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WIREs Syst Biol Med
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Dynamics of the mammalian cell cycle in physiological and pathological conditions

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A network of cyclin‐dependent kinases (Cdks) controls progression along the successive phases G1, S, G2, and M of the mammalian cell cycle. Deregulations in the expression of molecular components in this network often lead to abusive cell proliferation and cancer. Given the complex nature of the Cdk network, it is fruitful to resort to computational models to grasp its dynamical properties. Investigated by means of bifurcation diagrams, a detailed computational model for the Cdk network shows how the balance between quiescence and proliferation is affected by activators (oncogenes) and inhibitors (tumor suppressors) of cell cycle progression, as well as by growth factors and other external factors such as the extracellular matrix (ECM) and cell contact inhibition. Suprathreshold changes in all these factors can trigger a switch in the dynamical behavior of the network corresponding to a bifurcation between a stable steady state, associated with cell cycle arrest, and sustained oscillations of the various cyclin/Cdk complexes, corresponding to cell proliferation. The model for the Cdk network accounts for the dependence or independence of cell proliferation on serum and/or cell anchorage to the ECM. Such computational approach provides an integrated view of the control of cell proliferation in physiological or pathological conditions. Whether the balance is tilted toward cell cycle arrest or cell proliferation depends on the direction in which the threshold associated with the bifurcation is passed once the cell integrates the multiple signals, internal or external to the Cdk network, that promote or impede progression in the cell cycle. WIREs Syst Biol Med 2016, 8:140–156. doi: 10.1002/wsbm.1325 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Biological Mechanisms > Regulatory Biology
Model for the cyclin‐dependent kinase (Cdk) network driving the mammalian cell cycle. The model is composed of four modules centered on the main cyclin/Cdk complexes: cyclin D/Cdk4–6, cyclin E/Cdk2, cyclin A/Cdk2, and cyclin B/Cdk1, which control the successive phases G1, S, G2, and M of the cell cycle. Entry from a quiescent phase G0 (not illustrated) into phase G1 of the cell cycle is controlled by growth factors (GF) and/or sufficient stiffness of the extracellular matrix (ECM). The presence of growth factors elicits the activation of signaling pathways, leading to the synthesis of AP1; this transcription factor in turn promotes the synthesis of cyclin D, which is followed by entry into G1. Moreover, ECM stiffness favors activation of the focal adhesion kinase (FAK), which also leads to the synthesis of cyclin D. Entry in the cell cycle is impeded by contact inhibition at high cell density, via the Hippo/YAP pathway. The transcription factor E2F promotes and the tumor suppressor pRB impedes cell cycle progression. Cyclin D/Cdk4–6 and cyclin E/Cdk2 drive progression in G1 and the G1/S transition by phosphorylating, and thereby inhibiting, pRB. Cyclin A/Cdk2 allows progression in S and G2, while cyclin B/Cdk1 brings about the G2/M transition. The active, unphosphorylated form of pRB inhibits E2F, which promotes cell cycle progression by inducing the synthesis of cyclins D, E, and A. The protein Cdh1, inhibited by cyclin A/Cdk2, promotes the degradation of cyclin B, and inhibits Skp2, which promotes the degradation of cyclin E; activation of cyclin A/Cdk2 thus leads to the activation of cyclin B/Cdk1 and to the inhibition of cyclin E/Cdk2. The protein Cdc20, activated by cyclin B/Cdk1, promotes the degradation of cyclin A and cyclin B, which leads to the decrease in cyclin A/Cdk2 and cyclin B/Cdk1. The roles of the Cdk inhibitor p21/p27 and of the Cdk inhibitory kinase Wee1 are also indicated, together with the positive feedback loop involving Wee1 and Cdk1; the role of the phosphatase Cdc25 that activates Cdk1 and is activated by it, thus creating another positive feedback loop, is not indicated for lack of space (see supporting information in Ref for more detailed schemes of the model for the Cdk network, for a list of kinetic equations and a definition of variables and parameters). The regulatory interactions between the four Cdk modules give rise to sustained Cdk oscillations (see Figures and ), which allow the repetitive, ordered progression along the successive phases of the cell cycle. (Scheme redrawn from Refs. and .)
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The balance between cell cycle arrest and cell proliferation. The scheme integrates the multiple antagonistic factors that promote the occurrence of either sustained cyclin‐dependent kinase (Cdk) oscillations, corresponding to cell proliferation, or a stable steady state of the Cdk network, corresponding to cell cycle arrest. These controlling factors are either intrinsic to the Cdk network—oncogenes, tumor suppressors, Cdk inhibitors—or extrinsic—growth factors, stiffness of the extracellular matrix, or cell density. Scheme adapted from Ref .
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Regulation of the cyclin‐dependent kinase (Cdk) network by extracellular matrix (ECM) and growth factor (GF): serum‐ and anchorage‐dependent or independent growth. The time evolution of cyclin D/Cdk4–6, cyclin E/Cdk2, cyclin A/Cdk2, and cyclin B/Cdk1 is shown in the presence ((a), (c), (e)) or absence of soluble growth factors ((b), (d), (f)), and in the presence ((a), (b), (d)) or absence of ECM stiffness ((c), (e), (f)). (a) Healthy cell proliferation, characterized by the repetitive, sequential activation of the various cyclin/Cdk complexes, depending on GF and on the stiffness in ECM. From that condition (GF = ECM = 1), removing GF in (b) (GF = 0, ECM = 1) or reducing the stiffness of ECM in (c) (GF = 1, ECM = 0) elicits cell cycle arrest. (d) Increasing the rate of focal adhesion kinase (FAK) activation leads to cell proliferation even without GF (GF = 0, ECM = 1), resulting in serum‐independent cell growth. Moreover, in (e) an increase in the rate of synthesis of AP1 allows cell proliferation without stiffness in ECM (GF = 1, ECM = 0), leading to anchorage‐independent growth. Overexpression of the transcription factor E2F by increasing its rate of synthesis elicits cell proliferation in the absence of GF and without stiffness in ECM (GF = 0, ECM = 0), which situation defines serum‐ and anchorage‐independent growth. The figure is adapted from Figure 4 in Ref .
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Controlling the dynamics of the cell cycle by factors intrinsic or extrinsic to the cyclin‐dependent kinase (Cdk) network. Sustained oscillatory regime (cell proliferation) and stable steady states domain (cell cycle arrest) are represented in a two‐parameter plane defined toward the rates of synthesis of Cdc25, VSPAI, and Cdh1, VSCDH1A in (a), as well as toward the level of contact inhibition (CI) and the stiffness of the extracellular matrix (ECM) in (b). From the condition illustrated by the black dot in (a), the model indicates that cell proliferation is elicited by decreasing the level of Cdh1 or by increasing the level of the phosphatase Cdc25. Similarly, the model shows that, from the black dot in (b), cell proliferation is impeded by decreasing ECM or by increasing the level of CI. In (a), parameter values are as in Figure S4C in Ref , while in (b), parameter values are as in Figure B in Ref . The diagrams are adapted from Refs and .
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Control of the cell cycle by factors external to the cyclin‐dependent kinase (Cdk) network. Relative amplitude of cyclin B/Cdk1 is represented as a function of the activation rate of focal adhesion kinase (FAK), V1FAK, in (a) and of contact inhibition (CI) in (b). Increasing the activity of FAK promotes the transition from a stable steady state to sustained oscillations of the Cdk network, while increasing the level of CI elicits the switch from proliferation (Cdk oscillations) to cell cycle arrest (stable steady state). The grey zone denotes a region of coexistence between a stable steady state and a stable oscillatory regime. (c) The time evolution of cyclin B/Cdk1, in the presence of a constant increase in FAK activity (V1FAK(t) = 0.0005 × t), illustrates the switch from cell cycle arrest to cell proliferation. (d) Plotting the time evolution of cyclin B/Cdk1, the active form of YAP and the level of CI indicate that cell proliferation is abolished when CI exceeds a critical level. In the latter simulation, we considered that CI is multiplied by an arbitrary factor of 1.5 after each cell division (peak of cyclin B/Cdk1). In (d), Vs1p27 = 0.6 μM h−1, V2cdh1 = 14 h−1, while other parameter values are as in Figure in Ref .
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Effect of the DNA replication checkpoint on the oscillatory behavior of the cyclin‐dependent kinase (Cdk) network. The checkpoint is mediated by the kinases ATR and Chk1. Time series (a, b) for sustained oscillations of cyclin E/Cdk2, cyclin A/Cdk2, and cyclin B/Cdk1, and the corresponding projection of the limit cycle oscillations (c, d) into the phase plane defined by cyclin B/Cdk1 and cyclin E/Cdk2 are shown in the absence (a and c) or presence (b and d) of the DNA replication checkpoint. The checkpoint slows down the progression in the cell cycle (compare time series in (a) and (b)). Moreover, it improves the separation between the peak of cyclin B/Cdk1 defining the G2/M transition and the peak of cyclin E/Cdk2 corresponding to G1/S (compare time series, and the corresponding limit cycles in (c) and (d)). In (a) and (c), kaatr = 0, while in (b) and (d), kaatr = 0.02 μM−1 h−1; other parameter values are as in Ref .
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Mechanism of oscillatory behavior in the cyclin‐dependent kinase (Cdk) network. (a) Sustained oscillations of cyclin A/Cdk2 (green curve) and cyclin B/Cdk1 (red curve). Bifurcation diagrams illustrating the dynamical behavior of the cyclin B/Cdk1 module as a function of cyclin A/Cdk2, considered as a parameter, are shown in (b) and (c). Black curves correspond to stable steady states, red dashed curves indicate unstable steady states, while blue curves show the envelope, i.e., the maximum (upper curve) and minimum (lower curve) of sustained oscillations. Sustained oscillations in the cyclin B/Cdk1 module occur above a critical level of cyclin A/Cdk2. (c) Superimposed on the bifurcation diagram is the limit cycle trajectory of the full Cdk network (green curve). The black dots 1–5 correspond to the vertical lines 1–5 in the time series of (a). The orange square defines the stable steady state of the Cdk network in the absence of GF (GF = 0), while the orange dot corresponds to the unstable steady state observed when GF = 1 μM. Adapted from Figure in Ref .
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Growth factors (GF) control the dynamical behavior of the cyclin‐dependent kinase (Cdk) network. (a) Relative amplitude of cyclin B/Cdk1 shown as a function of GF. Low levels of GF produce a stable steady state corresponding to cell cycle arrest, while high levels of GF elicit sustained oscillations of the different cyclin/Cdk complexes, which corresponds to active cell proliferation. For intermediate levels of GF, a stable steady state coexists with sustained oscillations (grey zone). The time evolution of cyclin B/Cdk1 for subthreshold (GF = 0.1 μM) or suprathreshold amounts of GF (GF = 2 μM) is shown in (b) and (c), respectively. In the sustained oscillatory regime (GF = 2 μM), the sequential, transient activation of the different cyclin/Cdk complexes drives the ordered progression along the different phases of the cell cycle (d). Parameter values are as in Figure (a) in Ref .
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Models of Systems Properties and Processes > Mechanistic Models
Physiology > Mammalian Physiology in Health and Disease
Biological Mechanisms > Regulatory Biology

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