the low dose used here (15 μM), no alterations of Erk or cyclin D:Cdk4/6 activity were detected (Figure 1E). Cyclin E:Cdk2 kinase activity peaks during early S phase (Figure 1B). However, pRb becomes hyperphosphorylated concomitant with the initial cyclin E:Cdk2/1 activation at/near the restriction point, suggesting that only a low level of cyclin E:Cdk2 activity is required to completely inactivate a cell's complement pRb (Figures 1B and 2E). These data also effectively exclude the potential for the modifier to act on a speculated early G1-phase pRb phosphatase that would keep pRb in an active state. In that case, the prediction would be that inactivation of downstream Cdk2/1 kinase activity would result in hyperphosphorylated (inactive) pRb, as the putative early G1 phosphatase would be inactivated by the modifier. However, the experimental data in Figure 1E clearly show that Cdk2/1 inactivation maintains pRb in the active state, and thereby excludes the involvement of a speculative pRb phosphatase. Moreover, a pRb early G1 phosphatase is also without precedent in the literature. Thus, our model accurately predicted the experimental outcome for both complete Cdk2 inactivation and partial Cdk2 inhibition (Figure 3).

Figure 3 Model of G1 cell-cycle progression. Combining the physiological data (Figure 1) with results from the data-driven mathematical model (Figure 2), we propose the following: growth factor stimulation of quiescent G0 cells activates cyclin D:Cdk4/6 complexes (more ...)

Most current explanations of G₁ cell-cycle progression are based primarily on data generated from serum deprivation/restimulation experiments and overexpression studies. In serum restimulation experiments, cyclin D:Cdk4/6 activity gradually increases during the first early G₁ phase. However, in proliferating cells, cyclin D:Cdk4/6 activity is essentially constitutive in early and late G₁ and S phases. In contrast, pRb oscillates between the active, hypophosphorylated form in early G₁ and the inactive, hyperphosphorylated form in late G₁ and S phases of the cell-cycle phases (see Figure 1) (Fang et al, 1996; Ezhevsky et al, 1997, 2001; Brugarolas et al, 1999; Nagahara et al, 1999). The G₁ cell-cycle paradigm will need to be adjusted to account for these experimental observations. Thus, either two completely independent regulatory networks controlling G₁ cell-cycle progression exist—one regulating early G₁ phase in cells coming from quiescence and another regulating G₁-phase transitions in cycling cells—or, there is a common mechanism that regulates G₁-phase progression that has been overshadowed by the ramping up of cyclin D:Cdk4/6 activity observed at the beginning of early G₁ phase in serum restimulation experiments. The data-driven mathematical approach (Christopher et al, 2004) presented here supports a single, regulatory mechanism where cyclin E:Cdk2 activation is independent of cyclin D:Cdk4/6. Our mathematical model is in agreement with recent reports showing genetic ablation of either all three D-type cyclins (Kozar et al, 2004) or their cognate Cdk4/6 kinases (Malumbres et al, 2004) has limited effect on the timing of cyclin E:Cdk2 activation. Importantly, these reports also exclude p27^Kip1 sequestration by cyclin D:Cdk4/6 complexes as the rate-limiting step for cyclin E:Cdk2 activation (Pagano and Jackson, 2004; Sherr and Roberts, 2004).

Inhibition of metabolic processes results in a G₁ arrest typified by continued active cyclin D:Cdk4/6 complexes, active hypophosphorylated pRb and inactive cyclin E:CDk2 complexes, suggesting that metabolism plays a key, yet undefined role in G₁ cell-cycle progression. Our mathematical model is consistent with evidence linking cell growth with regulation of proliferation (Tapon et al, 2001; Saucedo and Edgar, 2002). It postulates the existence of an unspecified activating ‘modifier' pathway that responds to cellular growth and results in activation of cyclin E:Cdk2 complexes at the restriction point allowing cells to progress through the cell cycle. Consistent with the presence of an activating modifier element in the mammalian G₁ cell cycle, the yeast G₁ cell cycle is positively regulated by both cyclin:cdk complexes (Cln3:Cdc28) and an uncharacterized activator, Bck2 (Newcomb et al, 2003; Costanzo et al, 2004; de Bruin et al, 2004). Bck2 is regulated by metabolic stimuli and genetically functions below Cln3 (cyclin D homologue) and activates the equivalent of cyclin E:Cdk2 complexes (Cln1/2:Cdc28) at the yeast restriction point (START). Bck2 is a non-cyclin, non-Cdk protein of unknown function that potentially allows for metabolic activation of G₁ cell-cycle progression. Unfortunately, similar to the lack of homology between pRb and the equivalent yeast transcription factor repressor, Whi5, a metazoan Bck2 homologue has not yet been identified. Elucidating the biochemical mechanism of Cdk2 activation and ascertaining the identity of the activating ‘modifier' proposed here is an important step in investigating the effects of therapeutics targeting G₁ cell-cycle progression to advance drug development.

cyclin A2 (GGCCGAAGACGAGACGGGTTGCACC),

(CAGGCCAGCTTTGTCCCGTGAC);

DHFR (ATGCCTTTCTCCTCCTGG), (CGCTAAACTGCATCGTCGC); and

β-actin (TGAACCCCAAGGCCAACCGCGAGAA), (AAGCAGCCGTGGCCATCTCTTG);

cyclin D1 (GCCTGAACCTGAGGAGCCCC), (GTCTAAGTCAGAGATGGAAGG);

cyclin E1 (TAAAGTGGCGTTTAAGTCCCC), (ATCTTCATCAGCGACGCC).

We thank L Felser, B Chaudhuri and R Hoetzlein for software and computational contributions, J Fox and C Hill for critical input and P Jackson for anti-Emi1 antibodies. This work was supported by Gene Network Sciences, the US Department of Commerce, National Institute of Standards and Technology, Advanced Technology Program, Cooperative Agreement Number 70NANB2H3060 and the Howard Hughes Medical Institute (SFD).