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The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth's soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model-experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved.The ISME Journal advance online publication, 29 March 2016; doi:10.1038/ismej.2016.45.

Building models is essential for understanding the functions and dynamics of microbial communities. Metabolic models built on genome‐scale metabolic network reconstructions (GENREs) are especially relevant as a means to decipher the complex interactions occurring among species. Model reconstruction increasingly relies on metagenomics, which permits direct characterisation of naturally occurring communities that may contain organisms that cannot be isolated or cultured. In this review, we provide an overview of the field of metabolic modelling and its increasing reliance on and synergy with metagenomics and bioinformatics. We survey the means of assigning functions and reconstructing metabolic networks from (meta‐)genomes, and present the variety and mathematical fundamentals of metabolic models that foster the understanding of microbial dynamics. We emphasise the characterisation of interactions and the scaling of model construction to large communities, two important bottlenecks in the applicability of these models. We give an overview of the current state of the art in metagenome sequencing and bioinformatics analysis, focusing on the reconstruction of genomes in microbial communities. Metagenomics benefits tremendously from third‐generation sequencing, and we discuss the opportunities of long‐read sequencing, strain‐level characterisation and eukaryotic metagenomics. We aim at providing algorithmic and mathematical support, together with tool and application resources, that permit bridging the gap between metagenomics and metabolic modelling. With this review we articulate two important topics in the context of deciphering the role and functions of microbial communities: metabolic modeling and metagenomics. We survey the methodological approaches, highlight the changes raised by third generation sequencing, and provide resources to bridge the gaps between the sequencing reads and the models.

Background Plant and soil microbiomes can interfere with pathogen life cycles, but their influence on disease epidemiology remains understudied. Here, we analyzed the relationships between plant and soil microbiomes and long-term epidemiological records of grapevine downy mildew, a major disease caused by the oomycete Plasmopara viticola . Results We found that certain microbial taxa were consistently more abundant in plots with lower disease incidence and severity and that the microbial community composition could predict disease incidence and severity. Microbial diversity was not strongly linked to epidemiological records, suggesting that disease incidence and severity is more related to the abundance of specific microbial taxa. These key taxa were identified in the topsoil, where the pathogen’s oospores overwinter, and in the phyllosphere, where zoospores infect leaves. By contrast, the leaf endosphere, where the pathogen’s mycelium develops, contained few taxa of interest. Surprisingly, the soil microbiota was a better predictor of disease incidence and severity than the leaf microbiota, suggesting that the soil microbiome could be a key indicator of the dynamics of this primarily aerial disease. Conclusion Our study integrates long-term epidemiological data with microbiome profiles of healthy plants to reveal fungi and bacteria relevant for the biocontrol of grapevine downy mildew. The resulting database provides a valuable resource for designing microbial consortia with potential biocontrol activity. The framework can be applied to other crop systems to guide the development of biocontrol strategies and reduce pesticide use in agriculture.

Biofilms are spatially organized communities of microorganisms embedded in a self-produced organic matrix, conferring to the population emerging properties such as an increased tolerance to the action of antimicrobials. It was shown that some bacilli were able to swim in the exogenous matrix of pathogenic biofilms and to counterbalance these properties. Swimming bacteria can deliver antimicrobial agents in situ, or potentiate the activity of antimicrobial by creating a transient vascularization network in the matrix. Hence, characterizing swimmer trajectories in the biofilm matrix is of particular interest to understand and optimize this new biocontrol strategy in particular, but also more generally to decipher ecological drivers of population spatial structure in natural biofilms ecosystems. In this study, a new methodology is developed to analyze time-lapse confocal laser scanning images to describe and compare the swimming trajectories of bacilli swimmers populations and their adaptations to the biofilm structure. The method is based on the inference of a kinetic model of swimmer populations including mechanistic interactions with the host biofilm. After validation on synthetic data, the methodology is implemented on images of three different species of motile bacillus species swimming in a Staphylococcus aureus biofilm. The fitted model allows to stratify the swimmer populations by their swimming behavior and provides insights into the mechanisms deployed by the micro-swimmers to adapt their swimming traits to the biofilm matrix. Anyone who has ever cleaned a bathroom probably faced biofilms, the dark, slimy deposits that lurk around taps and pipes. These structures are created by bacteria which abandon their solitary lifestyle to work together as a community, secreting various substances that allow the cells to organise themselves in 3D and to better resist external aggression. Unwanted biofilms can impair industrial operations or endanger health, for example when they form inside medical equipment or water supplies. Removing these structures usually involves massive application of substances which can cause long-term damage to the environment. Recently, researchers have observed that a range of small rod-shaped bacteria – or ‘bacilli’ – can penetrate a harmful biofilm and dig transient tunnels in its 3D structure. These ‘swimmers’ can enhance the penetration of anti-microbial agents, or could even be modified to deliver these molecules right inside the biofilm. However, little is known about how the various types of bacilli, which have very different shapes and propelling systems, can navigate the complex environment that is a biofilm. This knowledge would be essential for scientists to select which swimmers could be the best to harness for industrial and medical applications. To investigate this question, Ravel et al. established a way to track how three species of bacilli swim inside a biofilm compared to in a simple fluid. A mathematical model was created which integrated several swimming behaviors such as speed adaptation and direction changes in response to the structure and density of the biofilm. This modelling was then fitted on microscopy images of the different species navigating the two types of environments. Different motion patterns for the three bacilli emerged, each showing different degrees of adapting to moving inside a biofilm. One species, in particular, was able to run straight in and out of this environment because it could adapt its speed to the biofilm density as well as randomly change direction. The new method developed by Ravel et al. can be redeployed to systematically study swimmer candidates in different types of biofilms. This would allow scientists to examine how various swimming characteristics impact how bacteria-killing chemicals can penetrate the altered biofilms. In addition, as the mathematical model can predict trajectories, it could be used in computational studies to examine which species of bacilli would be best suited in industrial settings.

Background With the emergence of metagenomic data, multiple links between the gut microbiome and the host health have been shown. Deciphering these complex interactions require evolved analysis methods focusing on the microbial ecosystem functions. Despite the fact that host or diet-derived fibres are the most abundant nutrients available in the gut, the presence of distinct functional traits regarding fibre and mucin hydrolysis, fermentation and hydrogenotrophic processes has never been investigated. Results After manually selecting 91 KEGG orthologies and 33 glycoside hydrolases further aggregated in 101 functional descriptors representative of fibre and mucin degradation pathways in the gut microbiome, we used non-negative matrix factorization to mine metagenomic datasets. Four distinct metabolic profiles were further identified on a training set of 1153 samples and thoroughly validated on a large database of 2571 unseen samples from 5 external metagenomic cohorts. Profiles 1 and 2 are the main contributors to the fibre-degradation-related metagenome: they present contrasted involvement in fibre degradation and sugar metabolism and are differentially linked to dysbiosis, metabolic disease and inflammation. Profile 1 takes over Profile 2 inhealthy samples, and unbalance of these profiles characterize dysbiotic samples. Furthermore, high fibre diet favours a healthy balance between Profiles 1 and Profile 2. Profile 3 takes over Profile 2 during Crohn’s disease, inducing functional reorientations towards unusual metabolism such as fucose and H2S degradation or propionate, acetone and butanediol production. Profile 4 gathers under-represented functions, like methanogenesis. Two taxonomic makes up of the profiles were investigated, using either the covariation of 203 prevalent genomes or metagenomic species, both providing consistent results in line with their functional characteristics. This taxonomic characterization showed that Profiles 1 and 2 were respectively mainly composed of bacteria from the phyla Bacteroidetes and Firmicutes while Profile 3 is representative of Proteobacteria and Profile 4 of methanogens.Conclusions Integrating anaerobic microbiology knowledge with statistical learning can narrow down the metagenomic analysis to investigate functional profiles. Applying this approach to fibre degradation in the gut ended with 4 distinct functional profiles that can be easily monitored as markers of diet, dysbiosis, inflammation and disease.

Microbial proteolysis is understudied despite the availability of dietary proteins for the gut microbiota. Here, the proteolytic potential of the gut symbiont Bacteroides caccae was analyzed for the first time using pan-genomics. This sketches a well-equipped bacteria for protein breakdown, capable of producing 156 different proteases with a broad spectrum of cleavage targets. This functional potential was confirmed by the enhancement of growth and metabolic activities at high protein levels. Proteolysis was included in a B. caccae metabolic model which was fitted with the experiments and validated on external data. This model pinpoints the links between protein availability and short-chain fatty acids production, and the importance for B. caccae to gain access to glutamate and asparagine to promote growth. This integrated approach can be generalized to other symbionts and upscaled to complex microbiota to get insights into the ecological impact of proteins on the gut microbiota.

Mathematical and numerical models are increasingly used in microbial ecology to model the fate of microbial communities in their ecosystem. These models allow to connect in a mechanistic framework species-level informations, such as the microbial genomes, with macro-scale features, such as species spatial distributions or metabolite gradients. Numerous models are built upon species-level metabolic models that predict the metabolic behaviour of a microbe by solving an optimization problem knowing its genome and its nutritional environment. However, screening the community dynamics with these metabolic models implies to solve such an optimization problem by species at each time step, leading to a significant computational load further increased by several orders of magnitude when spatial dimensions are added. In this paper, we propose a statistical framework based on Reproducing Kernel Hilbert Space (RKHS) metamodels that are used to provide fast approximations of the original metabolic model. The metamodel can replace the optimization step in the system dynamics, providing comparable outputs at a much lower computational cost. We will first build a system dynamics model of a simplified gut microbiota composed of a unique commensal bacterial strain in interaction with the host and challenged by a Salmonella infection. Then, the machine learning method will be introduced, and particularly the ANOVA-RKHS that will be exploited to achieve variable selection and model parsimony. A training dataset will be constructed with the original system dynamics model and hyper-parameters will be carefully chosen to provide fast and accurate approximations of the original model. Finally, the accuracy of the trained metamodels will be assessed, in particular by comparing the system dynamics outputs when the original model is replaced by its metamodel. The metamodel allows an overall relative error of 4.71% but reducing the computational load by a speed-up factor higher than 45, while correctly reproducing the complex behaviour occurring during Salmonella infection. These results provide a proof-of-concept of the potentiality of machine learning methods to give fast approximations of metabolic model outputs and pave the way towards PDE-based spatio-temporal models of microbial communities including microbial metabolism and host-microbiota-pathogen interactions. Les modèles numériques et mathématiques sont de plus en plus utilisés en écologie microbienne pour modéliser le devenir de communautés microbiennes dans leur écosystème. Ces modèles permettent de coupler, dans des modèles mécanistiques, des informations à l’échelle de l’espèce microbienne, telles que le génome, avec des mécanismes à plus larges échelles, telles que des distributions spatiales ou des gradients de métabolites. De nombreux modèles sont construits à partir de modèles métaboliques qui prédisent le comportement métabolique d’un microbe en résolvant un problème d’optimisation basé sur son génome et son environnement nutritionnel. Cependant, l’analyse de la dynamique des communautés à l’aide de ces modèles métaboliques implique la résolution de ce problème d’optimisation par espèce à chaque pas de temps, ce qui entraîne une charge de calcul importante qui augmente encore de plusieurs ordres de grandeur lorsque des dimensions spatiales sont ajoutées. Dans cet article, nous proposons un cadre statistique basé sur des métamodèles RKHS (Reproducing Kernel Hilbert Space) qui sont utilisés pour fournir des approximations rapides du modèle métabolique original. Le métamodèle peut remplacer l’étape d’optimisation dans la dynamique du système, fournissant des résultats comparables à un coût de calcul beaucoup plus faible. Nous commencerons par construire un modèle de dynamique des systèmes d’un microbiote intestinal simplifié composé d’une souche bactérienne commensale unique en interaction avec l’hôte et confronté à une infection par Salmonella . Ensuite, la méthode d’apprentissage automatique sera présentée, basée sur la méthode ANOVA-RKHS qui permer de sélectionner des variables et d’assurer ainsi la parcimonie du modèle. Un ensemble de données d’entraînement sera construit avec le système dynamique original et les hyperparamètres seront soigneusement choisis pour fournir des approximations rapides et précises. Enfin, la précision de ces métamodèles sera évaluée, notamment en comparant les résultats du système dynamique lorsque le modèle original est remplacé par son métamodèle. Le métamodèle permet une erreur relative globale de 4.71% tout en réduisant la charge de calcul par un facteur d’accélération supérieur à 45, tout en reproduisant correctement le comportement complexe qui se produit pendant l’infection par Salmonella . Ces résultats fournissent une preuve de concept de la potentialité des méthodes d’apprentissage automatique pour donner des approximations rapides des sorties de modèles métaboliques et ouvrent la voie à des modèles spatio-temporels de communautés microbiennes basés sur les EDP, intégrant le métabolisme microbien et les interactions hôte-microbiote-pathogène.

We introduce a mixture model intended to describe the dynamics of the mucus layer that wraps the gut mucosa. This model takes into account the fluid mechanics of the gut content, the inhomogeneous rheology that depends on the fluid composition, and the main physiological mechanisms that ensure the homoeostasis of the mucus layer. Numerical simulations, based on a finite volume approach, prove the ability of the model to produce a stable steady-state mucus layer. We also perform a sensitivity analysis by using a meta-model based on polynomial chaos in order to identify the main parameters impacting the shape of the mucus layer. The effect of the interaction of the mucus with a population of bacteria is eventually discussed. Nous présentons un modèle de mélange qui décrit l’évolution de la couche de mucus qui recouvre la muqueuse du gros intestin. Ce modèle prend en compte la mécanique des fluides qui composent le contenu intestinal, la rhéologie inhomogène dépendant de la composition du fluide et les principaux mécanismes physiologiques qui assurent l’homéostasie de la couche de mucus. Des résultats numériques, obtenus par une méthode volumes finis, démontrent la capacité du modèle à reproduire une couche de mucus stationnaire stable. Nous pratiquons ensuite une analyse de sensibilité en construisant un métamodèle basé sur des polynômes de chaos afin d’identifier les paramètres impactant le plus la forme de la couche de mucus. Finalement, nous discutons les effets des interactions entre la couche de mucus et une population bactérienne chimiotactique.

We investigate a dimensional reduction problem of a reaction-diffusion system related to cardiac electrophysiology modeling in the atria. The atrial tissues are very thin. The physical problem is then routinely stated on a two-dimensional manifold. However, some electrophysiological heterogeneities are located through the thickness of the tissue. Despite their biomedical significance, the usual dimensional reduction techniques tend to average and erase their influence on the two-dimensional propagation. We introduce a two-dimensional model with two coupled superimposed layers that allows us to take into account three-dimensional phenomena, but retains a reasonable computational cost. We present its mathematical derivation, show its convergence toward the three-dimensional model, and check numerically its convergence speed.

Numerical simulations of the cardiac electrophysiology in the atria are often based on the standard bidomain or monodomain equations stated on a two-dimensional manifold. These simulations take advantage of the thinness of the atrial tissue, and their computational cost is reduced, as compared to three-dimensional simulations. However, these models do not take into account the heterogeneities located in the thickness of the tissue, like discontinuities of the fiber direction, although they can be a substrate for atrial arrhythmia (Hocini et al., Circulation 105(20):2442-2448, 2002; Ho et al., Cardiovasc Res 54(2):325-336, 2002; Nattel, Nature 415(6868):219-226, 2002). We investigate a two-dimensional model with two coupled, superimposed layers that allows to introduce three-dimensional heterogeneities, but retains a reasonable computational cost. We introduce the mathematical derivation of this model and error estimates with respect to the three-dimensional model. We give some numerical illustrations of its interest: we numerically show its convergence for vanishing thickness, introduce an optimization process of the coupling coefficient and assess its validity on physiologically relevant geometries. Our model would be an efficient tool to test the influence of three-dimensional fiber direction heterogeneities in reentries or atrial arrhythmia without using three-dimensional models.