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.

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.

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.

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.

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.

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.

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.

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.

Robust entrainment of circadian oscillators requires specific phase response curves.

The circadian clocks keeping time in many living organisms rely on self-sustained biochemical oscillations entrained by external cues, such as light, to the 24-h cycle induced by Earth's rotation. However, environmental cues are unreliable due to the variability of habitats, weather conditions, or cue-sensing mechanisms among individuals. A tempting hypothesis is that circadian clocks have evolved so as to be robust to fluctuations in the signal that entrains them. To support this hypothesis, we analyze the synchronization behavior of weakly and periodically forced oscillators in terms of their phase response curve (PRC), which measures phase changes induced by a perturbation applied at different times of the cycle. We establish a general relationship between the robustness of key entrainment properties, such as stability and oscillator phase, on the one hand, and the shape of the PRC as characterized by a specific curvature or the existence of a dead zone, on the other hand. The criteria obtained are applied to computational models of circadian clocks and account for the disparate robustness properties of various forcing schemes. Finally, the analysis of PRCs measured experimentally in several organisms strongly suggests a case of convergent evolution toward an optimal strategy for maintaining a clock that is accurate and robust to environmental fluctuations.

Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri.

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However, most gene circuits in a cell are under control of external signals and thus, quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present the first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in the Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intriguing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks.

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.

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.

The combination of positive and negative feedback loops confers exquisite flexibility to biochemical switches.

A wide range of cellular processes require molecular regulatory pathways to convert a graded signal into a discrete response. One prevalent switching mechanism relies on the coexistence of two stable states (bistability) caused by positive feedback regulations. Intriguingly, positive feedback is often supplemented with negative feedback, raising the question of whether and how these two types of feedback can cooperate to control discrete cellular responses. To address this issue, we formulate a canonical model of a protein-protein interaction network and analyze the dynamics of a prototypical two-component circuit. The appropriate combination of negative and positive feedback loops can bring a bistable circuit close to the oscillatory regime. Notably, sharply activated negative feedback can give rise to a bistable regime wherein two stable fixed points coexist and may collide pairwise with two saddle points. This specific type of bistability is found to allow for separate and flexible control of switch-on and switch-off events, for example (i) to combine fast and reversible transitions, (ii) to enable transient switching responses and (iii) to display tunable noise-induced transition rates. Finally, we discuss the relevance of such bistable switching behavior, and the circuit topologies considered, to specific biological processes such as adaptive metabolic responses, stochastic fate decisions and cell-cycle transitions. Taken together, our results suggest an efficient mechanism by which positive and negative feedback loops cooperate to drive the flexible and multifaceted switching behaviors arising in biological systems.

Minimal requirements for robust cell size control in eukaryotic cells.

Most cell types living in a stable environment tend to keep a constant characteristic size over successive generations. Size homeostasis requires that cells exert a tight control over the size at which they divide. Cell size control is not only robust against various noises, but also highly flexible since cell sizes can vary tremendously, notably as a function of nutrient levels. We formulated a minimal mathematical model of the eukaryotic cell cycle in which the cell size control operates through a cell growth-dependent bifurcation in the cell cycle dynamics. Such a bifurcation mechanism can readily explain the occurrence of a minimum critical size at division under limiting growth conditions. However, it also predicts that cells should become progressively larger and larger under prolific growth conditions. We argue that the cell size control can be reinforced at fast growth rates by adding a new cell cycle inhibitory activity whose strength would increase with the cell growth rate. We further show that various sources of noise may also generate a large variability in cell size at division and interdivision time that exhibit characteristic exponential tail distributions, without compromising the robustness of the cell size control.

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.

Electrical synapses and synchrony: the role of intrinsic currents.

Electrical synapses are ubiquitous in the mammalian CNS. Particularly in the neocortex, electrical synapses have been shown to connect low-threshold spiking (LTS) as well as fast spiking (FS) interneurons. Experiments have highlighted the roles of electrical synapses in the dynamics of neuronal networks. Here we investigate theoretically how intrinsic cell properties affect the synchronization of neurons interacting by electrical synapses. Numerical simulations of a network of conductance-based neurons randomly connected with electrical synapses show that potassium currents promote synchrony, whereas the persistent sodium current impedes it. Furthermore, synchrony varies with the firing rate in qualitatively different ways depending on the intrinsic currents. We also study analytically a network of quadratic integrate-and-fire neurons. We relate the stability of the asynchronous state of this network to the phase-response function (PRF), which characterizes the effect of small perturbations on the firing timing of the neurons. In particular, we show that the greater the skew of the PRF toward the first half of the period, the more stable the asynchronous state. Combining our simulations with our analytical results, we establish general rules to predict the dynamic state of large networks of neurons coupled with electrical synapses. Our work provides a natural explanation for surprising experimental observations that blocking electrical synapses may increase the synchrony of neuronal activity. It also suggests different synchronization properties for LTS and FS cells. Finally, we propose to further test our predictions in experiments using dynamic clamp techniques.

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.