Modeling the Circadian Control of the Cell Cycle and Its Consequences for Cancer Chronotherapy.

The mammalian cell cycle is governed by a network of cyclin/Cdk complexes which signal the progression into the successive phases of the cell division cycle. Once coupled to the circadian clock, this network produces oscillations with a 24 h period such that the progression into each phase of the cell cycle is synchronized to the day-night cycle. Here, we use a computational model for the circadian clock control of the cell cycle to investigate the entrainment in a population of cells characterized by some variability in the kinetic parameters. Our numerical simulations showed that successful entrainment and synchronization are only possible with a sufficient circadian amplitude and an autonomous period close to 24 h. Cellular heterogeneity, however, introduces some variability in the entrainment phase of the cells. Many cancer cells have a disrupted clock or compromised clock control. In these conditions, the cell cycle runs independently of the circadian clock, leading to a lack of synchronization of cancer cells. When the coupling is weak, entrainment is largely impacted, but cells maintain a tendency to divide at specific times of day. These differential entrainment features between healthy and cancer cells can be exploited to optimize the timing of anti-cancer drug administration in order to minimize their toxicity and to maximize their efficacy. We then used our model to simulate such chronotherapeutic treatments and to predict the optimal timing for anti-cancer drugs targeting specific phases of the cell cycle. Although qualitative, the model highlights the need to better characterize cellular heterogeneity and synchronization in cell populations as well as their consequences for circadian entrainment in order to design successful chronopharmacological protocols.

Temporal dynamics of a CSF1R signaling gene regulatory network involved in epilepsy.

Colony Stimulating Factor 1 Receptor (CSF1R) is a potential target for anti-epileptic drugs. However, inhibition of CSF1R is not well tolerated by patients, thereby prompting the need for alternative targets. To develop a framework for identification of such alternatives, we here develop a mathematical model of a pro-inflammatory gene regulatory network (GRN) involved in epilepsy and centered around CSF1R. This GRN comprises validated transcriptional and post-transcriptional regulations involving STAT1, STAT3, NFκB, IL6R, CSF3R, IRF8, PU1, C/EBPα, TNFR1, CSF1 and CSF1R. The model was calibrated on mRNA levels of all GRN components in lipopolysaccharide (LPS)-treated mouse microglial BV-2 cells, and allowed to predict that STAT1 and STAT3 have the strongest impact on the expression of the other GRN components. Microglial BV-2 cells were selected because, the modules from which the GRN was deduced are enriched for microglial marker genes. The function of STAT1 and STAT3 in the GRN was experimentally validated in BV-2 cells. Further, in silico analysis of the GRN dynamics predicted that a pro-inflammatory stimulus can induce irreversible bistability whereby the expression level of GRN components occurs as two distinct states. The irreversibility of the switch may enforce the need for chronic inhibition of the CSF1R GRN in order to achieve therapeutic benefit. The cell-to-cell heterogeneity driven by the bistability may cause variable therapeutic response. In conclusion, our modeling approach uncovered a GRN controlling CSF1R that is predominantly regulated by STAT1 and STAT3. Irreversible inflammation-induced bistability and cell-to-cell heterogeneity of the GRN provide a theoretical foundation to the need for chronic GRN control and the limited potential for disease modification via inhibition of CSF1R.

A Mouse Model of Cholangiocarcinoma Uncovers a Role for Tensin-4 in Tumor Progression.

BACKGROUND AND AIMS: Earlier diagnosis and treatment of intrahepatic cholangiocarcinoma (iCCA) are necessary to improve therapy, yet limited information is available about initiation and evolution of iCCA precursor lesions. Therefore, there is a need to identify mechanisms driving formation of precancerous lesions and their progression toward invasive tumors using experimental models that faithfully recapitulate human tumorigenesis. APPROACH AND RESULTS: To this end, we generated a mouse model which combines cholangiocyte-specific expression of KrasG12D with 3,5-diethoxycarbonyl-1,4-dihydrocollidine (DDC) diet-induced inflammation to mimic iCCA development in patients with cholangitis. Histological and transcriptomic analyses of the mouse precursor lesions and iCCA were performed and compared with human analyses. The function of genes overexpressed during tumorigenesis was investigated in human cell lines. We found that mice expressing KrasG12D in cholangiocytes and fed a DDC diet developed cholangitis, ductular proliferations, intraductal papillary neoplasms of bile ducts (IPNBs), and, eventually, iCCAs. The histology of mouse and human IPNBs was similar, and mouse iCCAs displayed histological characteristics of human mucin-producing, large-duct-type iCCA. Signaling pathways activated in human iCCA were also activated in mice. The identification of transition zones between IPNB and iCCA on tissue sections, combined with RNA-sequencing analyses of the lesions supported that iCCAs derive from IPNBs. We further provide evidence that tensin-4 (TNS4), which is stimulated by KRASG12D and SRY-related HMG box transcription factor 17, promotes tumor progression. CONCLUSIONS: We developed a mouse model that faithfully recapitulates human iCCA tumorigenesis and identified a gene cascade which involves TNS4 and promotes tumor progression.

Differential impact of the ERBB receptors EGFR and ERBB2 on the initiation of precursor lesions of pancreatic ductal adenocarcinoma.

Earlier diagnosis of pancreatic ductal adenocarcinoma (PDAC) requires better understanding of the mechanisms driving tumorigenesis. In this context, depletion of Epidermal Growth Factor Receptor (EGFR) is known to impair development of PDAC-initiating lesions called acinar-to-ductal metaplasia (ADM) and Pancreatic Intraepithelial Neoplasia (PanIN). In contrast, the role of v-erb-b2 erythroblastic leukemia viral oncogene homolog 2 (ERBB2), the preferred dimerization partner of EGFR, remains poorly understood. Here, using a mouse model with inactivation of Erbb2 in pancreatic acinar cells, we found that Erbb2 is dispensable for inflammation- and KRasG12D-induced development of ADM and PanIN. A mathematical model of EGFR/ERBB2-KRAS signaling, which was calibrated on mouse and human data, supported the observed roles of EGFR and ERBB2. However, this model also predicted that overexpression of ERBB2 stimulates ERBB/KRAS signaling; this prediction was validated experimentally. We conclude that EGFR and ERBB2 differentially impact ERBB signaling during PDAC tumorigenesis, and that the oncogenic potential of ERBB2 is only manifested when it is overexpressed. Therefore, the level of ERBB2, not only its mere presence, needs to be considered when designing therapies targeting ERBB signaling.

Modeling the Dynamics of Let-7-Coupled Gene Regulatory Networks Linking Cell Proliferation to Malignant Transformation.

Let-7 microRNA controls the expression of proteins that belong to two distinct gene regulatory networks, namely, a cyclin-dependent kinase (Cdk) network driving the cell cycle and a cell transformation network that can undergo an epigenetic switch between a non-transformed and a malignant transformed cell state. Using mathematical modeling and transcriptomic data analysis, we here investigate how Let-7 controls the Cdk-dependent cell cycle network, and how it couples the latter with the transformation network. We also assess the consequence of this coupling on cancer progression. Our analysis shows that the switch from a quiescent to a proliferative state depends on the relative levels of Let-7 and several cell cycle activators. Numerical simulations further indicate that the Let-7-coupled cell cycle and transformation networks mutually control each other, and our model identifies key players for this mutual control. Transcriptomic data analysis from The Cancer Genome Atlas (TCGA) suggests that the two networks are activated in cancer, in particular in gastrointestinal cancers, and that the activation levels vary significantly among patients affected by a same cancer type. Our mathematical model, when applied to a heterogeneous cell population, suggests that heterogeneity among tumors may in part result from stochastic switches between a non-transformed cell state with low proliferative capability and a transformed cell state with high proliferative property. The model further predicts that Let-7 may reduce tumor heterogeneity by decreasing the occurrence of stochastic switches toward a transformed, proliferative cell state. In conclusion, we identified the key components responsible for the qualitative dynamics of two networks interconnected by Let-7. The two networks are heterogeneously activated in several cancers, thereby stressing the need to consider patient's specific characteristics to optimize therapeutic strategies.

Dynamics and predicted drug response of a gene network linking dedifferentiation with beta-catenin dysfunction in hepatocellular carcinoma.

BACKGROUND & AIMS: Alterations of individual genes variably affect the development of hepatocellular carcinoma (HCC). Thus, we aimed to characterize the function of tumor-promoting genes in the context of gene regulatory networks (GRNs). METHODS: Using data from The Cancer Genome Atlas, from the LIRI-JP (Liver Cancer - RIKEN, JP project), and from our transcriptomic, transfection and mouse transgenic experiments, we identify a GRN which functionally links LIN28B-dependent dedifferentiation with dysfunction of ß-catenin (CTNNB1). We further generated and validated a quantitative mathematical model of the GRN using human cell lines and in vivo expression data. RESULTS: We found that LIN28B and CTNNB1 form a GRN with SMARCA4, Let-7b (MIRLET7B), SOX9, TP53 and MYC. GRN functionality is detected in HCC and gastrointestinal cancers, but not in other cancer types. GRN status negatively correlates with HCC prognosis, and positively correlates with hyperproliferation, dedifferentiation and HGF/MET pathway activation, suggesting that it contributes to a transcriptomic profile typical of the proliferative class of HCC. The mathematical model predicts how the expression of GRN components changes when the expression of another GRN member varies or is inhibited by a pharmacological drug. The dynamics of GRN component expression reveal distinct cell states that can switch reversibly in normal conditions, and irreversibly in HCC. The mathematical model is available via a web-based tool which can evaluate the GRN status of HCC samples and predict the impact of therapeutic agents on the GRN. CONCLUSIONS: We conclude that identification and modelling of the GRN provide insights into the prognosis of HCC and the mechanisms by which tumor-promoting genes impact on HCC development. LAY SUMMARY: Hepatocellular carcinoma (HCC) is a heterogeneous disease driven by the concomitant deregulation of several genes functionally organized as networks. Here, we identified a gene regulatory network involved in a subset of HCCs. This subset is characterized by increased proliferation and poor prognosis. We developed a mathematical model which uncovers the dynamics of the network and allows us to predict the impact of a therapeutic agent, not only on its specific target but on all the genes belonging to the network.

Revisiting a skeleton model for the mammalian cell cycle: From bistability to Cdk oscillations and cellular heterogeneity.

A network of cyclin-dependent kinases (Cdks) regulated by multiple negative and positive feedback loops controls progression in the mammalian cell cycle. We previously proposed a detailed computational model for this network, which consists of four coupled Cdk modules. Both this detailed model and a reduced, skeleton version show that the Cdk network is capable of temporal self-organization in the form of sustained Cdk oscillations, which correspond to the orderly progression along the different cell cycle phases G1, S (DNA replication), G2 and M (mitosis). We use the skeleton model to revisit the role of positive feedback (PF) loops on the dynamics of the mammalian cell cycle by showing that the multiplicity of PF loops extends the range of bistability in the isolated Cdk modules controlling the G1/S and G2/M transitions. Resorting to stochastic simulations we show that, through their effect on the range of bistability, multiple PF loops enhance the robustness of Cdk oscillations with respect to molecular noise. The model predicts that a rise in the total level of Cdk1 also enlarges the domain of bistability in the isolated Cdk modules as well as the range of oscillations in the full Cdk network. Surprisingly, stochastic simulations indicate that Cdk1 overexpression reduces the robustness of Cdk oscillations towards molecular noise; this result is due to the increased distance between the two branches of the bistable switch at higher levels of Cdk1. At intermediate levels of growth factor stochastic simulations show that cells may randomly switch between cell cycle arrest and cell proliferation, as a consequence of fluctuations. In the presence of Cdk1 overexpression, these transitions occur even at low levels of growth factor. Extending stochastic simulations from single cells to cell populations suggests that stochastic switches between cell cycle arrest and proliferation may provide a source of heterogeneity in a cell population, as observed in cancer cells characterized by Cdk1 overexpression.

Modeling-Based Investigation of the Effect of Noise in Cellular Systems.

Noise is pervasive in cellular biology and inevitably affects the dynamics of cellular processes. Biological systems have developed regulatory mechanisms to ensure robustness with respect to noise or to take advantage of stochasticity. We review here, through a couple of selected examples, some insights on possible robustness factors and constructive roles of noise provided by computational modeling. In particular, we focus on (1) factors that likely contribute to the robustness of oscillatory processes such as the circadian clocks and the cell cycle, (2) how reliable coding/decoding of calcium-mediated signaling could be achieved in presence of noise and, in some cases, enhanced through stochastic resonance, and (3) how embryonic cell differentiation processes can exploit stochasticity to create heterogeneity in a population of identical cells.

MicroRNA-337-3p controls hepatobiliary gene expression and transcriptional dynamics during hepatic cell differentiation.

Transcriptional networks control the differentiation of the hepatocyte and cholangiocyte lineages from embryonic liver progenitor cells and their subsequent maturation to the adult phenotype. However, how relative levels of hepatocyte and cholangiocyte gene expression are determined during differentiation remains poorly understood. Here, we identify microRNA (miR)-337-3p as a regulator of liver development. miR-337-3p stimulates expression of cholangiocyte genes and represses hepatocyte genes in undifferentiated progenitor cells in vitro and in embryonic mouse livers. Beyond the stage of lineage segregation, miR-337-3p controls the transcriptional network dynamics of developing hepatocytes and balances both cholangiocyte populations that constitute the ductal plate. miR-337-3p requires Notch and transforming growth factor-ß signaling and exerts a biphasic control on the hepatocyte transcription factor hepatocyte nuclear factor 4α by modulating its activation and repression. With the help of an experimentally validated mathematical model, we show that this biphasic control results from an incoherent feedforward loop between miR-337-3p and hepatocyte nuclear factor 4α. CONCLUSION: Our results identify miR-337-3p as a regulator of liver development and highlight how tight quantitative control of hepatic cell differentiation is exerted through specific gene regulatory network motifs. (Hepatology 2018;67:313-327).

Modelling the propagation of a dynamical signature in gene expression mediated by the transport of extracellular microRNAs.

Extracellular microRNAs (miRNAs) carried by exosomes can play a key role in cell-to-cell communication. Deregulation of miRNA expression and exosome secretion have been related to pathological conditions such as cancer. While it is known that circulating miRNAs can alter gene expression in recipient cells, it remains unclear how significant the dynamical impact of these extracellular miRNAs is. To shed light on this issue, we propose a model for the spatio-temporal evolution of the protein expression in a cell tissue altered by abnormal miRNA expression in a donor cell. This results in a nonhomogeneous cellular response in the tissue, which we quantify by studying the range of action of the donor cell on the surrounding cells. Key model parameters that control the range of action are identified. Based on a model for a heterogeneous cell population, we show that the dynamics of gene expression in the tissue is robust to random changes of the parameter values. Furthermore, we study the propagation of gene expression oscillations in a tissue induced by extracellular miRNAs. In the donor cell, the miRNA inhibits its own transcription which can give rise to local oscillations in gene expression. The resulting oscillations of the concentration of extracellular miRNA induce oscillations of the protein concentration in recipient cells. We analyse the nonmonotonic spatial evolution of the oscillation amplitude of the protein concentration in the tissue which may have implications for the propagation of oscillations in biological rhythms such as the circadian clock.

Gene regulatory networks in differentiation and direct reprogramming of hepatic cells.

Liver development proceeds by sequential steps during which gene regulatory networks (GRNs) determine differentiation and maturation of hepatic cells. Characterizing the architecture and dynamics of these networks is essential for understanding how cell fate decisions are made during development, and for recapitulating these processes during in vitro production of liver cells for toxicology studies, disease modelling and regenerative therapy. Here we review the GRNs that control key steps of liver development and lead to differentiation of hepatocytes and cholangiocytes in mammals. We focus on GRNs determining cell fate decisions and analyse subcircuitry motifs that may confer specific dynamic properties to the networks. Finally, we put our analysis in the perspective of recent attempts to directly reprogram cells to hepatocytes by forced expression of transcription factors.

Dynamics of the mammalian cell cycle in physiological and pathological conditions.

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.

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.

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.

A model for the epigenetic switch linking inflammation to cell transformation: deterministic and stochastic approaches.

Recently, a molecular pathway linking inflammation to cell transformation has been discovered. This molecular pathway rests on a positive inflammatory feedback loop between NF-κB, Lin28, Let-7 microRNA and IL6, which leads to an epigenetic switch allowing cell transformation. A transient activation of an inflammatory signal, mediated by the oncoprotein Src, activates NF-κB, which elicits the expression of Lin28. Lin28 decreases the expression of Let-7 microRNA, which results in higher level of IL6 than achieved directly by NF-κB. In turn, IL6 can promote NF-κB activation. Finally, IL6 also elicits the synthesis of STAT3, which is a crucial activator for cell transformation. Here, we propose a computational model to account for the dynamical behavior of this positive inflammatory feedback loop. By means of a deterministic model, we show that an irreversible bistable switch between a transformed and a non-transformed state of the cell is at the core of the dynamical behavior of the positive feedback loop linking inflammation to cell transformation. The model indicates that inhibitors (tumor suppressors) or activators (oncogenes) of this positive feedback loop regulate the occurrence of the epigenetic switch by modulating the threshold of inflammatory signal (Src) needed to promote cell transformation. Both stochastic simulations and deterministic simulations of a heterogeneous cell population suggest that random fluctuations (due to molecular noise or cell-to-cell variability) are able to trigger cell transformation. Moreover, the model predicts that oncogenes/tumor suppressors respectively decrease/increase the robustness of the non-transformed state of the cell towards random fluctuations. Finally, the model accounts for the potential effect of competing endogenous RNAs, ceRNAs, on the dynamics of the epigenetic switch. Depending on their microRNA targets, the model predicts that ceRNAs could act as oncogenes or tumor suppressors by regulating the occurrence of cell transformation.

microRNA as a potential vector for the propagation of robustness in protein expression and oscillatory dynamics within a ceRNA network.

microRNAs (miRNAs) are small noncoding RNAs that are important post-transcriptional regulators of gene expression. miRNAs can induce thresholds in protein synthesis. Such thresholds in protein output can be also achieved by oligomerization of transcription factors (TF) for the control of gene expression. First, we propose a minimal model for protein expression regulated by miRNA and by oligomerization of TF. We show that miRNA and oligomerization of TF generate a buffer, which increases the robustness of protein output towards molecular noise as well as towards random variation of kinetics parameters. Next, we extend the model by considering that the same miRNA can bind to multiple messenger RNAs, which accounts for the dynamics of a minimal competing endogenous RNAs (ceRNAs) network. The model shows that, through common miRNA regulation, TF can control the expression of all proteins formed by the ceRNA network, even if it drives the expression of only one gene in the network. The model further suggests that the threshold in protein synthesis mediated by the oligomerization of TF can be propagated to the other genes, which can increase the robustness of the expression of all genes in such ceRNA network. Furthermore, we show that a miRNA could increase the time delay of a "Goodwin-like" oscillator model, which may favor the occurrence of oscillations of large amplitude. This result predicts important roles of miRNAs in the control of the molecular mechanisms leading to the emergence of biological rhythms. Moreover, a model for the latter oscillator embedded in a ceRNA network indicates that the oscillatory behavior can be propagated, via the shared miRNA, to all proteins formed by such ceRNA network. Thus, by means of computational models, we show that miRNAs could act as vectors allowing the propagation of robustness in protein synthesis as well as oscillatory behaviors within ceRNA networks.

Minimal models for cell-cycle control based on competitive inhibition and multisite phosphorylations of Cdk substrates.

The eukaryotic cell cycle is characterized by alternating oscillations in the activities of cyclin-dependent kinase (Cdk) and the anaphase-promoting complex (APC). Successful completion of the cell cycle is dependent on the precise, temporally ordered appearance of these activities. A modest level of Cdk activity is sufficient to initiate DNA replication, but mitosis and APC activation require an elevated Cdk activity. In present-day eukaryotes, this temporal order is provided by a complex network of regulatory proteins that control both Cdk and APC activities via sharp thresholds, bistability, and time delays. Using simple computational models, we show here that these dynamical features of cell-cycle organization could emerge in a control system driven by a single Cdk/cyclin complex and APC wired in a negative-feedback loop. We show that ordered phosphorylation of cellular proteins could be explained by multisite phosphorylation/dephosphorylation and competition of substrates for interconverting kinase (Cdk) and phosphatase. In addition, the competition of APC substrates for ubiquitylation can create and maintain sustained oscillations in cyclin levels. We propose a sequence of models that gets closer and closer to a realistic model of cell-cycle control in yeast. Since these models lack the elaborate control mechanisms characteristic of modern eukaryotes, they suggest that bistability and time delay may have characterized eukaryotic cell divisions before the current cell-cycle control network evolved in all its complexity.

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.

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.

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 G(1), S, G(2) 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 USA 106, 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 Focus 1, 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 G(1)/S and G(2)/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 G(2)/M transition of the cell cycle markedly enhances the robustness of the Cdk oscillations with respect to molecular noise.