An automaton model for the cell cycle

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.

Eight Aging-Related Genes Prognostic Signature for Cervical Cancer

This study searched for aging-related genes (ARGs) to predict the prognosis of patients with cervical cancer (CC). All data were obtained from Molecular Signatures Database, Cancer Genome Atlas, Gene Expression Integration, and Genotype Organization Expression. The R software was used to screen out the differentially expressed ARGs (DE-ARGs) between CC and normal tissues. A protein-protein interaction network was established by the DE-ARGs. The univariate and multivariate Cox regression analyses were conducted on the first extracted Molecular Complex Detection component, and a prognostic model was constructed. The prognostic model was further validated in the testing set and GSE44001 dataset. Prognosis was analyzed by Kaplan-Meier curves, and accuracy of the prognostic model was assessed by receiver operating characteristic area under the curve analysis. An independent prognostic analysis of risk score and some clinicopathological factors of CC was also performed. The copy-number variant (CNV) and single-nucleotide variant (SNV) of prognostic ARGs were analyzed by the BioPortal database. A clinical practical nomogram was established to predict individual survival probability. Finally, we carried out cell experiment to further verify the prognostic model. An eight-ARG prognostic signature for CC was constructed. High-risk CC patients had significantly shorter overall survival than low-risk patients. The receiver operating characteristic (ROC) curve validated the good performance of the signature in survival prediction. The Figo_stage and risk score served as independent prognostic factors. The eight ARGs mainly enriched in growth factor regulation and cell cycle pathway, and the deep deletion of FN1 was the most common CNV. An eight-ARG prognostic signature for CC was successfully constructed.

Modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells

As a result of the development of experimental technologies and the accumulation of data, biological and molecular processes can be described as complex networks of signaling pathways. These networks are often directed and signed, where nodes represent entities (genes/proteins) and arrows interactions. They are translated into mathematical models by adding a dynamic layer onto them. Such mathematical models help to understand and interpret non-intuitive experimental observations and to anticipate the response to external interventions such as drug effects on phenotypes. Several frameworks for modeling signaling pathways exist. The choice of the appropriate framework is often driven by the experimental context. In this review, we present MaBoSS, a tool based on Boolean modeling using a continuous time approach, which predicts time-dependent probabilities of entities in different biological contexts. MaBoSS was initially built to model the intracellular signaling in non-interacting homogeneous cell populations. MaBoSS was then adapted to model heterogeneous cell populations (EnsembleMaBoSS) by considering families of models rather than a unique model. To account for more complex questions, MaBoSS was extended to simulate dynamical interacting populations (UPMaBoSS), with a precise spatial distribution (PhysiBoSS). To illustrate all these levels of description, we show how each of these tools can be used with a running example of a simple model of cell fate decisions. Finally, we present practical applications to cancer biology and studies of the immune response.

A mathematical model for cell cycle control: graded response or quantized response

Cell cycle is an important and complex biological system. A lot of efforts have been put in understanding cell cycle arrest for its vital role in clinical therapies. The cell-cycle-arrest outcomes upon stimulation are complicated. The response could be stringent or relaxed, and graded or quantized. A model fully addressing various cell-cycle-arrest outcomes is to be developed. Here, we developed a mathematical model of cell cycle control incorporating distinct characteristics of various cell-cycle-arrest outcomes. The model can simulate two typical properties of cell cycle arrest, quantized and graded. We also characterized the inheritable quiescence and refractory state, which were crucial in long-term response of the population. Then, we monitored cells respond to multiple stimulations, and the results indicated that cells responded to stimulations with small interval did not induce significantly sustained cell cycle arrest as the existence of refractory state. Our work will benefit fundamental research and make efforts to predicting outcomes of clinical therapeutics.

DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

New experimental data have shown how the periodic exposure of cells to low oxygen levels (i.e., cyclic hypoxia) impacts their progress through the cell-cycle. Cyclic hypoxia has been detected in tumours and linked to poor prognosis and treatment failure. While fluctuating oxygen environments can be reproduced in vitro, the range of oxygen cycles that can be tested is limited. By contrast, mathematical models can be used to predict the response to a wide range of cyclic dynamics. Accordingly, in this paper we develop a mechanistic model of the cell-cycle that can be combined with in vitro experiments, to better understand the link between cyclic hypoxia and cell-cycle dysregulation. A distinguishing feature of our model is the inclusion of impaired DNA synthesis and cell-cycle arrest due to periodic exposure to severely low oxygen levels. Our model decomposes the cell population into five compartments and a time-dependent delay accounts for the variability in the duration of the S phase which increases in severe hypoxia due to reduced rates of DNA synthesis. We calibrate our model against experimental data and show that it recapitulates the observed cell-cycle dynamics. We use the calibrated model to investigate the response of cells to oxygen cycles not yet tested experimentally. When the re-oxygenation phase is sufficiently long, our model predicts that cyclic hypoxia simply slows cell proliferation since cells spend more time in the S phase. On the contrary, cycles with short periods of re-oxygenation are predicted to lead to inhibition of proliferation, with cells arresting from the cell-cycle in the G2 phase. While model predictions on short time scales (about a day) are fairly accurate (i.e, confidence intervals are small), the predictions become more uncertain over longer periods. Hence, we use our model to inform experimental design that can lead to improved model parameter estimates and validate model predictions.

UPMaBoSS: A Novel Framework for Dynamic Cell Population Modeling

Mathematical modeling aims at understanding the effects of biological perturbations, suggesting ways to intervene and to reestablish proper cell functioning in diseases such as cancer or in autoimmune disorders. This is a difficult task for obvious reasons: the level of details needed to describe the intra-cellular processes involved, the numerous interactions between cells and cell types, and the complex dynamical properties of such populations where cells die, divide and interact constantly, to cite a few. Another important difficulty comes from the spatial distribution of these cells, their diffusion and motility. All of these aspects cannot be easily resolved in a unique mathematical model or with a unique formalism. To cope with some of these issues, we introduce here a novel framework, UPMaBoSS (for Update Population MaBoSS), dedicated to modeling dynamic populations of interacting cells. We rely on the preexisting tool MaBoSS, which enables probabilistic simulations of cellular networks. A novel software layer is added to account for cell interactions and population dynamics, but without considering the spatial dimension. This modeling approach can be seen as an intermediate step towards more complex spatial descriptions. We illustrate our methodology by means of a case study dealing with TNF-induced cell death. Interestingly, the simulation of cell population dynamics with UPMaBoSS reveals a mechanism of resistance triggered by TNF treatment. Relatively easy to encode, UPMaBoSS simulations require only moderate computational power and execution time. To ease the reproduction of simulations, we provide several Jupyter notebooks that can be accessed within the CoLoMoTo Docker image, which contains all software and models used for this study.

Data Driven Cell Cycle Model to Quantify the Efficacy of Cancer Therapeutics Targeting Specific Cell-Cycle Phases From Flow Cytometry Results

Many chemotherapeutic drugs target cell processes in specific cell cycle phases. Determining the specific phases targeted is key to understanding drug mechanism of action and efficacy against specific cancer types. Flow cytometry experiments, combined with cell cycle phase and division round specific staining, can be used to quantify the current cell cycle phase and number of mitotic events of each cell within a population. However, quantification of cell interphase times and the efficacy of cytotoxic drugs targeting specific cell cycle phases cannot be determined directly. We present a data driven computational cell population model for interpreting experimental results, where in-silico populations are initialized to match observable results from experimental populations. A two-stage approach is used to determine the efficacy of cytotoxic drugs in blocking cell-cycle phase transitions. In the first stage, our model is fitted to experimental multi-parameter flow cytometry results from untreated cell populations to identify parameters defining probability density functions for phase transitions. In the second stage, we introduce a blocking routine to the model which blocks a percentage of attempted transitions between cell-cycle phases due to therapeutic treatment. The resulting model closely matches the percentage of cells from experiment in each cell-cycle phase and division round. From untreated cell populations, interphase and intermitotic times can be inferred. We then identify the specific cell-cycle phases that cytotoxic compounds target and quantify the percentages of cell transitions that are blocked compared with the untreated population, which will lead to improved understanding of drug efficacy and mechanism of action.

Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

Spotlight on Circadian Genes and Colorectal Cancer Crosstalk

Mammalian physiology is regulated by circadian clock through oscillating feedback loops controlling cellular processes and behaviors. Recent findings have led to an interesting connection between circadian disruption and colorectal cancer progression and incidence through controlling the hallmarks of cancer, namely cell cycle, cell metabolism and cell death. Deeper understanding of the circadian mechanisms that define the colorectal cancer pathophysiology is the need of the hour to define a chronotherapy for improving colorectal cancer patient survival. This review identifies the key areas in which circadian genes interact with cellular pathways to modify the outcome with respect to colorectal cancer incidence and progression.

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling

MOTIVATION

Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell).

RESULTS

PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen.

AVAILABILITY AND IMPLEMENTATION

PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

ESRP1 Induces Cervical Cancer Cell G1-Phase Arrest Via Regulating Cyclin A2 mRNA Stability

Accumulating evidence indicates that epithelial splicing regulatory protein 1 (ESRP1) can inhibit the epithelial-to-mesenchymal transition (EMT), thus playing a central role in regulating the metastatic progression of tumors. However, it is still not clear whether ESRP1 directly influences the cell cycle, or what the possible underlying molecular mechanisms are. In this study, we showed that ESRP1 protein levels were significantly correlated with the Ki-67 proliferative index (r = −0.521; p < 0.01), and that ESRP1 overexpression can significantly inhibit cervical carcinoma cell proliferation and induced G1-phase arrest by downregulating cyclin A2 expression. Importantly, ESRP1 can bind to GGUGGU sequence in the 3′UTR of the cyclin A2 mRNA, and ESRP1 overexpression significantly decreases the stability of the cyclin A2 mRNA. In addition, our experimental results confirm that ESRP1 overexpression results in enhanced CDC20 expression, which is known to be responsible for cyclin A2 degradation. This study provides the first evidence that ESRP1 overexpression induces G1-phase cell cycle arrest via reducing the stability of the cyclin A2 mRNA, and inhibits cervical carcinoma cell proliferation. The findings suggest that the ESRP1/cyclin A2 regulatory axis may be essential as a regulator of cell proliferation, and may thus represent an attractive target for cervical cancer prevention and treatment.

Cancer and the Circadian Clock

The circadian clock is a master regulator of mammalian physiology, regulating daily oscillations of crucial biological processes and behaviors. Notably, circadian disruption has recently been identified as an independent risk factor for cancer and classified as a carcinogen. As such, it is imperative to discern the underpinning mechanisms by which circadian disruption alters cancer risk. Emergent data, reviewed herein, demonstrate that circadian regulatory functions play critical roles in several hallmarks of cancer, including control of cell proliferation, cell death, DNA repair, and metabolic alteration. Developing a deeper understanding of circadian-cancer regulation cross-talk holds promise for developing new strategies for cancer interception, prevention, and management.

Towards a computational prediction for the tumor selective accumulation of paramagnetic nanoparticles in retinoblastoma cells

Retinoblastoma is a malignant growth affecting retina. An original combination of modified Non-Markov and Gompertzian computational approaches is proven of being a reliable tool for prediction of tumor selective accumulation of the bivalent metal isotopes (25Mg, 43Ca, 60Co, 67Zn, …) — releasing nanoparticles in human retinoblastoma cells. This mathematical model operates with a starting point of the discriminative drug uptake caused by a gap-like distinction between the neighboring malignant and normal cell proliferation rates. This takes into account both pharmacokinetic and pharmacodynamic peculiarities of PMC16, fullerene-C60 based nanoparticles, known for their unique capabilities for a cancer-targeted delivery of paramagnetic metal isotopes followed by an essential chemotherapeutic effect. Being dependent on a tumor growth rate but not on the neoplasm steady state mass, a randomized level of drug accumulation in retinoblastoma cells has been formalized as a predictive paradigm suitable to optimize an ongoing PMC16 preclinical research.

Evaluation of multidrug cancer chronotherapy based on cell cycle model under influences of circadian clock

The intracellular circadian clock mechanisms are known to affect various substantial cellular machinery such as cell cycle progression, inflammatory response, apoptosis, and DNA repair. Cancer growth in various tissues is still under circadian control, which may be at least partly underlain by the survived connections between the intracellular machinery and the clock. Considering such findings, chronotherapy has been applied to cancer treatments, in which anti-cancer drugs are administered in scheduled circadian times so as to resolve the trade-off between damages against the normal and cancer cells. However, any effective administration strategy has not yet been established especially in a quantitative sense. In this study, we develop an automaton model of cell division cycle interacting with circadian clock and suffering from a probability of cell death. A cancer cell is modeled by shortening/ lengthening the cell division interval and a transition to motility state under starving condition. Population proliferating dynamics in 3D space are simulated under the diffusion of nutrient factor and the anti-cancer drugs from a vessel. The simulation results show that the drug administration schedule could differentiate the damages against proliferation of normal and cancer cells. This implies the existence of optimal timing for the drug administration, which could provide an efficient strategy of chronotherapeutic treatment of cancer.

Systems Chronotherapeutics

Chronotherapeutics aim at treating illnesses according to the endogenous biologic rhythms, which moderate xenobiotic metabolism and cellular drug response. The molecular clocks present in individual cells involve approximately fifteen clock genes interconnected in regulatory feedback loops. They are coordinated by the suprachiasmatic nuclei, a hypothalamic pacemaker, which also adjusts the circadian rhythms to environmental cycles. As a result, many mechanisms of diseases and drug effects are controlled by the circadian timing system. Thus, the tolerability of nearly 500 medications varies by up to fivefold according to circadian scheduling, both in experimental models and/or patients. Moreover, treatment itself disrupted, maintained, or improved the circadian timing system as a function of drug timing. Improved patient outcomes on circadian-based treatments (chronotherapy) have been demonstrated in randomized clinical trials, especially for cancer and inflammatory diseases. However, recent technological advances have highlighted large interpatient differences in circadian functions resulting in significant variability in chronotherapy response. Such findings advocate for the advancement of personalized chronotherapeutics through interdisciplinary systems approaches. Thus, the combination of mathematical, statistical, technological, experimental, and clinical expertise is now shaping the development of dedicated devices and diagnostic and delivery algorithms enabling treatment individualization. In particular, multiscale systems chronopharmacology approaches currently combine mathematical modeling based on cellular and whole-body physiology to preclinical and clinical investigations toward the design of patient-tailored chronotherapies. We review recent systems research works aiming to the individualization of disease treatment, with emphasis on both cancer management and circadian timing system–resetting strategies for improving chronic disease control and patient outcomes.

The finite state projection approach to analyze dynamics of heterogeneous populations

Population modeling aims to capture and predict the dynamics of cell populations in constant or fluctuating environments. At the elementary level, population growth proceeds through sequential divisions of individual cells. Due to stochastic effects, populations of cells are inherently heterogeneous in phenotype, and some phenotypic variables have an effect on division or survival rates, as can be seen in partial drug resistance. Therefore, when modeling population dynamics where the control of growth and division is phenotype dependent, the corresponding model must take account of the underlying cellular heterogeneity. The finite state projection (FSP) approach has often been used to analyze the statistics of independent cells. Here, we extend the FSP analysis to explore the coupling of cell dynamics and biomolecule dynamics within a population. This extension allows a general framework with which to model the state occupations of a heterogeneous, isogenic population of dividing and expiring cells. The method is demonstrated with a simple model of cell-cycle progression, which we use to explore possible dynamics of drug resistance phenotypes in dividing cells. We use this method to show how stochastic single-cell behaviors affect population level efficacy of drug treatments, and we illustrate how slight modifications to treatment regimens may have dramatic effects on drug efficacy.

Steady-State-Preserving Simulation of Genetic Regulatory Systems

A novel family of exponential Runge-Kutta (expRK) methods are designed incorporating the stable steady-state structure of genetic regulatory systems. A natural and convenient approach to constructing new expRK methods on the base of traditional RK methods is provided. In the numerical integration of the one-gene, two-gene, and p53-mdm2 regulatory systems, the new expRK methods are shown to be more accurate than their prototype RK methods. Moreover, for nonstiff genetic regulatory systems, the expRK methods are more efficient than some traditional exponential RK integrators in the scientific literature.

Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems

Oscillation is one of the most important phenomena in the chemical reaction systems in living cells. The general purpose simulation algorithms fail to take into account this special character and produce unsatisfying results. In order to enhance the accuracy of the integrator, the second-order derivative is incorporated in the scheme. The oscillatory feature of the solution is captured by the integrators with an exponential fitting property. Three practical exponentially fitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRK methods, the two-gene system with cross-regulation and the circadian oscillation of the period protein in Drosophila are simulated. Each EFTDRK method has the best fitting frequency which minimizes the global error. The numerical results show that the new EFTDRK methods are more accurate and more efficient than their prototype TDRK methods or RK methods of the same order and the traditional exponentially fitted RK method in the literature.

Bridging the gap between in vitro and in vivo: Dose and schedule predictions for the ATR inhibitor AZD6738

Understanding the therapeutic effect of drug dose and scheduling is critical to inform the design and implementation of clinical trials. The increasing complexity of both mono, and particularly combination therapies presents a substantial challenge in the clinical stages of drug development for oncology. Using a systems pharmacology approach, we have extended an existing PK-PD model of tumor growth with a mechanistic model of the cell cycle, enabling simulation of mono and combination treatment with the ATR inhibitor AZD6738 and ionizing radiation. Using AZD6738, we have developed multi-parametric cell based assays measuring DNA damage and cell cycle transition, providing quantitative data suitable for model calibration. Our in vitro calibrated cell cycle model is predictive of tumor growth observed in in vivo mouse xenograft studies. The model is being used for phase I clinical trial designs for AZD6738, with the aim of improving patient care through quantitative dose and scheduling prediction.

Modeling circadian clock-cell cycle interaction effects on cell population growth rates

The circadian clock and the cell cycle are two tightly coupled oscillators. Recent analytical studies have shown counter-intuitive effects of circadian gating of the cell cycle on growth rates of proliferating cells which cannot be explained by a molecular model or a population model alone. In this work, we present a combined molecular-population model that studies how coupling the circadian clock to the cell cycle, through the protein WEE1, affects a proliferating cell population. We show that the cell cycle can entrain to the circadian clock with different rational period ratios and characterize multiple domains of entrainment. We show that coupling increases the growth rate for autonomous periods of the cell cycle around 24 h and above 48 h. We study the effect of mutation of circadian genes on the growth rate of cells and show that disruption of the circadian clock can lead to abnormal proliferation. Particularly, we show that Cry 1, Cry 2 mutations decrease the growth rate of cells, Per 2 mutation enhances it and Bmal 1 knockout increases it for autonomous periods of the cell cycle less than 21 h and decreases it elsewhere. Combining a molecular model to a population model offers new insight on the influence of the circadian clock on the growth of a cell population. This can help chronotherapy which takes benefits of physiological rhythms to improve anti-cancer efficacy and tolerance to drugs by administering treatments at a specific time of the day.

Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle

Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer.

Quantitative analysis of the effects of iododeoxyuridine and ionising radiation treatment on the cell cycle dynamics of DNA mismatch repair deficient human colorectal cancer cells

DNA mismatch repair (MMR) is involved in processing DNA damage following treatment with ionising radiation (IR) and various classes of chemotherapy drugs including iododeoxyuridine (IUdR), a known radiosensitiser. In this study, the authors have developed asynchronous probabilistic cell cycle models to assess the isolated effects of IUdR and IR and the combined effects of IUdR + IR treatments on MMR damage processing. The authors used both synchronous and asynchronous MMR-proficient/MMR-deficient cell populations and followed treated cells for up to two cell cycle times. They have observed and quantified differential cell cycle responses to MMR damage processing following IR and IUdR + IR treatments, principally in the duration of both G1 and G2/M cell cycle phases. The models presented in this work form the foundation for the development of an approach to maximise the therapeutic index for IR and IUdR + IR treatments in MMR-deficient (damage tolerant) cancers.

MicroRNA-mediated regulation in biological systems with oscillatory behavior

As a class of small noncoding RNAs, microRNAs (miRNAs) regulate stability or translation of mRNA transcripts. Some reports bring new insights into possible roles of microRNAs in modulating cell cycle. In this paper, we focus on the mechanism and effectiveness of microRNA-mediated regulation in the cell cycle. We first describe two specific regulatory circuits that incorporate base-pairing microRNAs and show their fine-tuning roles in the modulation of periodic behavior. Furthermore, we analyze the effects of miR369-3 on the modulation of the cell cycle, confirming that miR369-3 plays a role in shortening the period of the cell cycle. These results are consistent with experimental observations.

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.

The cell cycle and the circadian clock are two major cellular rhythms. These two periodic processes are tightly coupled through multiple regulatory interactions; several components of the cell cycle machinery are indeed controlled by the circadian network. By using detailed computational models for the cell cycle and circadian networks we investigate the conditions in which the mammalian cell cycle can be entrained by the circadian clock. We show that entrainment to a circadian period can occur when the period of the cell cycle prior to coupling is either smaller or larger than 24 h. Entrainment to 48 h can also be observed. The presence of multiple modes of coupling does not enlarge the domain of entrainment. Coupling to the circadian clock may also lead to complex oscillatory dynamics of the cell cycle in the form of endoreplication, complex periodic oscillations, or chaotic oscillations. The model predicts that entrainment of the cell cycle could also result from the circadian variation of a growth factor gating entry into G1, and that the transition from an entrained period of 24 h to 48 h might result from a decrease in coupling strength or in the level of growth factor.