Modeling oscillatory control in NF-κB, p53 and Wnt signaling

Negative feedback systems for modelling NF-κB transcription factor oscillatory activity

Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-κB caused by interactions with its inhibitor IκBα. The NFSs were established as 3rd- and 4th-order linear systems containing unperturbed and perturbed negative feedback (NF) loops with constant or time-varying NF strengths and a feed-forward loop. NF-related analytical solutions to the NFSs representing the time courses of NF-κB and IκBα were determined and their exact mathematical relationship was found. The NFS's parameters were determined to fit the experimental time courses of NF-κB in TNF-α-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking Iκβ and IκBε, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively. The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic IκBα after stimulation of NF-κB were determined. A significant divergence between the IκBα solutions to the NFSs and the IκBα experimental courses led to a rejection of the NF coupling between NF-κB and IκBα in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the IκBα solutions to the NFS and IκBα experimental time courses. Although the NF relationship between IκBα and NF-κB was not confirmed in all the experimental data analyzed, delayed negative feedback was found in some cases.

Coupled oscillator cooperativity as a control mechanism in chronobiology

Control of dynamical processes is vital for maintaining correct cell regulation and cell-fate decisions. Numerous regulatory networks show oscillatory behavior; however, our knowledge of how one oscillator behaves when stimulated by two or more external oscillatory signals is still missing. We explore this problem by constructing a synthetic oscillatory system in yeast and stimulate it with two external oscillatory signals. Letting model verification and prediction operate in a tight interplay with experimental observations, we find that stimulation with two external signals expands the plateau of entrainment and reduces the fluctuations of oscillations. Furthermore, by adjusting the phase differences of external signals, one can control the amplitude of oscillations, which is understood through the signal delay of the unperturbed oscillatory network. With this we reveal a direct amplitude dependency of downstream gene transcription. Taken together, these results suggest a new path to control oscillatory systems by coupled oscillator cooperativity.

Enhanced DNA repair through droplet formation and p53 oscillations

Living organisms are constantly exposed to DNA damage, and optimal repair is therefore crucial. A characteristic hallmark of the response is the formation of sub-compartments around the site of damage, known as foci. Following multiple DNA breaks, the transcription factor p53 exhibits oscillations in its nuclear concentration, but how this dynamics can affect the repair remains unknown. Here, we formulate a theory for foci formation through droplet condensation and discover how oscillations in p53, with its specific periodicity and amplitude, optimize the repair process by preventing Ostwald ripening and distributing protein material in space and time. Based on the theory predictions, we reveal experimentally that the oscillatory dynamics of p53 does enhance the repair efficiency. These results connect the dynamical signaling of p53 with the microscopic repair process and create a new paradigm for the interplay of complex dynamics and phase transitions in biology.

A common pathway to cancer: Oncogenic mutations abolish p53 oscillations

The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, we employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby, we suggest, impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis.

Temperature Controls Onset and Period of NF-κB Oscillations and can Lead to Chaotic Dynamics

The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

A tale of two rhythms: Locked clocks and chaos in biology

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

Amplitude Effects Allow Short Jet Lags and Large Seasonal Phase Shifts in Minimal Clock Models

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jet lag, and seasonal phase shifts. Instead of building a single best model, we take an approach where we study the properties of a set of models satisfying certain constraints; here, a 1h-pulse PRC with a range of 3h and clock periods between 22h and 26h is designed. Surprisingly, almost all these randomly parameterized models showed a 4h change in phase of entrainment between long and short days and jet lag durations of three to seven days in advance and delay. Moreover, intrinsic clock period influenced jet lag duration and entrainment amplitude and phase. Fast jet lag was realized in this model by means of an interesting amplitude effect: the association between clock amplitude and clock period termed "twist." This twist allows amplitude changes to speed up and slow down clocks enabling faster shifts. These findings were robust to the addition of positive feedback to the model. In summary, the known design principles of rhythm generation - negative feedback, long delay, and switch-like inhibition (we review these in detail) - are sufficient to reproduce the essential clock phenotypes. Furthermore, amplitudes play a role in determining clock properties and must be always considered, although they are difficult to measure.

Inferring Leading Interactions in the p53/Mdm2/Mdmx Circuit through Live-Cell Imaging and Modeling

The tumor-suppressive transcription factor p53 is a master regulator of stress responses. In non-stressed conditions, p53 is maintained at low levels by the ubiquitin ligase Mdm2 and its binding partner Mdmx. Mdmx depletion leads to a biphasic p53 response, with an initial post-mitotic pulse followed by oscillations. The mechanism underlying this dynamical behavior is unknown. Two different roles for Mdmx have been proposed: enhancing p53 ubiquitination by Mdm2 and inhibiting p53 activity. Here, we developed a mathematical model of the p53/Mdm2/Mdmx network to investigate which Mdmx functions quantitatively affect specific features of p53 dynamics under various conditions. We found that enhancement of Mdm2 activity was the most critical role of Mdmx under unstressed conditions. The model also accurately predicted p53 dynamics in Mdmx-depleted cells following DNA damage. This work outlines a strategy for rapidly testing possible network interactions to reveal those most impactful in regulating the dynamics of key proteins.

Constraints on somite formation in developing embryos

Segment formation in vertebrate embryos is a stunning example of biological self-organization. Here, we present an idealized framework, in which we treat the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the framework to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in ex vivo cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our analysis makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

On chaotic dynamics in transcription factors and the associated effects in differential gene regulation

The control of proteins by a transcription factor with periodically varying concentration exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors vary their dynamics in response to different situations, insight into how this affects downstream genes is lacking. Here, we investigate how oscillations and chaotic dynamics in the transcription factor NF-κB can affect downstream protein production. We describe how it is possible to control the effective dynamics of the transcription factor by stimulating it with an oscillating ligand. We find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, we show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments.

It is becoming clear that the dynamics of transcription factors may be important for gene regulation. Here, the authors study the implications of oscillatory and chaotic dynamics of NF-κB and demonstrate that it allows a degree of control of gene expression and can generate phenotypic heterogeneity.

BCG-induced cytokine release in bladder cancer cells is regulated by Ca2+ signaling

Bacillus Calmette-Guérin (BCG) is widely used in the clinic to effectively treat superficial urinary bladder cancer. However, a significant proportion of patients who fail to respond to BCG risk cystectomy or death. Though more than 3 million cancer treatments with BCG occur annually, surprisingly little is known about the initial signaling cascades activated by BCG. Here, we report that BCG induces a rapid intracellular Ca²⁺ (calcium ion) signal in bladder cancer cells that is essential for activating the transcription factor nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) and for synthesizing and secreting proinflammatory cytokines, including interleukin 8 (IL-8). A similar Ca²⁺ response was observed when cells were exposed to the supernatant of BCG. Studying cellular molecular mechanisms involved in the BCG signaling event, we found pivotal roles for phospholipase C and the Toll-like receptor 4. Further assessment revealed that this signaling pathway induces synthesis of IL-8, whereas exocytosis appeared to be controlled by global Ca²⁺ signaling. These results shed new light on the molecular mechanisms underlying BCG treatment of bladder cancer, which can help in improving therapeutic efficacy and reducing adverse side effects.

Homogeneous Time Constants Promote Oscillations in Negative Feedback Loops

Biological oscillators are present in nearly all self-regulating systems, from individual cells to entire organisms. In any oscillator structure, a negative feedback loop is necessary, but not sufficient to guarantee the emergence of periodic behaviors. The likelihood of oscillations can be improved by careful tuning of the system time constants and by increasing the loop gain, yet it is unclear whether there is any general relationship between optimal time constants and loop gain. This issue is particularly relevant in genetic oscillators resulting from a chain of different subsequent biochemical events, each with distinct (and uncertain) kinetics. Using two families of genetic oscillators as model examples, we show that the loop gain required for oscillations is minimum when all elements in the loop have the same time constant. On the contrary, we show that homeostasis is ensured if a single element is considerably slower than the others.

System-based strategies for p53 recovery

The authors have proposed a systems theory-based novel drug design approach for the p53 pathway. The pathway is taken as a dynamic system represented by ordinary differential equations-based mathematical model. Using control engineering practices, the system analysis and subsequent controller design is performed for the re-activation of wild-type p53. p53 revival is discussed for both modes of operation, i.e. the sustained and oscillatory. To define the problem in control system paradigm, modification in the existing mathematical model is performed to incorporate the effect of Nutlin. Attractor point analysis is carried out to select the suitable domain of attraction. A two-loop negative feedback control strategy is devised to drag the system trajectories to the attractor point and to regulate cellular concentration of Nutlin, respectively. An integrated framework is constituted to incorporate the pharmacokinetic effects of Nutlin in the cancerous cells. Bifurcation analysis is also performed on the p53 model to see the conditions for p53 oscillation.

Temperature regulates NF-κB dynamics and function through timing of A20 transcription

NF-κB signaling plays a pivotal role in control of the inflammatory response. We investigated how the dynamics and function of NF-κB were affected by temperature within the mammalian physiological range (34 °C to 40 °C). An increase in temperature led to an increase in NF-κB nuclear/cytoplasmic oscillation frequency following Tumor Necrosis Factor alpha (TNFα) stimulation. Mathematical modeling suggested that this temperature sensitivity might be due to an A20-dependent mechanism, and A20 silencing removed the sensitivity to increased temperature. The timing of the early response of a key set of NF-κB target genes showed strong temperature dependence. The cytokine-induced expression of many (but not all) later genes was insensitive to temperature change (suggesting that they might be functionally temperature-compensated). Moreover, a set of temperature- and TNFα-regulated genes were implicated in NF-κB cross-talk with key cell-fate-controlling pathways. In conclusion, NF-κB dynamics and target gene expression are modulated by temperature and can accurately transmit multidimensional information to control inflammation.

Oscillatory dynamics of p38 activity with transcriptional and translational time delays

Recent experimental evidence reports that oscillations of p38 MAPK (p38) activity would efficiently induce pro-inflammatory gene expression, which might be deleterious to immune systems and may even cause cellular damage and apoptosis. It is widely accepted now that transcriptional and translational delays are ubiquitous in gene expression, which can typically result in oscillatory responses of gene regulations. Consequently, delay-driven sustained oscillations in p38 activity (p38*) could in principle be commonplace. Nevertheless, so far the studies of the impact of such delays on p38* have been lacking both experimentally and theoretically. Here, we use experimental data to develop a delayed mathematical model, with the aim of understanding how such delays affect oscillatory behaviour on p38*. We analyze the stability and oscillation of the model with and without explicit time delays. We show that a sufficiently input stimulation strength is prerequisite for generating p38* oscillations, and that an optimal rate of model parameters is also essential to these oscillations. Moreover, we find that the time delays required for transcription and translation in mitogen-activated protein kinase phosphatase-1 (MKP-1) gene expression can drive p38* to be oscillatory even when the concentration of p38* level is at a stable state. Furthermore, the length of these delays can determine the amplitude and period of the oscillations and can enormously extend the oscillatory ranges of model parameters. These results indicate that time delays in MKP-1 synthesis are required, albeit not sufficient, for p38* oscillations, which may lead to new insights related to p38 oscillations.

Adjustment of the Arabidopsis circadian oscillator by sugar signalling dictates the regulation of starch metabolism

Arabidopsis plants store part of the carbon fixed by photosynthesis as starch to sustain growth at night. Two competing hypotheses have been proposed to explain this diel starch turnover based on either the measurement of starch abundance with respect to circadian time, or the sensing of sugars to feedback to the circadian oscillator to dynamically adjust the timing of starch turnover. We report a phase oscillator model that permitted derivation of the ideal responses of the circadian regulation of starch breakdown to maintain sucrose homeostasis. Testing the model predictions using a sugar-unresponsive mutant of Arabidopsis demonstrated that the dynamics of starch turnover arise from the circadian clock measuring and responding to the rate of change of cellular sucrose. Our theory and experiments suggest that starch turnover is controlled by the circadian clock acting as a dynamic homeostat responding to sucrose signals to maintain carbon homeostasis.

The protective effect of PFTα on alcohol-induced osteonecrosis of the femoral head

Epidemiologic studies have shown alcohol plays a pivotal role in the development of osteonecrosis of the femoral head (ONFH). The aim of this study was to explore the underlying mechanism of alcohol-induced ONFH and the protective effect of pifithrin-α (PFTα). In vitro, we found ethanol treatment significantly activated p53, suppressed Wnt/β-catenin signaling and inhibited osteogenic-related proteins. Furthermore, by separating the cytoplasmic and nuclear proteins, we found ethanol inhibited osteogenesis by impairing the accumulation of β-catenin in both the cytoplasm and nucleus in human bone mesenchymal stem cells (hBMSCs), which resulted from activating glycogen synthase kinase-3β (GSK-3β). Therefore, PFTα, a p53 inhibitor, was introduced in this study to block the ethanol-triggered activation of p53 in hBMSCs and alcohol-induced ONFH in a rat model. In vivo, we established alcohol-induced ONFH in rats and investigated the protective effect of PFTα. Hematoxylin & eosin (H&E) staining combined with TdT-mediated dUTP nick end labeling (TUNEL), cleaved caspase-3 immunohistochemical staining, and micro-CT images revealed substantial ONFH in the alcohol-administered rats, whereas significantly less osteonecrosis developed in the rats injected with PFTα. Osteogenic-related proteins, including osteocalcin, osteopontin and collagen I, were significantly decreased in the alcohol-administered rats, whereas these results were reversed in the PFTα-injected rats. Fluorochrome labeling similarly showed that alcohol significantly reduced the osteogenic activity in the rat femoral head, which was blocked by the injection of PFTα. In conclusion, PFTα had an antagonistic effect against the effects of ethanol on hBMSCs and could be a clinical strategy to prevent the development of alcohol-induced ONFH.

Transcription factor oscillations in neural stem cells: Implications for accurate control of gene expression

Naturally occurring oscillations in glucocorticoids induce a cyclic activation of the glucocorticoid receptor (GR), a well-characterized ligand-activated transcription factor. These cycles of GR activation/deactivation result in rapid GR exchange at genomic response elements and GR recycling through the chaperone machinery, ultimately generating pulses of GR-mediated transcriptional activity of target genes. In a recent article we have discussed the implications of circadian and high-frequency (ultradian) glucocorticoid oscillations for the dynamic control of gene expression in hippocampal neural stem/progenitor cells (NSPCs) (Fitzsimons et al., Front. Neuroendocrinol., 2016). Interestingly, this oscillatory transcriptional activity is common to other transcription factors, many of which regulate key biological functions in NSPCs, such as NF-kB, p53, Wnt and Notch. Here, we discuss the oscillatory behavior of these transcription factors, their role in a biologically accurate target regulation and the potential importance for a dynamic control of transcription activity and gene expression in NSPCs.

Self-assembly of pifithrin-α-loaded layered double hydroxide/chitosan nanohybrid composites as a drug delivery system for bone repair materials

The self-assembly of pifithrin-α-loaded layered double hydroxide/chitosan nanohybrid composites as a drug delivery system was demonstrated for the first time to improve the cytocompatibility and enhance the osteoinductivity for the treatment of bone defects.

On p53 revival using system oriented drug dosage design

We propose a new paradigm in the drug design for the revival of the p53 pathway in cancer cells. It is shown that the current strategy of using small molecule based Mdm2 inhibitors is not enough to adequately revive p53 in cancerous cells, especially when it comes to the extracting pulsating behavior of p53. This fact has come to notice when a novel method for the drug dosage design is introduced using system oriented concepts. As a test case, small molecule drug Mdm2 repressor Nutlin 3a is considered. The proposed method determines the dose of Nutlin to revive p53 pathway functionality. For this purpose, PBK dynamics of Nutlin have also been integrated with p53 pathway model. The p53 pathway is the focus of researchers for the last thirty years for its pivotal role as a frontline cancer suppressant protein due to its effect on cell cycle checkpoints and cell apoptosis in response to a DNA strand break. That is the reason for finding p53 being absent in more than 50% of tumor cancers. Various drugs have been proposed to revive p53 in cancer cells. Small molecule based drugs are at the foremost and are the subject of advanced clinical trials. The dosage design of these drugs is an important issue. We use control systems concepts to develop the drug dosage so that the cancer cells can be treated in appropriate time. We investigate by using a computational model how p53 protein responds to drug Nutlin 3a, an agent that interferes with the MDM2-mediated p53 regulation. The proposed integrated model describes in some detail the regulation network of p53 including the negative feedback loop mediated by MDM2 and the positive feedback loop mediated by Mdm2 mRNA as well as the reversible represses of MDM2 caused by Nutlin. The reported PBK dynamics of Nutlin 3a are also incorporated to see the full effect. It has been reported that p53 response to stresses in two ways. Either it has a sustained (constant) p53 response, or there are oscillations in p53 concentration. The claimed dosage strategy achieves the p53 response in the first case. However, for the induction of oscillations, it is shown through bifurcation analysis that to achieve oscillating behavior of p53 inhibition of Mdm2 is not enough, rather antirepression of the p53-Mdm2 complex is also needed which leads to the need of a new drug design paradigm.

Noise Induces Hopping between NF-κB Entrainment Modes

Oscillations and noise drive many processes in biology, but how both affect the activity of the transcription factor nuclear factor κB (NF-κB) is not understood. Here, we observe that when NF-κB oscillations are entrained by periodic tumor necrosis factor (TNF) inputs in experiments, NF-κB exhibits jumps between frequency modes, a phenomenon we call “cellular mode-hopping.” By comparing stochastic simulations of NF-κB oscillations to deterministic simulations conducted inside and outside the chaotic regime of parameter space, we show that noise facilitates mode-hopping in all regimes. However, when the deterministic system is driven by chaotic dynamics, hops between modes are erratic and short-lived, whereas in experiments, the system spends several periods in one entrainment mode before hopping and rarely visits more than two modes. The experimental behavior matches our simulations of noise-induced mode-hopping outside the chaotic regime. We suggest that mode-hopping is a mechanism by which different NF-κB-dependent genes under frequency control can be expressed at different times.

Oscillatory expression in Escherichia coli mediated by microRNAs with transcriptional and translational time delays

The primary objective of this study is to study oscillatory expression of gene regulatory network in Escherichia coli mediated by microRNAs (sRNAs) with transcriptional and translational time delays. Motivated by the regulation of gene expression proposed by Shimoni et al. (Molecular Systems Biology, 2007), a general model of delayed gene regulatory network by sRNAs is formulated. This model can well describe many practical architectures of gene regulatory network by sRNAs, particularly when both transcriptional and translational time delays are introduced. Two functional issues on oscillatory expression of the gene regulatory network, i.e. stability and bifurcation, are investigated. Furthermore, an explicit algorithm determining the direction of Hopf bifurcation and stability of bifurcating periodic solutions is presented. It turns out that both transcriptional and translational time delays can induce gene expression in E. coli to be oscillatory even when its deterministic counterpart exhibits no oscillations. Moreover, the obtained results are in consistence with the experimental observations found in the biological literatures (Elowitz MB et al.: Nature, 2000, 403, pp. 335-338; Lennart Hilbert et al.: Mol. BioSyst, 2011, 7, pp. 2599-2607), which demonstrates that both transcriptional and translational time delays play an important role in the gene regulatory process of E. coli.

A novel mathematical model of ATM/p53/NF- κB pathways points to the importance of the DDR switch-off mechanisms

Background

Ataxia telangiectasia mutated (ATM) is a detector of double-strand breaks (DSBs) and a crucial component of the DNA damage response (DDR) along with p53 and NF- κB transcription factors and Wip1 phosphatase. Despite the recent advances in studying the DDR, the mechanisms of cell fate determination after DNA damage induction is still poorly understood.

Results

To investigate the importance of various DDR elements with particular emphasis on Wip1, we developed a novel mathematical model of ATM/p53/NF- κB pathways. Our results from in silico and in vitro experiments performed on U2-OS cells with Wip1 silenced to 25 % (Wip1-RNAi) revealed a strong dependence of cellular response to DNA damages on this phosphatase. Notably, Wip1-RNAi cells exhibited lower resistance to ionizing radiation (IR) resulting in smaller clonogenicity and higher apoptotic fraction.

Conclusions

In this article, we demonstrated that Wip1 plays a role as a gatekeeper of apoptosis and influences the pro-survival behaviour of cells – the level of Wip1 increases to block the apoptotic decision when DNA repair is successful. Moreover, we were able to verify the dynamics of proteins and transcripts, apoptotic fractions and cells viability obtained from stochastic simulations using in vitro approaches. Taken together, we demonstrated that the model can be successfully used in prediction of cellular behaviour after exposure to IR. Thus, our studies may provide further insights into key elements involved in the underlying mechanisms of the DDR.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0293-0) contains supplementary material, which is available to authorized users.

Heterodimer Autorepression Loop: A Robust and Flexible Pulse-Generating Genetic Module

We investigate the dynamics of the heterodimer autorepression loop (HAL), a small genetic module in which a protein A acts as an autorepressor and binds to a second protein B to form an AB dimer. For suitable values of the rate constants, the HAL produces pulses of A alternating with pulses of B. By means of analytical and numerical calculations, we show that the duration of A pulses is extremely robust against variation of the rate constants while the duration of the B pulses can be flexibly adjusted. The HAL is thus a minimal genetic module generating robust pulses with a tunable duration, an interesting property for cellular signaling.

Computational Framework for Modeling Multiple Noncooperative Transcription Factor Binding and Its Application to the Analysis of Nuclear Factor Kappa B Oscillatory Response

Recent studies have shown that regulation of many important genes is achieved with multiple transcription factor (TF) binding sites with low or no cooperativity. Additionally, noncooperative binding sites are gaining more and more importance in the field of synthetic biology. Here, we introduce a computational framework that can be applied to dynamical modeling and analysis of gene regulatory networks with multiple noncooperative TF binding sites. We propose two computational methods to be used within the framework, that is, average promoter state approximation and expression profiles based modeling. We demonstrate the application of the proposed framework on the analysis of nuclear factor kappa B (NF-κB) oscillatory response. We show that different promoter expression hypotheses in a combination with the number of TF binding sites drastically affect the dynamics of the observed system and should not be ignored in the process of quantitative dynamical modeling, as is usually the case in existent state-of-the-art computational analyses.

Role of Computational Modeling in Understanding Cell Cycle Oscillators

The periodic oscillations in the activity of the cell cycle regulatory program, drives the timely activation of key cell cycle events. Interesting dynamical systems, such as oscillators, have been investigated by various theoretical and computational modeling methods. Thanks to the insights achieved by these modeling efforts we have gained considerable insights about the underlying molecular regulatory networks that can drive cell cycle oscillations. Here we review the basic features and characteristics of biological oscillators, discussing from a computational modeling point of view their specific architectures and the current knowledge about the dynamics that the life evolution selected to drive cell cycle oscillations.

RELB Alters Proliferation of Human Pluripotent Stem Cells via IMP3- and LIN28-Mediated Modulation of the Expression of IGF2 and Other Cell-Cycle Regulators

The molecular mechanisms that orchestrate the exit from pluripotency, cell cycle progression, and lineage-specific differentiation in human pluripotent stem cells (hPSCs) are poorly understood. RELB, a key protein in the noncanonical nuclear factor-kappaB (NFκB) signaling pathway, was previously implicated in controlling the switch between human embryonic stem cell (hESC) proliferation and differentiation. Here, we show that RELB enhances the proliferation of hESCs and human-induced pluripotent stem cells (hiPSCs) without affecting their pluripotency. We demonstrate that RELB does this by interacting with two RNA-binding proteins LIN28A and IMP3 (IGF2 mRNA-binding protein 3); further, these interactions control mRNA levels and protein expression of insulin-like growth factor 2 (IGF2) and key cell-cycle genes. Finally, after stress, these proteins co-localize in stress granules in hESCs and iPSCs. Our data identify RELB as a novel regulator of hPSC proliferation, and suggest a new function for RELB, in addition to its widely accepted role as a transcription factor, that involves recruitment of IMP3 and LIN28 to the cytosolic mRNA translation-control domains for post-transcriptional modulation of IGF2 and cell-cycle gene expression.

Transcriptional control of vertebrate neurogenesis by the proneural factor Ascl1

Proneural transcription factors (TFs) such as Ascl1 function as master regulators of neurogenesis in vertebrates, being both necessary and sufficient for the activation of a full program of neuronal differentiation. Novel insights into the dynamics of Ascl1 expression at the cellular level, combined with the progressive characterization of its transcriptional program, have expanded the classical view of Ascl1 as a differentiation factor in neurogenesis. These advances resulted in a new model, whereby Ascl1 promotes sequentially the proliferation and differentiation of neural/stem progenitor cells. The multiple activities of Ascl1 are associated with the activation of distinct direct targets at progressive stages along the neuronal lineage. How this temporal pattern is established is poorly understood. Two modes of Ascl1 expression recently described (oscillatory vs. sustained) are likely to be of importance, together with additional mechanistic determinants such as the chromatin landscape and other transcriptional pathways. Here we revise these latest findings, and discuss their implications to the gene regulatory functions of Ascl1 during neurogenesis.

Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene

Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.

TRPV6 calcium channel translocates to the plasma membrane via Orai1-mediated mechanism and controls cancer cell survival

Transient receptor potential vanilloid subfamily member 6 (TRPV6) is a highly selective calcium channel that has been considered as a part of store-operated calcium entry (SOCE). Despite its first discovery in the early 2000s, the role of this channel in prostate cancer (PCa) remained, until now, obscure. Here we show that TRPV6 mediates calcium entry, which is highly increased in PCa due to the remodeling mechanism involving the translocation of the TRPV6 channel to the plasma membrane via the Orai1/TRPC1-mediated Ca(2+)/Annexin I/S100A11 pathway, partially contributing to SOCE. The TRPV6 calcium channel is expressed de novo by the PCa cell to increase its survival by enhancing proliferation and conferring apoptosis resistance. Xenografts in nude mice and bone metastasis models confirmed the remarkable aggressiveness of TRPV6-overexpressing tumors. Immunohistochemical analysis of these demonstrated the increased expression of clinical markers such as Ki-67, prostate specific antigen, synaptophysin, CD31, and CD56, which are strongly associated with a poor prognosis. Thus, the TRPV6 channel acquires its oncogenic potential in PCa due to the remodeling mechanism via the Orai1-mediated Ca(2+)/Annexin I/S100A11 pathway.

The p53 response in single cells is linearly correlated to the number of DNA breaks without a distinct threshold

BACKGROUND

The tumor suppressor protein p53 is activated by cellular stress. DNA double strand breaks (DSBs) induce the activation of the kinase ATM, which stabilizes p53 and activates its transcriptional activity. Single cell analysis revealed that DSBs induced by gamma irradiation trigger p53 accumulation in a series of pulses that vary in number from cell to cell. Higher levels of irradiation increase the number of p53 pulses suggesting that they arise from periodic examination of the damage by ATM. If damage persists, additional pulses of p53 are triggered. The threshold of damage required for activating a p53 pulse is unclear. Previous studies that averaged the response across cell populations suggested that one or two DNA breaks are sufficient for activating ATM and p53. However, it is possible that by averaging over a population of cells important features of the dependency between DNA breaks and p53 dynamics are missed.

RESULTS

Using fluorescent reporters we developed a system for following in individual cells the number of DSBs, the kinetics of repair and the p53 response. We found a large variation in the initial number of DSBs and the rate of repair between individual cells. Cells with higher number of DSBs had higher probability of showing a p53 pulse. However, there was no distinct threshold number of breaks for inducing a p53 pulse. We present evidence that the decision to activate p53 given a specific number of breaks is not entirely stochastic, but instead is influenced by both cell-intrinsic factors and previous exposure to DNA damage. We also show that the natural variations in the initial amount of p53, rate of DSB repair and cell cycle phase do not affect the probability of activating p53 in response to DNA damage.

CONCLUSIONS

The use of fluorescent reporters to quantify DNA damage and p53 levels in live cells provided a quantitative analysis of the complex interrelationships between both processes. Our study shows that p53 activation differs even between cells that have a similar number of DNA breaks. Understanding the origin and consequences of such variability in normal and cancerous cells is crucial for developing efficient and selective therapeutic interventions.

The dynamics of genetic control in the cell: the good and bad of being late

The expression of genes in the cell is controlled by a complex interaction network involving proteins, RNA and DNA. The molecular events associated with the nodes of such a network take place on a variety of time scales, and thus cannot be regarded as instantaneous. In many cases, the cell is robust with respect to the delay in gene expression control, behaving as if it were instantaneous. However, there are specific cases in which delay gives rise to temporal oscillations. This is the case, for example, of the expression of tumour-suppressor protein p53, of protein Hes1, involved in the differentiation of stem cells, of NFkB and Wnt, in which case delay arises implicitly from the structure of the associated network. By means of delay rate equations, we study the kinetics of small regulatory networks, emphasizing the role of delay in an evolutionary context. These models suggest that oscillations are a typical outcome of the dynamics of regulatory networks, and evolution has to work to avoid them when not required (and not vice versa).

Desflurane preconditioning induces oscillation of NF-κB in human umbilical vein endothelial cells

Background

Nuclear factor kappa B (NF-κB) has been implicated in anesthetic preconditioning (APC) induced protection against anoxia and reoxygenation (A/R) injury. The authors hypothesized that desflurane preconditioning would induce NF-κB oscillation and prevent endothelial cells apoptosis.

Methods

A human umbilical vein endothelial cells (HUVECs) A/R injury model was used. A 30 minute desflurane treatment was initiated before anoxia. NF-κB inhibitor BAY11-7082 was administered in some experiments before desflurane preconditioning. Cells apoptosis was analyzed by flow cytometry using annexin V–fluorescein isothiocyanate staining and cell viability was evaluated by modified tertrozalium salt (MTT) assay. The cellular superoxide dismutases (SOD) activitiy were tested by water-soluble tetrazolium salt (WST-1) assay. NF-κB p65 subunit nuclear translocation was detected by immunofluorescence staining. Expression of inhibitor of NF-κB-α (IκBα), NF-κB p65 and cellular inhibitor of apoptosis 1 (c-IAP1), B-cell leukemia/lymphoma 2 (Bcl-2), cysteine containing aspartate specific protease 3 (caspases-3) and second mitochondrial-derived activator of caspase (SMAC/DIABLO) were determined by western blot.

Results

Desflurane preconditioning caused phosphorylation and nuclear translocation of NF-κB before anoxia, on the contrary, induced the synthesis of IκBα and inhibition of NF-κB after reoxygenation. Desflurane preconditioning up-regulated the expression of c-IAP1 and Bcl-2, blocked the cleavage of caspase-3 and reduced SMAC release, and decreased the cell death of HUVECs after A/R. The protective effect was abolished by BAY11-7082 administered before desflurane.

Conclusions

The results demonstrated that desflurane activated NF-κB during the preconditioning period and inhibited excessive activation of NF-κB in reperfusion. And the oscillation of NF-κB induced by desflurane preconditioning finally up-regulated antiapoptotic proteins expression and protected endothelial cells against A/R.

A motor-driven mechanism for cell-length sensing

Size homeostasis is fundamental in cell biology, but it is not clear how large cells such as neurons can assess their own size or length. We examined a role for molecular motors in intracellular length sensing. Computational simulations suggest that spatial information can be encoded by the frequency of an oscillating retrograde signal arising from a composite negative feedback loop between bidirectional motor-dependent signals. The model predicts that decreasing either or both anterograde or retrograde signals should increase cell length, and this prediction was confirmed upon application of siRNAs for specific kinesin and/or dynein heavy chains in adult sensory neurons. Heterozygous dynein heavy chain 1 mutant sensory neurons also exhibited increased lengths both in vitro and during embryonic development. Moreover, similar length increases were observed in mouse embryonic fibroblasts upon partial downregulation of dynein heavy chain 1. Thus, molecular motors critically influence cell-length sensing and growth control.

Robustness in angiogenesis: notch and BMP shaping waves

Vascular patterning involves sprouting of blood vessels, which is governed by orchestrated communication between cells in the surrounding tissue and endothelial cells (ECs) lining the blood vessels. Single ECs are selected for sprouting by hypoxia-induced stimuli and become the 'tip' or leader cell that guides new sprouts. The 'stalk' or trailing ECs proliferate for tube extension and lumenize the nascent vessel. Stalk and tip cells can dynamically switch their identities during this process in a Notch-dependent manner. Here, we review recent studies showing that bone morphogenetic protein (BMP) signaling coregulates Notch target genes in ECs. In particular, we focus on how Delta-like ligand 4 (DLL4)-Notch and BMP effector interplay may drive nonsynchronized oscillatory gene expression in ECs essential for setting sharp tip-stalk cell boundaries while sustaining a dynamic pool of nonsprouting ECs. Deeper knowledge about the coregulation of vessel plasticity in different vascular beds may result in refinement of anti-angiogenesis and vessel normalization therapies.

Dynamical principles of cell-cycle arrest: reversible, irreversible, and mixed strategies

Living cells often alternate between proliferating and nonproliferating states as part of individual or collective strategies to adapt to complex and changing environments. To this aim, they have evolved a biochemical regulatory network enabling them to switch between cell-division cycles (i.e., oscillatory state) and cell-cycle arrests (i.e., steady state) in response to extracellular cues. This can be achieved by means of a variety of bifurcation mechanisms that potentially give rise to qualitatively distinct cell-cycle arrest properties. In this paper, we study the dynamics of a minimal biochemical network model in which a cell-division oscillator and a differentiation switch mutually antagonize. We identify the existence of three biologically plausible bifurcation scenarios organized around a codimension-four swallowtail-homoclinic singularity. As a result, the model exhibits a broad repertoire of cell-cycle arrest properties in terms of reversibility of these arrests, tunability of interdivision time, and ability to track time-varying signals. This dynamic versatility would explain the diversity of cell-cycle arrest strategies developed in different living species and functional contexts.

Analysing the role of UVB-induced translational inhibition and PP2Ac deactivation in NF-κB signalling using a minimal mathematical model

Activation of nuclear factor κB (NF-κB) by interleukin-1β (IL-1) usually results in an anti-apoptotic activity that is rapidly terminated by a negative feedback loop involving NF-κB dependent resynthesis of its own inhibitor IκBα. However, apoptosis induced by ultraviolet B radiation (UVB) is not attenuated, but significantly enhanced by co-stimulation with IL-1 in human epithelial cells. Under these conditions NF-κB remains constitutively active and turns into a pro-apoptotic factor by selectively repressing anti-apoptotic genes. Two different mechanisms have been separately proposed to explain UV-induced lack of IκBα recurrence: global translational inhibition as well as deactivation of the Ser/Thr phosphatase PP2Ac. Using mathematical modelling, we show that the systems behaviour requires a combination of both mechanisms, and we quantify their contribution in different settings. A mathematical model including both mechanisms is developed and fitted to various experimental data sets. A comparison of the model results and predictions with model variants lacking one of the mechanisms shows that both mechanisms are present in our experimental setting. The model is successfully validated by the prediction of independent data. Weak constitutive IKKβ phosphorylation is shown to be a decisive process in IκBα degradation induced by UVB stimulation alone, but irrelevant for (co-)stimulations with IL-1. In silico knockout experiments show that translational inhibition is predominantly responsible for lack of IκBα recurrence following IL-1+UVB stimulation. In case of UVB stimulation alone, cooperation of both processes causes the observed decrease of IκBα. This shows that the processes leading to activation of transcription factor NF-κB upon stimulation with ultraviolet B radiation with and without interleukin-1 costimulation are more complex than previously thought, involving both a cross talk of UVB induced translational inhibition and PP2Ac deactivation. The importance of each of the mechanisms depends on the specific cellular setting.

Mechanisms generating bistability and oscillations in microRNA-mediated motifs

The importance of post-transcriptional regulation by microRNAs (miRNAs) has recently been recognized in almost all cellular processes. When participating in cellular processes, miRNAs mainly mediate mRNA degradation or translational repression. Recently computational and experimental studies have identified an abundance of motifs involving miRNAs and transcriptional factors (TFs). The simplest motif is a two-node miRNA-mediated feedback loop (MFL) in which a TF regulates an miRNA and the TF itself is negatively regulated by the miRNA. In this paper we present a general computational model for the MFL based on biochemical regulations and explore its dynamics by using bifurcation analysis. Our results show that the MFL can behave either as switches or as oscillators, depending on the TF as a repressor or an activator. These functional features are consistent with the widespread appearance of miRNAs in fate decisions such as proliferation, differentiation, and apoptosis during development. We found that under the interplay of a TF and an miRNA, the MFL model can behave as switches for wide ranges of parameters even without cooperative binding of the TF. In addition, oscillations induced by the miRNA in the MFL model require neither an additional positive feedback loop, nor self-activation of the gene, nor cooperative binding of the TF, nor saturated degradation. Therefore, the MFL may provide a general network structure to induce bistability or oscillations. It is hoped that the results presented here will provide a new view on how gene expression is regulated by miRNAs and further guidance for experiments. Moreover, the insight gained from this study is also expected to provide a basis for the investigation of more complex networks assembled by simple building blocks.

Emerging role of NF-κB signaling in the induction of senescence-associated secretory phenotype (SASP)

The major hallmark of cellular senescence is an irreversible cell cycle arrest and thus it is a potent tumor suppressor mechanism. Genotoxic insults, e.g. oxidative stress, are important inducers of the senescent phenotype which is characterized by an accumulation of senescence-associated heterochromatic foci (SAHF) and DNA segments with chromatin alterations reinforcing senescence (DNA-SCARS). Interestingly, senescent cells secrete pro-inflammatory factors and thus the condition has been called the senescence-associated secretory phenotype (SASP). Emerging data has revealed that NF-κB signaling is the major signaling pathway which stimulates the appearance of SASP. It is known that DNA damage provokes NF-κB signaling via a variety of signaling complexes containing NEMO protein, an NF-κB essential modifier, as well as via the activation of signaling pathways of p38MAPK and RIG-1, retinoic acid inducible gene-1. Genomic instability evoked by cellular stress triggers epigenetic changes, e.g. release of HMGB1 proteins which are also potent enhancers of inflammatory responses. Moreover, environmental stress and chronic inflammation can stimulate p38MAPK and ceramide signaling and induce cellular senescence with pro-inflammatory responses. On the other hand, two cyclin-dependent kinase inhibitors, p16INK4a and p14ARF, are effective inhibitors of NF-κB signaling. We will review in detail the signaling pathways which activate NF-κB signaling and trigger SASP in senescent cells.

Using imaging methods to interrogate radiation-induced cell signaling

There is increasing emphasis on the use of systems biology approaches to define radiation-induced responses in cells and tissues. Such approaches frequently rely on global screening using various high throughput 'omics' platforms. Although these methods are ideal for obtaining an unbiased overview of cellular responses, they often cannot reflect the inherent heterogeneity of the system or provide detailed spatial information. Additionally, performing such studies with multiple sampling time points can be prohibitively expensive. Imaging provides a complementary method with high spatial and temporal resolution capable of following the dynamics of signaling processes. In this review, we utilize specific examples to illustrate how imaging approaches have furthered our understanding of radiation-induced cellular signaling. Particular emphasis is placed on protein colocalization, and oscillatory and transient signaling dynamics.

Negative regulation by amidase PGRPs shapes the Drosophila antibacterial response and protects the fly from innocuous infection

Peptidoglycan recognition proteins (PGRPs) are key regulators of insect immune responses. In addition to recognition PGRPs, which activate the Toll and Imd pathways, the Drosophila genome encodes six catalytic PGRPs with the capacity to scavenge peptidoglycan. We have performed a systematic analysis of catalytic PGRP function using deletions, separately and in combination. Our findings support the role of PGRP-LB as a negative regulator of the Imd pathway and brought to light a synergy of PGRP-SCs with PGRP-LB in the systemic response. Flies lacking all six catalytic PGRPs were still viable but exhibited deleterious immune responses to innocuous gut infections. Together with recent studies on mammalian PGRPs, our study uncovers a conserved role for PGRPs in gut homeostasis. Analysis of the immune phenotype of flies lacking all catalytic PGRPs and the Imd regulator Pirk reveals that the Imd-mediated immune response is highly constrained by the existence of multiple negative feedbacks.

Communicating oscillatory networks: frequency domain analysis

Background

Constructing predictive dynamic models of interacting signalling networks remains one of the great challenges facing systems biology. While detailed dynamical data exists about individual pathways, the task of combining such data without further lengthy experimentation is highly nontrivial. The communicating links between pathways, implicitly assumed to be unimportant and thus excluded, are precisely what become important in the larger system and must be reinstated. To maintain the delicate phase relationships between signals, signalling networks demand accurate dynamical parameters, but parameters optimised in isolation and under varying conditions are unlikely to remain optimal when combined. The computational burden of estimating parameters increases exponentially with increasing system size, so it is crucial to find precise and efficient ways of measuring the behaviour of systems, in order to re-use existing work.

Results

Motivated by the above, we present a new frequency domain-based systematic analysis technique that attempts to address the challenge of network assembly by defining a rigorous means to quantify the behaviour of stochastic systems. As our focus we construct a novel coupled oscillatory model of p53, NF-kB and the mammalian cell cycle, based on recent experimentally verified mathematical models. Informed by online databases of protein networks and interactions, we distilled their key elements into simplified models containing the most significant parts. Having coupled these systems, we constructed stochastic models for use in our frequency domain analysis. We used our new technique to investigate the crosstalk between the components of our model and measure the efficacy of certain network-based heuristic measures.

Conclusions

We find that the interactions between the networks we study are highly complex and not intuitive: (i) points of maximum perturbation do not necessarily correspond to points of maximum proximity to influence; (ii) increased coupling strength does not necessarily increase perturbation; (iii) different perturbations do not necessarily sum and (iv) overall, susceptibility to perturbation is amplitude and frequency dependent and cannot easily be predicted by heuristic measures.

Our methodology is particularly relevant for oscillatory systems, though not limited to these, and is most revealing when applied to the results of stochastic simulation. The technique is able to characterise precisely the distance in behaviour between different models, different systems and different parts within the same system. It can also measure the difference between different simulation algorithms used on the same system and can be used to inform the choice of dynamic parameters. By measuring crosstalk between subsystems it can also indicate mechanisms by which such systems may be controlled in experiments and therapeutics. We have thus found our technique of frequency domain analysis to be a valuable benchmark systems-biological tool.

A novel function of the proneural factor Ascl1 in progenitor proliferation identified by genome-wide characterization of its targets

Proneural genes such as Ascl1 are known to promote cell cycle exit and neuronal differentiation when expressed in neural progenitor cells. The mechanisms by which proneural genes activate neurogenesis--and, in particular, the genes that they regulate--however, are mostly unknown. We performed a genome-wide characterization of the transcriptional targets of Ascl1 in the embryonic brain and in neural stem cell cultures by location analysis and expression profiling of embryos overexpressing or mutant for Ascl1. The wide range of molecular and cellular functions represented among these targets suggests that Ascl1 directly controls the specification of neural progenitors as well as the later steps of neuronal differentiation and neurite outgrowth. Surprisingly, Ascl1 also regulates the expression of a large number of genes involved in cell cycle progression, including canonical cell cycle regulators and oncogenic transcription factors. Mutational analysis in the embryonic brain and manipulation of Ascl1 activity in neural stem cell cultures revealed that Ascl1 is indeed required for normal proliferation of neural progenitors. This study identified a novel and unexpected activity of the proneural gene Ascl1, and revealed a direct molecular link between the phase of expansion of neural progenitors and the subsequent phases of cell cycle exit and neuronal differentiation.

A robust two-gene oscillator at the core of Ostreococcus tauri circadian clock

The microscopic green alga Ostreococcus tauri is rapidly emerging as a promising model organism in the green lineage. In particular, recent results by Corellou et al. [Plant Cell 21, 3436 (2009)] and Thommen et al. [PLOS Comput. Biol. 6, e1000990 (2010)] strongly suggest that its circadian clock is a simplified version of Arabidopsis thaliana clock, and that it is architectured so as to be robust to natural daylight fluctuations. In this work, we analyze the time series data from luminescent reporters for the two central clock genes TOC1 and CCA1 and correlate them with microarray data previously analyzed. Our mathematical analysis strongly supports both the existence of a simple two-gene oscillator at the core of Ostreococcus tauri clock and the fact that its dynamics is not affected by light in normal entrainment conditions, a signature of its robustness.