Starvation responses impact interaction dynamics of human gut bacteria Bacteroides thetaiotaomicron and Roseburia intestinalis.

Bacterial growth often alters the environment, which in turn can impact interspecies interactions among bacteria. Here, we used an in vitro batch system containing mucin beads to emulate the dynamic host environment and to study its impact on the interactions between two abundant and prevalent human gut bacteria, the primary fermenter Bacteroides thetaiotaomicron and the butyrate producer Roseburia intestinalis. By combining machine learning and flow cytometry, we found that the number of viable B. thetaiotaomicron cells decreases with glucose consumption due to acid production, while R. intestinalis survives post-glucose depletion by entering a slow growth mode. Both species attach to mucin beads, but only viable cell counts of B. thetaiotaomicron increase significantly. The number of viable co-culture cells varies significantly over time compared to those of monocultures. A combination of targeted metabolomics and RNA-seq showed that the slow growth mode of R. intestinalis represents a diauxic shift towards acetate and lactate consumption, whereas B. thetaiotaomicron survives glucose depletion and low pH by foraging on mucin sugars. In addition, most of the mucin monosaccharides we tested inhibited the growth of R. intestinalis but not B. thetaiotaomicron. We encoded these causal relationships in a kinetic model, which reproduced the observed dynamics. In summary, we explored how R. intestinalis and B. thetaiotaomicron respond to nutrient scarcity and how this affects their dynamics. We highlight the importance of understanding bacterial metabolic strategies to effectively modulate microbial dynamics in changing conditions.

Deciphering Interactions Within a 4-Strain Riverine Bacterial Community.

The dynamics of a community of four planktonic bacterial strains isolated from river water was followed in R2 broth for 72 h in batch experiments. These strains were identified as Janthinobacterium sp., Brevundimonas sp., Flavobacterium sp. and Variovorax sp. 16S rRNA gene sequencing and flow cytometry analyses were combined to monitor the change in abundance of each individual strain in bi-cultures and quadri-culture. Two interaction networks were constructed that summarize the impact of the strains on each other's growth rate in exponential phase and carrying capacity in stationary phase. The networks agree on the absence of positive interactions but also show differences, implying that ecological interactions can be specific to particular growth phases. Janthinobacterium sp. was the fastest growing strain and dominated the co-cultures. However, its growth rate was negatively affected by the presence of other strains 10 to 100 times less abundant than Janthinobacterium sp. In general, we saw a positive correlation between growth rate and carrying capacity in this system. In addition, growth rate in monoculture was predictive of carrying capacity in co-culture. Taken together, our results highlight the necessity to take growth phases into account when measuring interactions within a microbial community. In addition, evidence that a minor strain can greatly influence the dynamics of a dominant one underlines the necessity to choose population models that do not assume a linear dependency of interaction strength to abundance of other species for accurate parameterization from such empirical data.

Modeling the Circadian Control of the Cell Cycle and Its Consequences for Cancer Chronotherapy.

The mammalian cell cycle is governed by a network of cyclin/Cdk complexes which signal the progression into the successive phases of the cell division cycle. Once coupled to the circadian clock, this network produces oscillations with a 24 h period such that the progression into each phase of the cell cycle is synchronized to the day-night cycle. Here, we use a computational model for the circadian clock control of the cell cycle to investigate the entrainment in a population of cells characterized by some variability in the kinetic parameters. Our numerical simulations showed that successful entrainment and synchronization are only possible with a sufficient circadian amplitude and an autonomous period close to 24 h. Cellular heterogeneity, however, introduces some variability in the entrainment phase of the cells. Many cancer cells have a disrupted clock or compromised clock control. In these conditions, the cell cycle runs independently of the circadian clock, leading to a lack of synchronization of cancer cells. When the coupling is weak, entrainment is largely impacted, but cells maintain a tendency to divide at specific times of day. These differential entrainment features between healthy and cancer cells can be exploited to optimize the timing of anti-cancer drug administration in order to minimize their toxicity and to maximize their efficacy. We then used our model to simulate such chronotherapeutic treatments and to predict the optimal timing for anti-cancer drugs targeting specific phases of the cell cycle. Although qualitative, the model highlights the need to better characterize cellular heterogeneity and synchronization in cell populations as well as their consequences for circadian entrainment in order to design successful chronopharmacological protocols.

Metabolic models of human gut microbiota: Advances and challenges.

The human gut is a complex ecosystem consisting of hundreds of microbial species interacting with each other and with the human host. Mathematical models of the gut microbiome integrate our knowledge of this system and help to formulate hypotheses to explain observations. The generalized Lotka-Volterra model has been widely used for this purpose, but it does not describe interaction mechanisms and thus does not account for metabolic flexibility. Recently, models that explicitly describe gut microbial metabolite production and consumption have become popular. These models have been used to investigate the factors that shape gut microbial composition and to link specific gut microorganisms to changes in metabolite concentrations found in diseases. Here, we review how such models are built and what we have learned so far from their application to human gut microbiome data. In addition, we discuss current challenges of these models and how these can be addressed in the future.

Application of comparative genomics of Acetobacter species facilitates genome-scale metabolic reconstruction of the Acetobacter ghanensis LMG 23848T and Acetobacter senegalensis 108B cocoa strains.

Acetobacter species play an import role during cocoa fermentation. However, Acetobacter ghanensis and Acetobacter senegalensis are outcompeted during fermentation of the cocoa pulp-bean mass, whereas Acetobacter pasteurianus prevails. In this paper, an in silico approach aimed at delivering some insights into the possible metabolic adaptations of A. ghanensis LMG 23848T and A. senegalensis 108B, two candidate starter culture strains for cocoa fermentation processes, by reconstructing genome-scale metabolic models (GEMs). Therefore, genome sequence data of a selection of strains of Acetobacter species were used to perform a comparative genomic analysis. Combining the predicted orthologous groups of protein-encoding genes from the Acetobacter genomes with gene-reaction rules of GEMs from two reference bacteria, namely a previously manually curated model of A. pasteurianus 386B (iAp386B454) and two manually curated models of Escherichia coli (EcoCyc and iJO1366), allowed to predict the set of reactions present in A. ghanensis LMG 23848T and A. senegalensis 108B. The predicted metabolic network was manually curated using genome re-annotation data, followed by the reconstruction of species-specific GEMs. This approach additionally revealed possible differences concerning the carbon core metabolism and redox metabolism among Acetobacter species, pointing to a hitherto unexplored metabolic diversity. More specifically, the presence or absence of reactions related to citrate catabolism and the glyoxylate cycle for assimilation of C2 compounds provided not only new insights into cocoa fermentation but also interesting guidelines for future research. In general, the A. ghanensis LMG 23848T and A. senegalensis 108B GEMs, reconstructed in a semi-automated way, provided a proof-of-concept toward accelerated formation of GEMs of candidate functional starter cultures for food fermentation processes.

Initial source of heterogeneity in a model for cell fate decision in the early mammalian embryo.

During development, cells from a population of common progenitors evolve towards different fates characterized by distinct levels of specific transcription factors, a process known as cell differentiation. This evolution is governed by gene regulatory networks modulated by intercellular signalling. In order to evolve towards distinct fates, cells forming the population of common progenitors must display some heterogeneity. We applied a modelling approach to obtain insights into the possible sources of cell-to-cell variability initiating the specification of cells of the inner cell mass into epiblast or primitive endoderm cells in early mammalian embryo. At the single-cell level, these cell fates correspond to three possible steady states of the model. A combination of numerical simulations and bifurcation analyses predicts that the behaviour of the model is preserved with respect to the source of variability and that cell-cell coupling induces the emergence of multiple steady states associated with various cell fate configurations, and to a distribution of the levels of expression of key transcription factors. Statistical analysis of these time-dependent distributions reveals differences in the evolutions of the variance-to-mean ratios of key variables of the system, depending on the simulated source of variability, and, by comparison with experimental data, points to the rate of synthesis of the key transcription factor NANOG as a likely initial source of heterogeneity.

Quantifying the impact of ecological memory on the dynamics of interacting communities.

Ecological memory refers to the influence of past events on the response of an ecosystem to exogenous or endogenous changes. Memory has been widely recognized as a key contributor to the dynamics of ecosystems and other complex systems, yet quantitative community models often ignore memory and its implications. Recent modeling studies have shown how interactions between community members can lead to the emergence of resilience and multistability under environmental perturbations. We demonstrate how memory can be introduced in such models using the framework of fractional calculus. We study how the dynamics of a well-characterized interaction model is affected by gradual increases in ecological memory under varying initial conditions, perturbations, and stochasticity. Our results highlight the implications of memory on several key aspects of community dynamics. In general, memory introduces inertia into the dynamics. This favors species coexistence under perturbation, enhances system resistance to state shifts, mitigates hysteresis, and can affect system resilience both ways depending on the time scale considered. Memory also promotes long transient dynamics, such as long-standing oscillations and delayed regime shifts, and contributes to the emergence and persistence of alternative stable states. Our study highlights the fundamental role of memory in communities, and provides quantitative tools to introduce it in ecological models and analyse its impact under varying conditions.

Stochastic simulation of a model for circadian rhythms in plants.

Circadian clocks allow living organisms to anticipate and adapt to the daily variations of the environment. The interlocked feedback loops of the transcription factors network in the plant clock generate oscillations with expression peaks at specific times of the day. In this work, we explore the effect of molecular noise on the behavior of the plant circadian clock through numerical simulations. The influence of system size, photoperiod, and mutations of clock genes on the robustness of the oscillations are discussed. Our simulations show that the oscillations remain robust when the mRNA and protein levels are in the range of a few hundreds molecules. Entrainment by light-dark cycles enhances the robustness compared to constant conditions. Multiple light inputs and inter-cellular coupling also contribute to the robustness of the oscillations. The comparison between deterministic and stochastic simulations of single and double mutants shows that stochasticity does not qualitatively affect the behaviour of mutants but that they do not have the same robustness to noise. Finally, the model shows that noise can induce transitions between two limit cycles in a birhythmic clock mutant.

Circadian Misalignment and Metabolic Disorders: A Story of Twisted Clocks.

Biological clocks are cell-autonomous oscillators that can be entrained by periodic environmental cues. This allows organisms to anticipate predictable daily environmental changes and, thereby, to partition physiological processes into appropriate phases with respect to these changing external conditions. Nowadays our 24/7 society challenges this delicate equilibrium. Indeed, many studies suggest that perturbations such as chronic jet lag, ill-timed eating patterns, or shift work increase the susceptibility to cardiometabolic disorders, diabetes, and cancers. However the underlying mechanisms are still poorly understood. A deeper understanding of this complex, dynamic system requires a global holistic approach for which mathematical modeling can be highly beneficial. In this review, we summarize several experimental works pertaining to the effect of adverse conditions on clock gene expression and on physiology, and we show how computational models can bring interesting insights into the links between circadian misalignment and metabolic diseases.

Magnesium maintains the length of the circadian period in Arabidopsis.

The circadian clock coordinates the physiological responses of a biological system to day and night rhythms through complex loops of transcriptional/translational regulation. It can respond to external stimuli and adjust generated circadian oscillations accordingly to maintain an endogenous period close to 24 h. However, the interaction between nutritional status and circadian rhythms in plants is poorly understood. Magnesium (Mg) is essential for numerous biological processes in plants, and its homeostasis is crucial to maintain optimal development and growth. Magnesium deficiency in young Arabidopsis thaliana seedlings increased the period of circadian oscillations of the CIRCADIAN CLOCK-ASSOCIATED 1 (CCA1) promoter (pCCA1:LUC) activity and dampened their amplitude under constant light in a dose-dependent manner. Although the circadian period increase caused by Mg deficiency was light dependent, it did not depend on active photosynthesis. Mathematical modeling of the Mg input into the circadian clock reproduced the experimental increase of the circadian period and suggested that Mg is likely to affect global transcription/translation levels rather than a single component of the circadian oscillator. Upon addition of a low dose of cycloheximide to perturb translation, the circadian period increased further under Mg deficiency, which was rescued when sufficient Mg was supplied, supporting the model's prediction. These findings suggest that sufficient Mg supply is required to support proper timekeeping in plants.

The Goodwin Oscillator and its Legacy.

In the 1960's Brian Goodwin published a couple of mathematical models showing how feedback inhibition can lead to oscillations and discussed possible implications of this behaviour for the physiology of the cell. He also presented key ideas about the rich dynamics that may result from the coupling between such biochemical oscillators. Goodwin's work motivated a series of theoretical investigations aiming at identifying minimal mechanisms to generate limit cycle oscillations and deciphering design principles of biological oscillators. The three-variable Goodwin model (adapted by Griffith) can be seen as a core model for a large class of biological systems, ranging from ultradian to circadian clocks. We summarize here main ideas and results brought by Goodwin and review a couple of modeling works directly or indirectly inspired by Goodwin's findings.

A Computational Model for the Cold Response Pathway in Plants.

Understanding the mechanism by which plants respond to cold stress and strengthen their tolerance to low temperatures is an important and challenging task in plant sciences. Experiments have established that the first step in the perception and transduction of the cold stress signal consists of a transient influx of Ca2+. This Ca2+ influx triggers the activation of a cascade of phosphorylation-dephosphorylation reactions that eventually affects the expression of C-repeat-binding factors (CBFs, notably CBF3), which were shown in many plants to control resistance to cold stress by regulating the expression of cold-regulated (COR) genes. Based on experimental observations mostly made on Arabidopsis thaliana, we build a computational model for the cold response pathway in plants, from the transduction of the cold signal via the transient influx of Ca2+ to the activation of the phosphorylation cascade leading to CBF3 expression. We explore the dynamics of this regulatory network by means of numerical simulations and compare the results with experimental observations on the dynamics of the cold response, both for the wild type and for mutants. The simulations show how, in response to cold stress, a brief Ca2+ influx, which is over in minutes, is transduced along the successive steps of the network to trigger the expression of cold response genes such as CBF3 within hours. Sometimes, instead of a single Ca2+ spike the decrease in temperature brings about a train of high-frequency Ca2+ oscillations. The model is applied to both types of Ca2+ signaling. We determine the dynamics of the network in response to a series of identical cold stresses, to account for the observation of desensitization and resensitization. The analysis of the model predicts the possibility of an oscillatory expression of CBF3 originating from the negative feedback exerted by ZAT12, a factor itself controlled by CBF3. Finally, we extend the model to incorporate the circadian control of CBF3 expression, to account for the gating of the response to cold stress by the plant circadian clock.

Genome-scale metabolic modeling of Acetobacter pasteurianus 386B reveals its metabolic adaptation to cocoa fermentation conditions.

Acetobacter pasteurianus 386B has been selected as a candidate functional starter culture to better control the cocoa fermentation process. Previously, its genome has been sequenced and a genome-scale metabolic model (GEM) has been reconstructed. To understand its metabolic adaptation to cocoa fermentation conditions, different flux balance analysis (FBA) simulations were performed and compared with experimental data. In particular, metabolic flux distributions were simulated for two phases that characterize the growth of A. pasteurianus 386B under cocoa fermentation conditions, predicting a switch in respiratory chain usage in between these phases. The possible influence on the resulting energy production was shown using a reduced version of the GEM. FBA simulations revealed the importance of the compartmentalization of the ethanol oxidation reactions, namely in the periplasm or in the cytoplasm, and highlighted the potential role of ethanol as a source of carbon, energy, and NADPH. Regarding the latter, the physiological function of a proton-translocating NAD(P)+ transhydrogenase was further investigated in silico. This study revealed the potential of using a GEM to simulate the metabolism of A. pasteurianus 386B, and may provide a general framework toward a better physiological understanding of functional starter cultures in food fermentation processes.

Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect.

In microbial ecosystems, species not only compete for common resources but may also display mutualistic interactions as a result from metabolic cross-feeding. Such mutualism can lead to bistability. Depending on the initial population sizes, species will either survive or go extinct. Various phenomenological models have been suggested to describe bistability in mutualistic systems. However, these models do not account for interaction mediators such as nutrients. In contrast, nutrient-explicit models do not provide an intuitive understanding of what causes bistability. Here, we reduce a theoretical nutrient-explicit model of two mutualistic cross-feeders in a chemostat, uncovering an explicit relation to a growth model with an Allee effect. We show that the dilution rate in the chemostat leads to bistability by turning a weak Allee effect into a strong Allee effect. This happens as long as there is more production than consumption of cross-fed nutrients. Thanks to the explicit relationship of the reduced model with the underlying experimental parameters, these results allow to predict the biological conditions that sustain or prevent the survival of mutualistic species.

Modeling the Dynamics of Let-7-Coupled Gene Regulatory Networks Linking Cell Proliferation to Malignant Transformation.

Let-7 microRNA controls the expression of proteins that belong to two distinct gene regulatory networks, namely, a cyclin-dependent kinase (Cdk) network driving the cell cycle and a cell transformation network that can undergo an epigenetic switch between a non-transformed and a malignant transformed cell state. Using mathematical modeling and transcriptomic data analysis, we here investigate how Let-7 controls the Cdk-dependent cell cycle network, and how it couples the latter with the transformation network. We also assess the consequence of this coupling on cancer progression. Our analysis shows that the switch from a quiescent to a proliferative state depends on the relative levels of Let-7 and several cell cycle activators. Numerical simulations further indicate that the Let-7-coupled cell cycle and transformation networks mutually control each other, and our model identifies key players for this mutual control. Transcriptomic data analysis from The Cancer Genome Atlas (TCGA) suggests that the two networks are activated in cancer, in particular in gastrointestinal cancers, and that the activation levels vary significantly among patients affected by a same cancer type. Our mathematical model, when applied to a heterogeneous cell population, suggests that heterogeneity among tumors may in part result from stochastic switches between a non-transformed cell state with low proliferative capability and a transformed cell state with high proliferative property. The model further predicts that Let-7 may reduce tumor heterogeneity by decreasing the occurrence of stochastic switches toward a transformed, proliferative cell state. In conclusion, we identified the key components responsible for the qualitative dynamics of two networks interconnected by Let-7. The two networks are heterogeneously activated in several cancers, thereby stressing the need to consider patient's specific characteristics to optimize therapeutic strategies.

Computational models for the dynamics of early mouse embryogenesis.

Early embryonic development, from the zygote to the blastocyst, is a paradigm of a dynamic, self-organised process. It involves gene expression, mechanical interactions between cells, cell division and inter- and intracellular signalling. Imaging and transcriptomic data have significantly improved our understanding of early embryogenesis in mammals. However, they also reveal a great level of complexity. How the genetic, mechanical, and regulatory processes interact to ensure reproducible development is thus much investigated by computational modelling, which allows a dissection of the mechanisms controlling cell fate decisions. In this review, we discuss the main types of modelling approaches that have been used to investigate the dynamics of preimplantation mammalian development. We also discuss the insights provided by modelling into our understanding of the specification processes leading to the three types of cells in the embryo 4.5 days after fertilization: the trophectoderm, the epiblast and the primitive endoderm.

Genome-Scale Metabolic Reconstruction of Acetobacter pasteurianus 386B, a Candidate Functional Starter Culture for Cocoa Bean Fermentation.

Acetobacter pasteurianus 386B is a candidate functional starter culture for the cocoa bean fermentation process. To allow in silico simulations of its related metabolism in response to different environmental conditions, a genome-scale metabolic model for A. pasteurianus 386B was reconstructed. This is the first genome-scale metabolic model reconstruction for a member of the genus Acetobacter. The metabolic network reconstruction process was based on extensive genome re-annotation and comparative genomics analyses. The information content related to the functional annotation of metabolic enzymes and transporters was placed in a metabolic context by exploring and curating a Pathway/Genome Database of A. pasteurianus 386B using the Pathway Tools software. Metabolic reactions and curated gene-protein-reaction associations were bundled into a genome-scale metabolic model of A. pasteurianus 386B, named iAp386B454, containing 454 genes, 322 reactions, and 296 metabolites embedded in two cellular compartments. The reconstructed model was validated by performing growth experiments in a defined medium, which revealed that lactic acid as the sole carbon source could sustain growth of this strain. Further, the reconstruction of the A. pasteurianus 386B genome-scale metabolic model revealed knowledge gaps concerning the metabolism of this strain, especially related to the biosynthesis of its cell envelope and the presence or absence of metabolite transporters.

Revisiting a skeleton model for the mammalian cell cycle: From bistability to Cdk oscillations and cellular heterogeneity.

A network of cyclin-dependent kinases (Cdks) regulated by multiple negative and positive feedback loops controls progression in the mammalian cell cycle. We previously proposed a detailed computational model for this network, which consists of four coupled Cdk modules. Both this detailed model and a reduced, skeleton version show that the Cdk network is capable of temporal self-organization in the form of sustained Cdk oscillations, which correspond to the orderly progression along the different cell cycle phases G1, S (DNA replication), G2 and M (mitosis). We use the skeleton model to revisit the role of positive feedback (PF) loops on the dynamics of the mammalian cell cycle by showing that the multiplicity of PF loops extends the range of bistability in the isolated Cdk modules controlling the G1/S and G2/M transitions. Resorting to stochastic simulations we show that, through their effect on the range of bistability, multiple PF loops enhance the robustness of Cdk oscillations with respect to molecular noise. The model predicts that a rise in the total level of Cdk1 also enlarges the domain of bistability in the isolated Cdk modules as well as the range of oscillations in the full Cdk network. Surprisingly, stochastic simulations indicate that Cdk1 overexpression reduces the robustness of Cdk oscillations towards molecular noise; this result is due to the increased distance between the two branches of the bistable switch at higher levels of Cdk1. At intermediate levels of growth factor stochastic simulations show that cells may randomly switch between cell cycle arrest and cell proliferation, as a consequence of fluctuations. In the presence of Cdk1 overexpression, these transitions occur even at low levels of growth factor. Extending stochastic simulations from single cells to cell populations suggests that stochastic switches between cell cycle arrest and proliferation may provide a source of heterogeneity in a cell population, as observed in cancer cells characterized by Cdk1 overexpression.

Signalling-modulated gene regulatory networks in early mammalian development.

Early mammalian embryo is a paradigm of dynamic, self-organised process. It involves gene expression, cell division and intercellular signalling. How these processes interact to ensure reproducible development is being often investigated by modelling, which allows to dissect the mechanisms controlling cell fate decisions. In this work, we present two models based on ordinary differential equations describing the first and second specification processes in the mouse embryo. Together, they describe the cell fate decisions leading to the first three cell lineages which form the blastocyst 4.5 days after fertilisation: the trophectoderm, the epiblast and the primitive endoderm. Both specifications rely on multistability, and signalling allows the selection of the appropriate steady-state. In addition to the gene regulatory network, the first specification process is indeed controlled by the Hippo pathway, which is itself controlled by cell polarity and cell-to-cell contacts. This leads to a spatially organised arrangement of cells. The second specification process is controlled by Fgf signalling and leads to a salt and pepper distribution of the two cell types. We discuss the respective mechanisms and their physiological implications.