Control Analysis of Cooperativity and Complementarity in Metabolic Regulations: The Case of NADPH Homeostasis.

Complex feedback regulation patterns shape the cellular metabolic response to external or internal perturbations. We propose here a framework consisting of a sampling-based metabolic control analysis of kinetic models to investigate the modes of regulatory interplay in metabolic functions. NADPH homeostasis, for instance in a context of oxidative stress, is an example of metabolic function that involves multiple feedback regulations which raises the issue of their concerted action. Our computational framework allows us to characterize both respective and combined effects of regulations, distinguishing between synergistic versus complementary modes of regulatory crosstalk. Synergistic regulation of G6PD enzymes and PGI enzymes is mediated by congruent effects between concentration sensitivities and reaction elasticities. Complementary regulation of pentose phosphate pathway and lower glycolysis relates to metabolic state-dependent range of regulation efficiency. These cooperative effects are shown to significantly improve metabolic flux response to support NADPH homeostasis, providing a rationale for the complex feedback regulation pattern at work.

Stochastic simulation algorithm for isotope-based dynamic flux analysis.

Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number of variables or operations in metabolic flux analysis (MFA), but lacks generalizability to non-stationary metabolic conditions. In this study, we present a stochastic simulation algorithm (SSA) derived from the chemical master equation of the isotope labeling system. This algorithm allows to compute the time evolution of isotopomer concentrations in non-stationary conditions, with the valuable property that computational time does not scale with the number of isotopomers. The efficiency and limitations of the algorithm is benchmarked for the forward and inverse problems of 13C-DMFA in the pentose phosphate pathways, and is compared with EMU-based methods for NMFA and MFA including the central carbon metabolism. Overall, SSA constitutes an alternative class to deterministic approaches for metabolic flux analysis that is well adapted to comprehensive dataset including parallel labeling experiments, and whose limitations associated to the sampling size can be overcome by using Monte Carlo sampling approaches.

Quantitative modeling of pentose phosphate pathway response to oxidative stress reveals a cooperative regulatory strategy.

Living cells use signaling and regulatory mechanisms to adapt to environmental stresses. Adaptation to oxidative stress involves the regulation of many enzymes in both glycolysis and pentose phosphate pathways (PPP), so as to support PPP-driven NADPH recycling for antioxidant defense. The underlying regulatory logic is investigated by developing a kinetic modeling approach fueled with metabolomics and 13C-fluxomics datasets from human fibroblast cells. Bayesian parameter estimation and phenotypic analysis of models highlight complementary roles for several metabolite-enzyme regulations. Specifically, carbon flux rerouting into PPP involves a tight coordination between the upregulation of G6PD activity concomitant to a decreased NADPH/NADP+ ratio and the differential control of downward and upward glycolytic fluxes through the joint inhibition of PGI and GAPD enzymes. Such functional interplay between distinct regulatory feedbacks promotes efficient detoxification and homeostasis response over a broad range of stress level, but can also explain paradoxical pertubation phenotypes for instance reported for 6PGD modulation in mammalian cells.

Multistability and transitions between spatiotemporal patterns through versatile Notch-Hes signaling.

The Delta-Notch-Hes signaling pathway is involved in various developmental processes ranging from the formation of somites to the dynamic fine-grained patterns of cell types in developing or regenerating tissues. Such broad patterning capabilities rely in part on the versatile and tunable dynamics of the Notch-Hes feedback circuit eliciting both pulsatile and switching behaviors. This raises the theoretical issue of which specific spatiotemporal features emerge from lateral inhibition between cells that can display and transit between monostable, oscillatory and bistable regimes. To address this issue, I consider a discrete cell lattice model where intracellular dynamics is described by a phase-like variable and displays a typical cross-shaped phase diagram. Model analysis determines how the existence and stability of many spatially inhomogeneous and temporally synchronized states depends on key intracellular and intercellular parameters. It reveals a parameter-dependent multistability between those diverse spatiotemporal patterns, giving rise to tunable and robust developmental transition scenarios ensuring defect-free spatial patterns. Such broad repertoire and multistability of spatiotemporal patterns is corroborated with regulatory network modeling of the Delta-Notch-Hes pathway.

Plasma membrane perforation by GSDME during apoptosis-driven secondary necrosis.

Secondary necrosis has long been perceived as an uncontrolled process resulting in total lysis of the apoptotic cell. Recently, it was shown that progression of apoptosis to secondary necrosis is regulated by Gasdermin E (GSDME), which requires activation by caspase-3. Although the contribution of GSDME in this context has been attributed to its pore-forming capacity, little is known about the kinetics and size characteristics of this. Here we report on the membrane permeabilizing features of GSDME by monitoring the influx and efflux of dextrans of different sizes into/from anti-Fas-treated L929sAhFas cells undergoing apoptosis-driven secondary necrosis. We found that GSDME accelerates cell lysis measured by SYTOX Blue staining but does not affect the exposure of phosphatidylserine on the plasma membrane. Furthermore, loss of GSDME expression clearly hampered the influx of fluorescently labeled dextrans while the efflux happened independently of the presence or absence of GSDME expression. Importantly, both in- and efflux of dextrans were dependent on their molecular weight. Altogether, our results demonstrate that GSDME regulates the passage of compounds together with other plasma membrane destabilizing subroutines.

Fine-tuned control of stress priming and thermotolerance.

A common signature of cell adaptation to stress is the improved resistance upon priming by prior stress exposure. In the context of hyperthermia, priming or preconditioning with sublethal heat shock can be a useful tool to confer thermotolerance and competitive advantage to cells. In the present study, we develop a data-driven modeling framework that is simple and generic enough to capture a broad set of adaptation behaviors to heat stress at both molecular and cellular levels. The model recovers the main features of thermotolerance and clarifies the tradeoff principles which maximize the thermotolerance effect. It therefore provides an effective predictive tool to design preconditioning and fractionation hyperthermia protocols for therapeutic purpose.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing.

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Scaling laws of cell-fate responses to transient stress.

Analysis and modelling of dose-survival curves of cells and tissues are often used to assess therapeutic efficacy or environmental risks, much less to infer the intracellular regulatory mechanisms of cellular stress response. However, systematic measurements of how cell survival depends on the time profile of stress, such as exposure duration, provide practical means to decipher the homeostatic dynamics of stress-response regulatory networks. In this paper, we propose a dynamical framework to theoretically address the relationship between cell fate response to a transient stress and the underlying regulatory feedback mechanisms. A simple network topology that couples a homeostatic negative feedback and a death-triggering positive feedback is shown to display four response regimes for which the iso-effect relationships between duration and intensity are captured by specific power laws. These distinct response regimes define several windows of stress duration for which lethality is not merely proportional to the product of intensity and duration, and, thus, for which cells are either more tolerant or more vulnerable to a given dose. Overall, this study highlights the differential roles of feedback strength, timescale and nonlinearity in promoting survivability to particular stress profiles, providing a valuable framework for a comparative analysis of diverse stress-specific regulatory networks.

Network Features and Dynamical Landscape of Naive and Primed Pluripotency.

Although the broad and unique differentiation potential of pluripotent stem cells relies on a complex transcriptional network centered around Oct4, Sox2, and Nanog, two well-distinct pluripotent states, called "naive" and "primed", have been described in vitro and markedly differ in their developmental potential, their expression profiles, their signaling requirements, and their reciprocal conversion. Aiming to determine the key features that segregate and coordinate these two states, data-driven optimization of network models is performed to identify relevant parameter regimes and reduce network complexity to its core structure. Decision dynamics of optimized networks is characterized by signal-dependent multistability and strongly asymmetric transitions among naive, primed, and nonpluripotent states. Further model perturbation and reduction approaches reveal that such a dynamical landscape of pluripotency involves a functional partitioning of the regulatory network. Specifically, two overlapping positive feedback modules, Klf4/Esrrb/Nanog and Oct4/Nanog, stabilize the naive or the primed state, respectively. In turn, their incoherent feedforward and negative feedback coupling mediated by the Erk/Gsk3 module is critical for robust segregation and sequential progression between naive and primed states before irreversible exit from pluripotency.

Adaptive Benefits of Storage Strategy and Dual AMPK/TOR Signaling in Metabolic Stress Response.

Cellular metabolism must ensure that supply of nutrient meets the biosynthetic and bioenergetic needs. Cells have therefore developed sophisticated signaling and regulatory pathways in order to cope with dynamic fluctuations of both resource and demand and to regulate accordingly diverse anabolic and catabolic processes. Intriguingly, these pathways are organized around a relatively small number of regulatory hubs, such as the highly conserved AMPK and TOR kinase families in eukaryotic cells. Here, the global metabolic adaptations upon dynamic environment are investigated using a prototypical model of regulated metabolism. In this model, the optimal enzyme profiles as well as the underlying regulatory architecture are identified by combining perturbation and evolutionary methods. The results reveal the existence of distinct classes of adaptive strategies, which differ in the management of storage reserve depending on the intensity of the stress and in the regulation of ATP-producing reaction depending on the nature of the stress. The regulatory architecture that optimally implements these adaptive features is characterized by a crosstalk between two specialized signaling pathways, which bears close similarities with the sensing and regulatory properties of AMPK and TOR pathways.

Probing entrainment of Ostreococcus tauri circadian clock by green and blue light through a mathematical modeling approach.

Most organisms anticipate daily environmental variations and orchestrate cellular functions thanks to a circadian clock which entrains robustly to the day/night cycle, despite fluctuations in light intensity due to weather or seasonal variations. Marine organisms are also subjected to fluctuations in light spectral composition as their depth varies, due to differential absorption of different wavelengths by sea water. Studying how light input pathways contribute to circadian clock robustness is therefore important. Ostreococcus tauri, a unicellular picoplanktonic marine green alga with low genomic complexity and simple cellular organization, has become a promising model organism for systems biology. Functional and modeling approaches have shown that a core circadian oscillator based on orthologs of Arabidopsis TOC1 and CCA1 clock genes accounts for most experimental data acquired under a wide range of conditions. Some evidence points at putative light input pathway(s) consisting of a two-component signaling system (TCS) controlled by the only two histidine kinases (HK) of O. tauri. LOV-HK is a blue light photoreceptor under circadian control, that is required for circadian clock function. An involvement of Rhodopsin-HK (Rhod-HK) is also conceivable since rhodopsin photoreceptors mediate blue to green light input in animal circadian clocks. Here, we probe the role of LOV-HK and Rhod-HK in mediating light input to the TOC1-CCA1 oscillator using a mathematical model incorporating the TCS hypothesis. This model agrees with clock gene expression time series representative of multiple environmental conditions in blue or green light, characterizing entrainment by light/dark cycles, free-running in constant light, and resetting. Experimental and theoretical results indicate that both blue and green light can reset O. tauri circadian clock. Moreover, our mathematical analysis suggests that Rhod-HK is a blue-green light receptor and drives the clock together with LOV-HK.

A computational model for the coordination of neural progenitor self-renewal and differentiation through Hes1 dynamics.

Proper tissue development requires that stem/progenitor cells precisely coordinate cell division and differentiation in space and time. Notch-Hes1 intercellular signaling, which affects both differentiation and cell cycle progression and directs cell fate decisions at various developmental stages in many cell types, is central to this process. This study explored whether the pattern of connections among the cell cycle regulatory module, the Notch effector Hes1 and the proneural factor Ngn2 could explain salient aspects of cell fate determination in neural progenitors. A mathematical model that includes mutual interactions between Hes1, Ngn2 and G1-phase regulators was constructed and simulated at the single- and two-cell levels. By differentially regulating G1-phase progression, Hes1 and Ngn2 are shown to induce two contrasting cell cycle arrest states in early and late G1, respectively. Indeed, steady Hes1 overexpression promotes reversible quiescence by downregulating activators of G0/G1 exit and Ngn2. Ngn2 also downregulates activators of G0/G1 exit, but cooperates with Cip/Kip proteins to prevent G1/S transit, whereby it promotes G1-phase lengthening and, ultimately, contributes to reinforcing an irreversible late G1 arrest coincident with terminal differentiation. In this scheme, Hes1 oscillation in single cells is able to maintain a labile proliferation state in dynamic balance with two competing cell fate outputs associated with Hes1-mediated and Ngn2-mediated cell cycle arrest states. In Delta/Notch-connected cells, Hes1 oscillations and a lateral inhibition mechanism combine to establish heterogeneous Hes1, Ngn2 and cell cycle dynamics between proliferating neural progenitors, thereby increasing the chances of asymmetric cell fate decisions and improving the reliability of commitment to differentiation.

Neuronal specification exploits the inherent flexibility of cell-cycle gap phases.

Starting from pluripotent stem cells that virtually proliferate indefinitely, the orderly emergence during organogenesis of lineage-restricted cell types exhibiting a decreased proliferative capacity concurrently with an increasing range of differentiation traits implies the occurrence of a stringent spatiotemporal coupling between cell-cycle progression and cell differentiation. A recent computational modeling study has explored in the context of neurogenesis whether and how the peculiar pattern of connections among the proneural Neurog2 factor, the Hes1 Notch effector and antagonistically-acting G1-phase regulators would be instrumental in this event. This study highlighted that the strong opposition to G1/S transit imposed by accumulating Neurog2 and CKI enables a sensitive control of G1-phase lengthening and terminal differentiation to occur concomitantly with late-G1 exit. Contrastingly, Hes1 promotes early-G1 cell-cycle arrest and its cell-autonomous oscillations combined with a lateral inhibition mechanism help maintain a labile proliferation state in dynamic balance with diverse cell-fate outputs, thereby, offering cells the choice to either keep self-renewing or differentiate into distinct cell types. These results, discussed in connection with Ascl1-dependent neural differentiation, suggest that developmental fate decisions exploit the inherent flexibility of cell-cycle gap phases to generate diversity by selecting subtly-differing patterns of connections among components of the cell-cycle machinery and differentiation pathways.

Minimal model of transcriptional elongation processes with pauses.

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.

Transcriptional versus non-transcriptional clocks: a case study in Ostreococcus.

Circadian rhythms are ubiquitous on earth from cyanobacteria to land plants and animals. Circadian clocks are synchronized to the day/night cycle by environmental factors such as light and temperature. In eukaryotes, clocks rely on complex gene regulatory networks involving transcriptional regulation but also post-transcriptional and post-translational regulations. In multicellular organisms clocks are found at multiple levels from cells to organs and whole organisms, making the study of clock mechanisms more complex. In recent years the picoalga Ostreococcus has emerged as a new circadian model organism thanks to its reduced gene redundancy and its minimalist cellular organization. A simplified version of the "green" plant clock, involving the master clock genes TOC1 and CCA1, has been revealed when the functional genomics and mathematical model approaches were combined. Specific photoreceptors such as a blue light sensing LOV histidine kinase mediate light input to the Ostreococcus clock. Non-transcriptional redox rhythms have also been identified recently in Ostreococcus and human red blood cells. This review highlights the progress made recently in the understanding of circadian clock architecture and function in Ostreococcus in the context of the marine environment.

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.

Circadian clocks in changing weather and seasons: lessons from the picoalga Ostreococcus tauri.

Daylight is the primary cue used by circadian clocks to entrain to the day/night cycle so as to synchronize physiological processes with periodic environmental changes induced by Earth rotation. However, the temporal daylight pattern is not the same every day due to erratic weather fluctuations or regular seasonal changes. Then, how do circadian clocks operate properly in varying weather and seasons? In this paper, we discuss the strategy unveiled by recent studies of the circadian clock of Ostreococcus tauri, the smallest free-living eukaryotic organism. It combines mechanisms controlling light inputs and clock sensitivity, shaping both the dynamics of the core circadian oscillator and its forcing by light so as to ensure stable and precise synchronization in all weather and seasons.

Robust and flexible response of the Ostreococcus tauri circadian clock to light/dark cycles of varying photoperiod.

The green microscopic alga Ostreococcus tauri has recently emerged as a promising model for understanding how circadian clocks, which drive the daily biological rhythms of many organisms, synchronize to the day/night cycle in changing weather and seasons. Here, we analyze translational reporter time series data for the central clock genes CCA1 and TOC1 for a wide range of daylight durations (photoperiods). The variation of temporal expression profiles with day duration is complex, with the two protein peaks tracking different times of the day. Nevertheless, all profiles are accurately reproduced by a simple two-gene transcriptional loop model whose parameters depend on light only through the photoperiod value. We show that this non-intuitive behavior allows the circadian clock to combine flexibility and robustness with respect to daylight fluctuations.

Strategic cell-cycle regulatory features that provide mammalian cells with tunable G1 length and reversible G1 arrest.

Transitions between consecutive phases of the eukaryotic cell cycle are driven by the catalytic activity of selected sets of cyclin-dependent kinases (Cdks). Yet, their occurrence and precise timing is tightly scheduled by a variety of means including Cdk association with inhibitory/adaptor proteins (CKIs). Here we focus on the regulation of G1-phase duration by the end of which cells of multicelled organisms must decide whether to enter S phase or halt, and eventually then, differentiate, senesce or die to obey the homeostatic rules of their host. In mammalian cells, entry in and progression through G1 phase involve sequential phosphorylation and inactivation of the retinoblastoma Rb proteins, first, by cyclin D-Cdk4,6 with the help of CKIs of the Cip/Kip family and, next, by the cyclin E-Cdk2 complexes that are negatively regulated by Cip/Kip proteins. Using a dynamical modeling approach, we show that the very way how the Rb and Cip/Kip regulatory modules interact differentially with cyclin D-Cdk4,6 and cyclin E-Cdk2 provides to mammalian cells a powerful means to achieve an exquisitely-sensitive control of G1-phase duration and fully reversible G1 arrests. Consistently, corruption of either one of these two modules precludes G1 phase elongation and is able to convert G1 arrests from reversible to irreversible. This study unveils fundamental design principles of mammalian G1-phase regulation that are likely to confer to mammalian cells the ability to faithfully control the occurrence and timing of their division process in various conditions.

A dynamical model of oocyte maturation unveils precisely orchestrated meiotic decisions.

Maturation of vertebrate oocytes into haploid gametes relies on two consecutive meioses without intervening DNA replication. The temporal sequence of cellular transitions driving eggs from G2 arrest to meiosis I (MI) and then to meiosis II (MII) is controlled by the interplay between cyclin-dependent and mitogen-activated protein kinases. In this paper, we propose a dynamical model of the molecular network that orchestrates maturation of Xenopus laevis oocytes. Our model reproduces the core features of maturation progression, including the characteristic non-monotonous time course of cyclin-Cdks, and unveils the network design principles underlying a precise sequence of meiotic decisions, as captured by bifurcation and sensitivity analyses. Firstly, a coherent and sharp meiotic resumption is triggered by the concerted action of positive feedback loops post-translationally activating cyclin-Cdks. Secondly, meiotic transition is driven by the dynamic antagonism between positive and negative feedback loops controlling cyclin turnover. Our findings reveal a highly modular network in which the coordination of distinct regulatory schemes ensures both reliable and flexible cell-cycle decisions.