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.

Novel opto-fluidic drug delivery system for efficient cellular transfection.

Intracellular drug delivery is at the heart of many diagnosis procedures and a key step in gene therapy. Research has been conducted to bypass cell barriers for controlled intracellular drug release and made consistent progress. However, state-of-the-art techniques based on non-viral carriers or physical methods suffer several drawbacks, including limited delivery yield, low throughput or low viability, which are key parameters in therapeutics, diagnostics and drug delivery. Nevertheless, gold nanoparticle (AuNP) mediated photoporation has stood out as a promising approach to permeabilize cell membranes through laser induced Vapour NanoBubble (VNB) generation, allowing the influx of external cargo molecules into cells. However, its use as a transfection technology for the genetic manipulation of therapeutic cells is hindered by the presence of non-degradable gold nanoparticles. Here, we report a new optofluidic method bringing gold nanoparticles in close proximity to cells for photoporation, while avoiding direct contact with cells by taking advantage of hydrodynamic focusing in a multi-flow device. Cells were successfully photoporated with [Formula: see text] efficiency with no significant reduction in cell viability at a throughput ranging from [Formula: see text] to [Formula: see text]. This optofluidic approach provides prospects of translating photoporation from an R &D setting to clinical use for producing genetically engineered therapeutic cells.

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.

Cellular Environment and Phenotypic Heterogeneity: How Data-Driven Modeling Finds the Smoking Gun.

The cellular environment modifies cellular phenotypes, in particular, the stress response phenotype, which easily exhibits high phenotypic heterogeneity due to the common characteristics of its regulatory networks. The aim of this work is to quantify and interpret the impact of collagen type I, a major component of the cellular environment, on the phenotypic heterogeneity of the cellular response. Our approach combines in an original way the monitoring of the response of a single cell and the mathematical modeling of the network. After a detailed statistical description of the phenotypic heterogeneity of the cellular response, the mathematical modeling explains how the observed changes can be explained by an induced increase in the average expression of a central protein of the regulatory network. The predictions of the data-driven model are fully consistent with the biochemical measurements performed. The framework presented here is also a new general methodology to study phenotypic heterogeneity, although we focus here on the response to proteotoxic stress in HeLa cells.

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.

Protein level variability determines phenotypic heterogeneity in proteotoxic stress response.

Cell-to-cell variability in stress response is a bottleneck for the construction of accurate and predictive models which could guide clinical diagnosis and treatment of certain diseases, for example, cancer. Indeed, such phenotypic heterogeneity can lead to fractional killing and persistence of a subpopulation of cells which are resistant to a given treatment. The heat shock response network plays a major role in protecting the proteome against several types of injuries. Here, we combine high-throughput measurements and mathematical modeling to unveil the molecular origin of the phenotypic variability in the heat shock response network. Although the mean response coincides with known biochemical measurements, we found a surprisingly broad diversity in single-cell dynamics with a continuum of response amplitudes and temporal shapes for several stimulus strengths. We theoretically predict that the broad phenotypic heterogeneity is due to network ultrasensitivity together with variations in the expression level of chaperones controlled by the transcription factor heat shock factor 1. Furthermore, we experimentally confirm this prediction by mapping the response amplitude to chaperone and heat shock factor 1 expression levels.

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.

A minimal titration model of the mammalian dynamical heat shock response.

Environmental stress, such as oxidative or heat stress, induces the activation of the heat shock response (HSR) and leads to an increase in the heat shock proteins (HSPs) level. These HSPs act as molecular chaperones to maintain cellular proteostasis. Controlled by highly intricate regulatory mechanisms, having stress-induced activation and feedback regulations with multiple partners, the HSR is still incompletely understood. In this context, we propose a minimal molecular model for the gene regulatory network of the HSR that reproduces quantitatively different heat shock experiments both on heat shock factor 1 (HSF1) and HSPs activities. This model, which is based on chemical kinetics laws, is kept with a low dimensionality without altering the biological interpretation of the model dynamics. This simplistic model highlights the titration of HSF1 by chaperones as the guiding line of the network. Moreover, by a steady states analysis of the network, three different temperature stress regimes appear: normal, acute, and chronic, where normal stress corresponds to pseudo thermal adaption. The protein triage that governs the fate of damaged proteins or the different stress regimes are consequences of the titration mechanism. The simplicity of the present model is of interest in order to study detailed modelling of cross regulation between the HSR and other major genetic networks like the cell cycle or the circadian clock.

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.

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.

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.

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.

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.

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.