Integrating microbial abundance time series with fermentation dynamics of the rumen microbiome via mathematical modelling.

The rumen represents a dynamic microbial ecosystem where fermentation metabolites and microbial concentrations change over time in response to dietary changes. The integration of microbial genomic knowledge and dynamic modelling can enhance our system-level understanding of rumen ecosystem's function. However, such an integration between dynamic models and rumen microbiota data is lacking. The objective of this work was to integrate rumen microbiota time series determined by 16S rRNA gene amplicon sequencing into a dynamic modelling framework to link microbial data to the dynamics of the volatile fatty acids (VFA) production during fermentation. For that, we used the theory of state observers to develop a model that estimates the dynamics of VFA from the data of microbial functional proxies associated with the specific production of each VFA. We determined the microbial proxies using CowPi to infer the functional potential of the rumen microbiota and extrapolate their functional modules from KEGG (Kyoto Encyclopedia of Genes and Genomes). The approach was challenged using data from an in vitro RUSITEC experiment and from an in vivo experiment with four cows. The model performance was evaluated by the coefficient of variation of the root mean square error (CRMSE). For the in vitro case study, the mean CVRMSE were 9.8% for acetate, 14% for butyrate and 14.5% for propionate. For the in vivo case study, the mean CVRMSE were 16.4% for acetate, 15.8% for butyrate and 19.8% for propionate. The mean CVRMSE for the VFA molar fractions were 3.1% for acetate, 3.8% for butyrate and 8.9% for propionate. Ours results show the promising application of state observers integrated with microbiota time series data for predicting rumen microbial metabolism.

ASAS-NANP symposium: Mathematical Modeling in Animal Nutrition: The power of identifiability analysis for dynamic modeling in animal science:a practitioner approach.

Constructing dynamic mathematical models of biological systems requires estimating unknown parameters from available experimental data, usually using a statistical fitting procedure. This procedure is usually called parameter identification, parameter estimation, model fitting, or model calibration. In animal science, parameter identification is often performed without analytic considerations on the possibility of determining unique values of the model parameters. These analytical studies are related to the mathematical property of structural identifiability, which refers to the theoretical ability to recover unique values of the model parameters from the measures defined in an experimental setup and use the model structure as the sole basis. The structural identifiability analysis is a powerful tool for model construction because it informs whether the parameter identification problem is well-posed (i.e., the problem has a unique solution). Structural identifiability analysis is helpful to determine which actions (e.g., model reparameterization, choice of new data measurements, and change of the model structure) are needed to render the model parameters identifiable (when possible). The mathematical technicalities associated with structural identifiability analysis are very sophisticated. However, the development of dedicated, freely available software tools enables the application of identifiability analysis without needing to be an expert in mathematics and computer programming. We refer to such a non-expert user as a practitioner for hands-on purposes. However, a practitioner should be familiar with the model construction and software implementation process. In this paper, we propose to adopt a practitioner approach that takes advantage of available software tools to integrate identifiability analysis in the modeling practice in the animal science field. The application of structural identifiability implies switching our regard of the parameter identification problem as a downstream process (after data collection) to an upstream process (before data collection) where experiment design is applied to guarantee identifiability. This upstream approach will substantially improve the workflow of model construction toward robust and valuable models in animal science. Illustrative examples with different levels of complexity support our work. The source codes of the examples were provided for learning purposes and to promote open science practices.

When modeling biological systems, one major step of the modeling exercise is connecting the theory (the model) with the reality (the data). Such a connection passes through the resolution of the parameter identification (model calibration) problem, which aims at finding a set of parameters that best fits the variables predicted by the model to the data. Traditionally, the parameter identification step is often addressed like a downstream process (after data collection). Using this traditional approach, the modeler has minimal room for maneuvering to improve the model's accuracy. This paper discusses the benefits of adopting an upstream approach (before data collection) during the model construction phase. This approach capitalizes on the identifiability analysis, a powerful tool seldom applied in dynamic models of the animal science domain, likely because of the lack of awareness or the specialized mathematical technicalities involved in the identifiability analysis. In this paper, we illustrate that the modeling community in animal science can easily integrate identifiability analysis in their model developments following a practitioner approach taking advantage of a variety of freely available software tools dedicated to identifiability testing.

Disentangling the dynamics of energy allocation to develop a proxy for robustness of fattening pigs.

BACKGROUND: There is a growing need to improve robustness of fattening pigs, but this trait is difficult to phenotype. Our first objective was to develop a proxy for robustness of fattening pigs by modelling the longitudinal energy allocation coefficient to growth, with the resulting environmental variance of this allocation coefficient considered as a proxy for robustness. The second objective was to estimate its genetic parameters and correlations with traits under selection and with phenotypes that are routinely collected. In total, 5848 pigs from a Pietrain NN paternal line were tested at the AXIOM boar testing station (Azay-sur-Indre, France) from 2015 to 2022. This farm is equipped with an automatic feeding system that records individual weight and feed intake at each visit. We used a dynamic linear regression model to characterize the evolution of the allocation coefficient between the available cumulative net energy, which was estimated from feed intake, and cumulative weight gain during the fattening period. Longitudinal energy allocation coefficients were analysed using a two-step approach to estimate both the genetic variance of the coefficients and the genetic variance in their residual variance, which will be referred to as the log-transformed squared residual (LSR). RESULTS: The LSR trait, which could be interpreted as an indicator of the response of the animal to perturbations/stress, showed a low heritability (0.05 ± 0.01), a high favourable genetic correlation with average daily growth (- 0.71 ± 0.06), and unfavourable genetic correlations with feed conversion ratio (- 0.76 ± 0.06) and residual feed intake (- 0.83 ± 0.06). Segmentation of the population in four classes using estimated breeding values for LSR showed that animals with the lowest estimated breeding values were those with the worst values for phenotypic proxies of robustness, which were assessed using records routinely collected on farm. CONCLUSIONS: Results of this study show that selection for robustness, based on estimated breeding values for environmental variance of the allocation coefficients to growth, can be considered in breeding programs for fattening pigs.

Dynamic genome-based metabolic modeling of the predominant cellulolytic rumen bacterium Fibrobacter succinogenes S85.

Fibrobacter succinogenes is a cellulolytic bacterium that plays an essential role in the degradation of plant fibers in the rumen ecosystem. It converts cellulose polymers into intracellular glycogen and the fermentation metabolites succinate, acetate, and formate. We developed dynamic models of F. succinogenes S85 metabolism on glucose, cellobiose, and cellulose on the basis of a network reconstruction done with the automatic reconstruction of metabolic model workspace. The reconstruction was based on genome annotation, five template-based orthology methods, gap filling, and manual curation. The metabolic network of F. succinogenes S85 comprises 1,565 reactions with 77% linked to 1,317 genes, 1,586 unique metabolites, and 931 pathways. The network was reduced using the NetRed algorithm and analyzed for the computation of elementary flux modes. A yield analysis was further performed to select a minimal set of macroscopic reactions for each substrate. The accuracy of the models was acceptable in simulating F. succinogenes carbohydrate metabolism with an average coefficient of variation of the root mean squared error of 19%. The resulting models are useful resources for investigating the metabolic capabilities of F. succinogenes S85, including the dynamics of metabolite production. Such an approach is a key step toward the integration of omics microbial information into predictive models of rumen metabolism. IMPORTANCE F. succinogenes S85 is a cellulose-degrading and succinate-producing bacterium. Such functions are central for the rumen ecosystem and are of special interest for several industrial applications. This work illustrates how information of the genome of F. succinogenes can be translated to develop predictive dynamic models of rumen fermentation processes. We expect this approach can be applied to other rumen microbes for producing a model of rumen microbiome that can be used for studying microbial manipulation strategies aimed at enhancing feed utilization and mitigating enteric emissions.

Seven steps to enhance Open Science practices in animal science.

The Open Science movement aims at ensuring accessibility, reproducibility, and transparency of research. The adoption of Open Science practices in animal science, however, is still at an early stage. To move ahead as a field, we here provide seven practical steps to embrace Open Science in animal science. We hope that this paper contributes to the shift in research practices of animal scientists towards open, reproducible, and transparent science, enabling the field to gain additional public trust and deal with future challenges to guarantee reliable research. Although the paper targets primarily animal science researchers, the steps discussed here are also applicable to other research domains.

Hydrogenotrophic methanogens of the mammalian gut: Functionally similar, thermodynamically different-A modelling approach.

Methanogenic archaea occupy a functionally important niche in the gut microbial ecosystem of mammals. Our purpose was to quantitatively characterize the dynamics of methanogenesis by integrating microbiology, thermodynamics and mathematical modelling. For that, in vitro growth experiments were performed with pure cultures of key methanogens from the human and ruminant gut, namely Methanobrevibacter smithii, Methanobrevibacter ruminantium and Methanobacterium formicium. Microcalorimetric experiments were performed to quantify the methanogenesis heat flux. We constructed an energetic-based mathematical model of methanogenesis. Our model captured efficiently the dynamics of methanogenesis with average concordance correlation coefficients of 0.95 for CO2, 0.98 for H2 and 0.97 for CH4. Together, experimental data and model enabled us to quantify metabolism kinetics and energetic patterns that were specific and distinct for each species despite their use of analogous methane-producing pathways. Then, we tested in silico the interactions between these methanogens under an in vivo simulation scenario using a theoretical modelling exercise. In silico simulations suggest that the classical competitive exclusion principle is inapplicable to gut ecosystems and that kinetic information alone cannot explain gut ecological aspects such as microbial coexistence. We suggest that ecological models of gut ecosystems require the integration of microbial kinetics with nonlinear behaviours related to spatial and temporal variations taking place in mammalian guts. Our work provides novel information on the thermodynamics and dynamics of methanogens. This understanding will be useful to construct new gut models with enhanced prediction capabilities and could have practical applications for promoting gut health in mammals and mitigating ruminant methane emissions.

Addressing Global Ruminant Agricultural Challenges Through Understanding the Rumen Microbiome: Past, Present, and Future.

The rumen is a complex ecosystem composed of anaerobic bacteria, protozoa, fungi, methanogenic archaea and phages. These microbes interact closely to breakdown plant material that cannot be digested by humans, whilst providing metabolic energy to the host and, in the case of archaea, producing methane. Consequently, ruminants produce meat and milk, which are rich in high-quality protein, vitamins and minerals, and therefore contribute to food security. As the world population is predicted to reach approximately 9.7 billion by 2050, an increase in ruminant production to satisfy global protein demand is necessary, despite limited land availability, and whilst ensuring environmental impact is minimized. Although challenging, these goals can be met, but depend on our understanding of the rumen microbiome. Attempts to manipulate the rumen microbiome to benefit global agricultural challenges have been ongoing for decades with limited success, mostly due to the lack of a detailed understanding of this microbiome and our limited ability to culture most of these microbes outside the rumen. The potential to manipulate the rumen microbiome and meet global livestock challenges through animal breeding and introduction of dietary interventions during early life have recently emerged as promising new technologies. Our inability to phenotype ruminants in a high-throughput manner has also hampered progress, although the recent increase in "omic" data may allow further development of mathematical models and rumen microbial gene biomarkers as proxies. Advances in computational tools, high-throughput sequencing technologies and cultivation-independent "omics" approaches continue to revolutionize our understanding of the rumen microbiome. This will ultimately provide the knowledge framework needed to solve current and future ruminant livestock challenges.

Modeling and optimization of lipid accumulation by Yarrowia lipolytica from glucose under nitrogen depletion conditions.

Oleaginous yeasts have been seen as a feasible alternative to produce the precursors of biodiesel due to their capacity to accumulate lipids as triacylglycerol having profiles with high content of unsaturated fatty acids. The yeast Yarrowia lipolytica is a promising microorganism that can produce lipids under nitrogen depletion conditions and excess of the carbon source. However, under these conditions, this yeast also produces citric acid (overflow metabolism) decreasing lipid productivity. This work presents two mathematical models for lipid production by Y. lipolytica from glucose. The first model is based on Monod and inhibition kinetics, and the second one is based on the Droop quota model approach, which is extended to yeast. The two models showed good agreements with the experimental data used for calibration and validation. The quota based model presented a better description of the dynamics of nitrogen and glucose dynamics leading to a good management of N/C ratio which makes this model interesting for control purposes. Then, quota model was used to evaluate, by means of simulation, a scenario for optimizing lipid productivity and lipid content. For that, a control strategy was designed by approximating the flow rates of glucose and nitrogen with piecewise linear functions. Simulation results achieved productivity of 0.95 g L-1 hr-1 and lipid content fraction of 0.23 g g-1 , which indicates that this strategy is a promising alternative for the optimization of lipid production.

A state of the art of metabolic networks of unicellular microalgae and cyanobacteria for biofuel production.

The most promising and yet challenging application of microalgae and cyanobacteria is the production of renewable energy: biodiesel from microalgae triacylglycerols and bioethanol from cyanobacteria carbohydrates. A thorough understanding of microalgal and cyanobacterial metabolism is necessary to master and optimize biofuel production yields. To this end, systems biology and metabolic modeling have proven to be very efficient tools if supported by an accurate knowledge of the metabolic network. However, unlike heterotrophic microorganisms that utilize the same substrate for energy and as carbon source, microalgae and cyanobacteria require light for energy and inorganic carbon (CO2 or bicarbonate) as carbon source. This double specificity, together with the complex mechanisms of light capture, makes the representation of metabolic network nonstandard. Here, we review the existing metabolic networks of photoautotrophic microalgae and cyanobacteria. We highlight how these networks have been useful for gaining insight on photoautotrophic metabolism.

Mathematical modeling of unicellular microalgae and cyanobacteria metabolism for biofuel production.

The conversion of microalgae lipids and cyanobacteria carbohydrates into biofuels appears to be a promising source of renewable energy. This requires a thorough understanding of their carbon metabolism, supported by mathematical models, in order to optimize biofuel production. However, unlike heterotrophic microorganisms that utilize the same substrate as sources of energy and carbon, photoautotrophic microorganisms require light for energy and CO2 as carbon source. Furthermore, they are submitted to permanent fluctuating light environments due to outdoor cultivation or mixing inducing a flashing effect. Although, modeling these nonstandard organisms is a major challenge for which classical tools are often inadequate, this step remains a prerequisite towards efficient optimization of outdoor biofuel production at an industrial scale.

DRUM: a new framework for metabolic modeling under non-balanced growth. Application to the carbon metabolism of unicellular microalgae.

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.

Optimizing microalgal production in raceway systems.

The industrial exploitation of microalgae is characterized by the production of high-value compounds. Optimization of the performance of microalgae culture systems is essential to render the process economically viable. For raceway systems, the optimization based on optimal control theory is rather challenging, because the process is by essence periodically forced and, as a consequence, optimization must be carried out in a periodic framework. In this article, we propose a simple operational criterion for raceway systems that when integrated in a strategy of closed-loop control allows attaining biomass productivities very near to the theoretical maximal productivities. The strategy developed was tested numerically using a mathematical model of microalgae growth in raceways. The model takes into account the temporal variation of the environmental variables temperature and light intensity and their influence on microalgae growth.

Kinetic modelling of lactate utilization and butyrate production by key human colonic bacterial species.

Butyrate is the preferred energy source for colonocytes and has an important role in gut health; in contrast, accumulation of high concentrations of lactate is detrimental to gut health. The major butyrate-producing bacterial species in the human colon belong to the Firmicutes. Eubacterium hallii and a new species, Anaerostipes coli SS2/1, members of clostridial cluster XIVa, are able to utilize lactate and acetate via the butyryl CoA : acetate CoA transferase route, the main metabolic pathway for butyrate synthesis in the human colon. Here we provide a mathematical model to analyse the production of butyrate by lactate-utilizing bacteria from the human colon. The model is an aggregated representation of the fermentation pathway. The parameters of the model were estimated using total least squares and maximum likelihood, based on in vitro experimental data with E. hallii L2-7 and A. coli SS2/1. The findings of the mathematical model adequately match those from the bacterial batch culture experiments. Such an in silico approach should provide insight into carbohydrate fermentation and short-chain fatty acid cross-feeding by dominant species of the human colonic microbiota.

Mathematical modelling of carbohydrate degradation by human colonic microbiota.

The human colon is an anaerobic ecosystem that remains largely unexplored as a result of its limited accessibility and its complexity. Mathematical models can play a central role for a better insight into its dynamics. In this context, this paper presents the development of a mathematical model of carbohydrate degradation. Our aim was to provide an in silico approach to contribute to a better understanding of the fermentation patterns in such an ecosystem. Our mathematical model is knowledge-based, derived by writing down mass-balance equations. It incorporates physiology of the intestine, metabolic reactions and transport phenomena. The model was used to study various nutritional scenarios and to assess the role of the mucus on the system behavior. Model simulations provided an adequate qualitative representation of the human colon. Our model is complementary to experimental studies on human colonic fermentation, which, of course, is not meant to replace. It may be helpful to gain insight on questions that are still difficult to elucidate by experimentation and suggest future experiments.

Towards the human intestinal microbiota phylogenetic core.

The paradox of a host specificity of the human faecal microbiota otherwise acknowledged as characterized by global functionalities conserved between humans led us to explore the existence of a phylogenetic core. We investigated the presence of a set of bacterial molecular species that would be altogether dominant and prevalent within the faecal microbiota of healthy humans. A total of 10 456 non-chimeric bacterial 16S rRNA sequences were obtained after cloning of PCR-amplified rDNA from 17 human faecal DNA samples. Using alignment or tetranucleotide frequency-based methods, 3180 operational taxonomic units (OTUs) were detected. The 16S rRNA sequences mainly belonged to the phyla Firmicutes (79.4%), Bacteroidetes (16.9%), Actinobacteria (2.5%), Proteobacteria (1%) and Verrumicrobia (0.1%). Interestingly, while most of OTUs appeared individual-specific, 2.1% were present in more than 50% of the samples and accounted for 35.8% of the total sequences. These 66 dominant and prevalent OTUs included members of the genera Faecalibacterium, Ruminococcus, Eubacterium, Dorea, Bacteroides, Alistipes and Bifidobacterium. Furthermore, 24 OTUs had cultured type strains representatives which should be subjected to genome sequence with a high degree of priority. Strikingly, 52 of these 66 OTUs were detected in at least three out of four recently published human faecal microbiota data sets, obtained with very different experimental procedures. A statistical model confirmed these OTUs prevalence. Despite the species richness and a high individual specificity, a limited number of OTUs is shared among individuals and might represent the phylogenetic core of the human intestinal microbiota. Its role in human health deserves further study.