Role of mitogen signaling in cell cycle progression
The ERK pathway plays an important role of integrating external signals from the presence of mitogens such as epidermal growth factor (EGF) into signaling events promoting cell growth and proliferation in many mammalian cell types. In a simplified model, the presence of mitogens and growth factors trigger the activation of canonical receptor tyrosine kinases such as EGFR leading to their dimerization and subsequent activation of the small GTPase Ras. This then leads to a series of phosphorylation events downstream in the MAPK cascade (Raf-MEK-ERK) ultimately resulting in the phosphorylation and activation of ERK. The phosphorylation of ERK results in an activation of its kinase activity and leads to phosphorylation  of its many downstream targets involved in regulation of cell proliferation. In most cells, some form of sustained ERK activity is required for cells to activate genes that induce cell cycle entry and suppress negative regulators of the cell cycle. Two such important targets include Cyclin D complexes with Cdk4 and Cdk6 (Cdk4/6) which are both phosphorylated by ERK. The transition from G1 to S phase is coordinated by the activity of Cyclin D-Cdk4/6, which increases during late G1 phase as cells prepare to enter S-phase in response to mitogens. Cdk4/6 activation contributes to hyper-phosphorylation and the subsequent destabilization of retinoblastoma protein (Rb). Hypo-phosphorylated Rb, is normally bound to transcription factor E2F in early G1 and inhibits its transcriptional activity, preventing expression of S-phase entry genes including Cyclin E, Cyclin A2 and Emi1. ERK1/2 activation downstream of mitogen induced Ras signaling is necessary and sufficient to remove this cell cycle block and allow cells to progress to S-phase in most mammalian cells.
Downstream feedback control and generation of a bistable G1/S switch
The restriction point (R-point) marks the critical event when a mammalian cell commits to proliferation and becomes independent of growth stimulation. It is fundamental for normal differentiation and tissue homeostasis, and seems to be dysregulated in virtually all cancers. Although the R-point has been linked to various activities involved in the regulation of G1–S transition of the mammalian cell cycle, the underlying mechanism remains unclear. Using single-cell measurements, Yao et al., shows that the Rb–E2F pathway functions as a bistable switch to convert graded serum inputs into all-or-none E2F responses. 
Growth and mitogen signals are transmitted downstream of the ERK pathway are incorporated into multiple positive feedback loops to generate a bistable switch at the level of E2F activation. This occurs due to three main interactions during late G1 phase. The first is a result of mitogen stimulation though the ERK leading to the expression of the transcription factor Myc, which is a direct activator of E2F.  The second pathway is a result of ERK activation leading to the accumulation of active complexes of Cyclin D and Cdk4/6 which destabilize Rb via phosphorylation and further serve to activate E2F and promote expression of its targets. Finally, these interactions are all reinforced by an additional positive feedback loop by E2F  on itself, as its own expression leads to production of the active complex of Cyclin E and CDK2, which further serves to lock in a cell's decision to enter S-phase. As a result, when serum concentration is increased in a gradual manner, most mammalian cells respond in a switch-like manner in entering S-phase. This mitogen stimulated, bistable E2F switch is exhibits hysteresis, as cells are inhibited from returning to G1 even after mitogen withdrawal post E2F activation.
'Dynamic signal processing by the ERK pathway
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The EGFR-ERK/MAPK (epidermal growth factor receptor extracellular-regulated kinase/mitogen-activated protein kinase) pathway stimulated by EGF is critical for cellular proliferation, but the temporal separation between signal and response obscures the signal-response relationship in previous research.In 2013, Albeck et al. provided key experimental evidence to fill this gap of knowledge. They measured signal strength and dynamics with steady-state EGF stimulation, in which the signaling and output can be easily related. They further mapped the signal-response relationship across the pathway’s full dynamic range. Using high-content immunofluorescence (HCIF) detection of phosphorylated ERK (pERK) and live cell FRET biosensors, they monitored downstream output of the ERK pathway in both live cells and fixed cells. To further link the quantitative characteristics of ERK signaling to proliferation rates, they established a series of steady-state conditions using a range of EGF concentrations by applying EGF with different concentrations.  
Single cell imaging experiments have shown ERK to be activated in stochastic bursts in the presence of EGF. Furthermore, the pathway has been shown to encode the strength of signaling inputs though frequency modulated pulses of its activity. Using live cell FRET biosensors, cells induced with different concentrations of EGF illicit activity bursts of different frequency, where higher levels of EGF resulted in more frequent bursts of ERK activity. To figure out how S phase entry can be affected by sporadic pulses of ERK activity at low EGF concentrations, they used MCF-10A cells co-expressing EKAR-EV and RFP-geminin and identified the pulses of ERK activity with  the scoring and then align this ERK activity profiles with time of GFP-geminin induction. They found that longer periods of ERK activity stimulate S phase entry, as suggested by increased pulse length. To understand the dynamics of EGFR-ERK pathway, specifically how is the frequency and amplitude modulated, they applied the EGFR inhibitor gefitinib or the highly selective MAPK/ERK kinase (MEK) inhibitor PD0325901 (PD). Two inhibitors yield actually a little bit different result: gefitinib, at intermediate concentration, would induce pulsatory behavior and also bimodal shift, which is not observed with PD. They further combine EGF and PD together and draw the conclusion that the frequency of ERK activities is modulated by quantitative variation while the amplitude is modulated by MEK activity’s change. Lastly they turned to Fra-1, one of downstream effectors of ERK pathway, as it’s technically challenging to estimate ERK activities directly. To understand how the integrated ERK pathway output (which should be independent of either frequency or amplitude) affect the proliferation rate, they used the combination of a wide range of EGF and PD concentrations and find that there’s actually an inverted “L” shape single curvilinear relationship, which suggests that at low levels of ERK pathway output, small changes in signal intensity correspond to large changes in proliferative rate, while large changes in signal intensity near the high end of the dynamic range have little impact on proliferation. The fluctuation of ERK signaling highlights potential issues with current therapeutic approaches, providing new perspective in terms of thinking about drug targeting in the ERK pathway in cancer. 
Integration of mitogen and stress signals in proliferation
Recent live cell imaging experiments in MCF10A and MCF7 cells have shown that a combination of mitogen signaling though ERK and stress signals through activation of p53 in mother cells contributes to the likelihood of whether newly formed daughter cells will immediately re-enter the cell cycle or enter quiescence (G0) preceding mitosis. Rather than daughter cells starting with no key signaling proteins after division, mitogen/ERK induced Cyclin D1 mRNA and DNA damage induced p53 protein, both long lived factors in cells, can be stably inherited from mother cells after cell division. The levels of these regulators vary from cell to cell after mitosis and stoichiometry between them strongly influences cell cycle commitment though activation of Cdk2. Chemical perturbations using inhibitors of ERK signaling or inducers p53 signaling in mother cells suggest daughter cells with high levels of p53 protein and low levels of Cyclin D1 transcripts were shown to primarily enter G0 whereas cells with high Cyclin D1 and low levels of p53 are most likely to reenter the cell cycle. These results illustrate a form of encoded molecular memory though the history of mitogen signaling through ERK and stress response though p53.