Claude Gérard

The orphan receptor cDNA RDC7 encodes an A1 adenosine receptor.

The extensive amino acid sequence conservation among G protein‐coupled receptors has been exploited to clone new members of this large family by homology screening or by PCR. Out of four such receptor cDNAs we cloned recently, RDC7 corresponds to a relatively abundant transcript in the brain cortex, the thyroid follicular cell and the testis. We have now identified RDC7 as an A1 adenosine receptor. The A1 agonist CPA [N6‐cyclopentyladenosine] decreased by 80% cAMP accumulation in forskolin‐stimulated CHO cells stably transfected with RDC7. Specific binding of another A1 adenosine agonist, [3H]CHA [N6‐cyclohexyladenosine], was demonstrated on membranes from Cos cells transfected with a pSVL construct harbouring the RDC7 cDNA insert. The binding characteristics were similar to those of the natural brain A1 receptor. The recombinant and the natural receptors behaved also in the same way in displacement experiments involving a series of A1 adenosine agonists. The binding characteristics of RDC7 were compared to those of RDC8, another orphan receptor recently identified as an A2 adenosine receptor. The two molecular species RDC7 and RDC8 correspond clearly to the A1 and A2 receptor entities defined hitherto on a purely pharmacological basis.

Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle

We propose an integrated computational model for the network of cyclin-dependent kinases (Cdks) that controls the dynamics of the mammalian cell cycle. The model contains four Cdk modules regulated by reversible phosphorylation, Cdk inhibitors, and protein synthesis or degradation. Growth factors (GFs) trigger the transition from a quiescent, stable steady state to self-sustained oscillations in the Cdk network. These oscillations correspond to the repetitive, transient activation of cyclin D/Cdk4–6 in G1, cyclin E/Cdk2 at the G1/S transition, cyclin A/Cdk2 in S and at the S/G2 transition, and cyclin B/Cdk1 at the G2/M transition. The model accounts for the following major properties of the mammalian cell cycle: (i) repetitive cell cycling in the presence of suprathreshold amounts of GF; (ii) control of cell-cycle progression by the balance between antagonistic effects of the tumor suppressor retinoblastoma protein (pRB) and the transcription factor E2F; and (iii) existence of a restriction point in G1, beyond which completion of the cell cycle becomes independent of GF. The model also accounts for endoreplication. Incorporating the DNA replication checkpoint mediated by kinases ATR and Chk1 slows down the dynamics of the cell cycle without altering its oscillatory nature and leads to better separation of the S and M phases. The model for the mammalian cell cycle shows how the regulatory structure of the Cdk network results in its temporal self-organization, leading to the repetitive, sequential activation of the four Cdk modules that brings about the orderly progression along cell-cycle phases.

Entrainment of the mammalian cell cycle by the circadian clock: modeling two coupled cellular rhythms.

The cell division cycle and the circadian clock represent two major cellular rhythms. These two periodic processes are coupled in multiple ways, given that several molecular components of the cell cycle network are controlled in a circadian manner. For example, in the network of cyclin-dependent kinases (Cdks) that governs progression along the successive phases of the cell cycle, the synthesis of the kinase Wee1, which inhibits the G2/M transition, is enhanced by the complex CLOCK-BMAL1 that plays a central role in the circadian clock network. Another component of the latter network, REV-ERBα, inhibits the synthesis of the Cdk inhibitor p21. Moreover, the synthesis of the oncogene c-Myc, which promotes G1 cyclin synthesis, is repressed by CLOCK-BMAL1. Using detailed computational models for the two networks we investigate the conditions in which the mammalian cell cycle can be entrained by the circadian clock. We show that the cell cycle can be brought to oscillate at a period of 24 h or 48 h when its autonomous period prior to coupling is in an appropriate range. The model indicates that the combination of multiple modes of coupling does not necessarily facilitate entrainment of the cell cycle by the circadian clock. Entrainment can also occur as a result of circadian variations in the level of a growth factor controlling entry into G1. Outside the range of entrainment, the coupling to the circadian clock may lead to disconnected oscillations in the cell cycle and the circadian system, or to complex oscillatory dynamics of the cell cycle in the form of endoreplication, complex periodic oscillations or chaos. The model predicts that the transition from entrainment to 24 h or 48 h might occur when the strength of coupling to the circadian clock or the level of growth factor decrease below critical values.

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.

A skeleton model for the network of cyclin-dependent kinases driving the mammalian cell cycle

We previously proposed a detailed, 39-variable model for the network of cyclin-dependent kinases (Cdks) that controls progression along the successive phases of the mammalian cell cycle. Here, we propose a skeleton, 5-variable model for the Cdk network that can be seen as the backbone of the more detailed model for the mammalian cell cycle. In the presence of sufficient amounts of growth factor, the skeleton model also passes from a stable steady state to sustained oscillations of the various cyclin/Cdk complexes. This transition corresponds to the switch from quiescence to cell proliferation. Sequential activation of the cyclin/Cdk complexes allows the ordered progression along the G1, S, G2 and M phases of the cell cycle. The 5-variable model can also account for the existence of a restriction point in G1, and for endoreplication. Like the detailed model, it contains multiple oscillatory circuits and can display complex oscillatory behaviour such as quasi-periodic oscillations and chaos. We compare the dynamical properties of the skeleton model with those of the more detailed model for the mammalian cell cycle.

The balance between cell cycle arrest and cell proliferation: control by the extracellular matrix and by contact inhibition

To understand the dynamics of the cell cycle, we need to characterize the balance between cell cycle arrest and cell proliferation, which is often deregulated in cancers. We address this issue by means of a detailed computational model for the network of cyclin-dependent kinases (Cdks) driving the mammalian cell cycle. Previous analysis of the model focused on how this balance is controlled by growth factors (GFs) or the levels of activators (oncogenes) and inhibitors (tumour suppressors) of cell cycle progression. Supra-threshold changes in the level of any of these factors can trigger a switch in the dynamical behaviour of the Cdk 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. Here, we focus on the regulation of cell proliferation by cellular environmental factors external to the Cdk network, such as the extracellular matrix (ECM), and contact inhibition, which increases with cell density. We extend the model for the Cdk network by including the phenomenological effect of both the ECM, which controls the activation of the focal adhesion kinase (FAK) that promotes cell cycle progression, and cell density, which inhibits cell proliferation via the Hippo/YAP pathway. The model shows that GFs and FAK activation are capable of triggering in a similar dynamical manner the transition to cell proliferation, while the Hippo/YAP pathway can arrest proliferation once cell density passes a critical threshold. The results account for the dependence or independence of cell proliferation on serum and/or cell anchorage to ECM. Whether the balance in the Cdk network is tilted towards cell cycle arrest or proliferation depends on the direction in which the threshold associated with the bifurcation is passed once the cell integrates the multiple, internal or external signals that promote or impede progression in the cell cycle.

From quiescence to proliferation: Cdk oscillations drive the mammalian cell cycle

We recently proposed a detailed model describing the dynamics of the network of cyclin-dependent kinases (Cdks) driving the mammalian cell cycle (Gérard and Goldbeter, 2009). The model contains four modules, each centered around one cyclin/Cdk complex. Cyclin D/Cdk4–6 and cyclin E/Cdk2 promote progression in G1 and elicit the G1/S transition, respectively; cyclin A/Cdk2 ensures progression in S and the transition S/G2, while the activity of cyclin B/Cdk1 brings about the G2/M transition. This model shows that in the presence of sufficient amounts of growth factor the Cdk network is capable of temporal self-organization in the form of sustained oscillations, which correspond to the ordered, sequential activation of the various cyclin/Cdk complexes that control the successive phases of the cell cycle. The results suggest that the switch from cellular quiescence to cell proliferation corresponds to the transition from a stable steady state to sustained oscillations in the Cdk network. The transition depends on a finely tuned balance between factors that promote or hinder progression in the cell cycle. We show that the transition from quiescence to proliferation can occur in multiple ways that alter this balance. By resorting to bifurcation diagrams, we analyze the mechanism of oscillations in the Cdk network. Finally, we show that the complexity of the detailed model can be greatly reduced, without losing its key dynamical properties, by considering a skeleton model for the Cdk network. Using such a skeleton model for the mammalian cell cycle we show that positive feedback (PF) loops enhance the amplitude and the robustness of Cdk oscillations with respect to molecular noise. We compare the relative merits of the detailed and skeleton versions of the model for the Cdk network driving the mammalian cell cycle.

Effect of positive feedback loops on the robustness of oscillations in the network of cyclin-dependent kinases driving the mammalian cell cycle.

The transitions between the G1, S, G2 and M phases of the mammalian cell cycle are driven by a network of cyclin‐dependent kinases (Cdks), whose sequential activation is regulated by intertwined negative and positive feedback loops. We previously proposed a detailed computational model for the Cdk network, and showed that this network is capable of temporal self‐organization in the form of sustained oscillations, which govern ordered progression through the successive phases of the cell cycle [Gérard and Goldbeter (2009) Proc Natl Acad Sci USA106, 21643–21648]. We subsequently proposed a skeleton model for the cell cycle that retains the core regulatory mechanisms of the detailed model [Gérard and Goldbeter (2011) Interface Focus1, 24–35]. Here we extend this skeleton model by incorporating Cdk regulation through phosphorylation/dephosphorylation and by including the positive feedback loops that underlie the dynamics of the G1/S and G2/M transitions via phosphatase Cdc25 and via phosphatase Cdc25 and kinase Wee1, respectively. We determine the effects of these positive feedback loops and ultrasensitivity in phosphorylation/dephosphorylation on the dynamics of the Cdk network. The multiplicity of positive feedback loops as well as the existence of ultrasensitivity promote the occurrence of bistability and increase the amplitude of the oscillations in the various cyclin/Cdk complexes. By resorting to stochastic simulations, we further show that the presence of multiple, redundant positive feedback loops in the G2/M transition of the cell cycle markedly enhances the robustness of the Cdk oscillations with respect to molecular noise.

Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations

Circadian rhythms, which occur spontaneously with a period of about 24 h in a variety of organisms, allow their adaptation to the periodic variations of the environment. These rhythms are generated by a genetic regulatory network involving a negative feedback loop on transcription. Mathematical models based on the negative autoregulation of gene expression by the protein product of a clock gene account for the occurrence of self-sustained circadian oscillations. These models differ by their degree of complexity and, hence, by the number of variables considered. Some of these models can be considered as minimal because they contain a reduced number of biochemical processes and variables capable of producing sustained oscillations. In three of these minimal models, the period of the oscillations significantly changes with the rate of degradation of the clock protein. However, depending on the model considered, the period increases, decreases or passes through a maximum as a function of the protein degradation rate. We clarify the bases for these markedly different results by bringing to light the roles of (i) protein phosphorylation, which is required for protein degradation, and (ii) the velocity and degree of saturation of mRNA and protein degradation. Changes in the parameter values of the more complex of the minimal models can produce the period profiles observed in the other two models. The analysis allows us to reconcile the contradictory predictions for the dependence of the period on the clock protein degradation rate in three minimal models used to describe circadian rhythms.

Cell Cycle Control by a Minimal Cdk Network

In present-day eukaryotes, the cell division cycle is controlled by a complex network of interacting proteins, including members of the cyclin and cyclin-dependent protein kinase (Cdk) families, and the Anaphase Promoting Complex (APC). Successful progression through the cell cycle depends on precise, temporally ordered regulation of the functions of these proteins. In light of this complexity, it is surprising that in fission yeast, a minimal Cdk network consisting of a single cyclin-Cdk fusion protein can control DNA synthesis and mitosis in a manner that is indistinguishable from wild type. To improve our understanding of the cell cycle regulatory network, we built and analysed a mathematical model of the molecular interactions controlling the G1/S and G2/M transitions in these minimal cells. The model accounts for all observed properties of yeast strains operating with the fusion protein. Importantly, coupling the model’s predictions with experimental analysis of alternative minimal cells, we uncover an explanation for the unexpected fact that elimination of inhibitory phosphorylation of Cdk is benign in these strains while it strongly affects normal cells. Furthermore, in the strain without inhibitory phosphorylation of the fusion protein, the distribution of cell size at division is unusually broad, an observation that is accounted for by stochastic simulations of the model. Our approach provides novel insights into the organization and quantitative regulation of wild type cell cycle progression. In particular, it leads us to propose a new mechanistic model for the phenomenon of mitotic catastrophe, relying on a combination of unregulated, multi-cyclin-dependent Cdk activities.