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.

Review: Towards the next-generation models of the rumen microbiome for enhancing predictive power and guiding sustainable production strategies

The rumen ecosystem harbours a galaxy of microbes working in syntrophy to carry out a metabolic cascade of hydrolytic and fermentative reactions. This fermentation process allows ruminants to harvest nutrients from a wide range of feedstuff otherwise inaccessible to the host. The interconnection between the ruminant and its rumen microbiota shapes key animal phenotypes such as feed efficiency and methane emissions and suggests the potential of reducing methane emissions and enhancing feed conversion into animal products by manipulating the rumen microbiota. Whilst significant technological progress in omics techniques has increased our knowledge of the rumen microbiota and its genome (microbiome), translating omics knowledge into effective microbial manipulation strategies remains a great challenge. This challenge can be addressed by modelling approaches integrating causality principles and thus going beyond current correlation-based approaches applied to analyse rumen microbial genomic data. However, existing rumen models are not yet adapted to capitalise on microbial genomic information. This gap between the rumen microbiota available omics data and the way microbial metabolism is represented in the existing rumen models needs to be filled to enhance rumen understanding and produce better predictive models with capabilities for guiding nutritional strategies. To fill this gap, the integration of computational biology tools and mathematical modelling frameworks is needed to translate the information of the metabolic potential of the rumen microbes (inferred from their genomes) into a mathematical object. In this paper, we aim to discuss the potential use of two modelling approaches for the integration of microbial genomic information into dynamic models. The first modelling approach explores the theory of state observers to integrate microbial time series data into rumen fermentation models. The second approach is based on the genome-scale network reconstructions of rumen microbes. For a given microorganism, the network reconstruction produces a stoichiometry matrix of the metabolism. This matrix is the core of the so-called genome-scale metabolic models which can be exploited by a plethora of methods comprised within the constraint-based reconstruction and analysis approaches. We will discuss how these methods can be used to produce the next-generation models of the rumen microbiome.

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.

Animal board invited review: Quantification of resilience in farm animals

Resilience, when defined as the capacity of an animal to respond to short-term environmental challenges and to return to the prechallenge status, is a dynamic and complex trait. Resilient animals can reinforce the capacity of the herd to cope with often fluctuating and unpredictable environmental conditions. The ability of modern technologies to simultaneously record multiple performance measures of individual animals over time is a huge step forward to evaluate the resilience of farm animals. However, resilience is not directly measurable and requires mathematical models with biologically meaningful parameters to obtain quantitative resilience indicators. Furthermore, interpretive models may also be needed to determine the periods of perturbation as perceived by the animal. These applications do not require explicit knowledge of the origin of the perturbations and are developed based on real-time information obtained in the data during and outside the perturbation period. The main objective of this paper was to review and illustrate with examples, different modelling approaches applied to this new generation of data (i.e., with high-frequency recording) to detect and quantify animal responses to perturbations. Case studies were developed to illustrate alternative approaches to real-time and post-treatment of data. In addition, perspectives on the use of hybrid models for better understanding and predicting animal resilience are presented. Quantification of resilience at the individual level makes possible the inclusion of this trait into future breeding programmes. This would allow improvement of the capacity of animals to adapt to a changing environment, and therefore potentially reduce the impact of disease and other environmental stressors on animal welfare. Moreover, such quantification allows the farmer to tailor the management strategy to help individual animals to cope with the perturbation, hence reducing the use of pharmaceuticals, and decreasing the level of pain of the animal.

Review: Reducing enteric methane emissions improves energy metabolism in livestock: is the tenet right?

The production of enteric methane in the gastrointestinal tract of livestock is considered as an energy loss in the equations for estimating energy metabolism in feeding systems. Therefore, the spared energy resulting from specific inhibition of methane emissions should be re-equilibrated with other factors of the equation. And, it is commonly assumed that net energy from feeds increases, thus benefitting production functions, particularly in ruminants due to the important production of methane in the rumen. Notwithstanding, we confirm in this work that inhibition of emissions in ruminants does not transpose into consistent improvements in production. Theoretical calculations of energy flows using experimental data show that the expected improvement in net energy for production is small and difficult to detect under the prevailing, moderate inhibition of methane production (≈25%) obtained using feed additives inhibiting methanogenesis. Importantly, the calculation of energy partitioning using canonical models might not be adequate when methanogenesis is inhibited. There is a lack of information on various parameters that play a role in energy partitioning and that may be affected under provoked abatement of methane. The formula used to calculate heat production based on respiratory exchanges should be validated when methanogenesis is inhibited. Also, a better understanding is needed of the effects of inhibition on fermentation products, fermentation heat, and microbial biomass. Inhibition induces the accumulation of H2, the main substrate used to produce methane, that has no energetic value for the host, and it is not extensively used by the majority of rumen microbes. Currently, the fate of this excess of H2 and its consequences on the microbiota and the host are not well known. All this additional information will provide a better account of energy transactions in ruminants when enteric methanogenesis is inhibited. Based on the available information, it is concluded that the claim that enteric methane inhibition will translate into more feed-efficient animals is not warranted.

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.

177 Peer Community in Animal Science: A Free Publication Model for Transparent and Open Science

The scientific publication system should evolve into practices that enhance free dissemination and full access to research findings. At the same time, it should ensure reproducibility and transparency and safeguard scientific integrity from the detrimental effects of the current “publish or perish” culture. The objective of this contribution is to introduce the Peer Community In (PCI) Animal Science initiative (https://animsci.peercommunityin.org/), which represents an alternative to the current publication system under the umbrella of the “Peer Community In” project (https://peercommunityin.org/ ). PCI Animal Science is an international community of researchers working in animal science and related areas and it promotes open science and research transparency. Although PCI Animal Science is not a scientific journal, it operates similarly with editors (here: recommenders) and reviewers. Currently, the PCI Animal Science community has 64 recommenders from 20 countries. PCI Animal Science is a non-profit initiative, run and managed by researchers. The PCI Animal Science community performs, at no cost, rigorous open reviews of preprints that have been deposited on repositories such as bioRxiv and Zenodo from a wide range of research areas related to animal science. Based on independent reviews, a recommender decides whether a paper is recommended or not. Recommended preprints are peer-reviewed and citable stand-alone articles of high scientific value that do not need publication in traditional journals. However, if the authors wish, they can also publish their recommended preprint in the Diamond Open Access Peer Community Journal (https://peercommunityjournal.org/section/animsci/) at no cost. Authors can also submit their recommended manuscript to PCI-friendly journals (i.e., journals that consider the PCI evaluation in their own review processes) or to other journals. This contribution shows the workflow of the evaluation of manuscripts by PCI Animal Science and the advantages of adopting this new publishing model.

75 The Power of Theoretical and Practical Identifiability Analysis for Modeling (Micro-) Biological Processes

When modeling biological systems, one major step of the modeling exercise is the confrontation between the theory (the model) and the reality (the data). Such a confrontation 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. The parameter identification step is often addressed like a downstream process. Using this approach, once the data are collected, the modeler has a minimal degree of freedom to improve the accuracy of her model. Instead, the modeler can identify opportunities for improving model accuracy if the parameter identification problem is addressed like an upstream process. For instance, one of these opportunities is to determine for a given experimental setup (before the actual data collection), whether the optimization problem is well-posed (that it is, if the problem has unique solution). Knowing this information beforehand is useful to set up an experimental protocol that guarantees the uniqueness of the parameter estimates. This question of uniqueness is related to the notion of structural (theoretical) identifiability. The modeler might also be interested in knowing whether the available data that will result from the experimental protocol will be informative enough to identify the model parameters accurately. The question of parameter accuracy based on the quality of available data is related to the notion of practical identifiability. This work aims to present the theoretical basis of structural and practical identifiability analysis. By capitalizing on the use of dedicated software tools, we will illustrate further the power of structural and practical identifiability analysis in the modeling exercise using relevant examples for the modeling of microbiological processes such as the rumen microbial fermentation.

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.

Towards the quantitative characterisation of piglets' robustness to weaning: a modelling approach

Weaning is a critical transition phase in swine production in which piglets must cope with different stressors that may affect their health. During this period, the prophylactic use of antibiotics is still frequent to limit piglet morbidity, which raises both economic and public health concerns such as the appearance of antimicrobial-resistant microbes. With the interest of developing tools for assisting health and management decisions around weaning, it is key to provide robustness indexes that inform on the animals' capacity to endure the challenges associated with weaning. This work aimed at developing a modelling approach for facilitating the quantification of piglet resilience to weaning. A total of 325 Large White pigs weaned at 28 days of age were monitored and further housed and fed conventionally during the post-weaning period without antibiotic administration. Body weight and diarrhoea scores were recorded before and after weaning, and blood was sampled at weaning and 1 week later for collecting haematological data. A dynamic model was constructed based on the Gompertz-Makeham law to describe live weight trajectories during the first 75 days after weaning, following the rationale that the animal response is partitioned in two time windows (a perturbation and a recovery window). Model calibration was performed for each animal. Our results show that the transition time between the two time windows, as well as the weight trajectories are characteristic for each individual. The model captured the weight dynamics of animals at different degrees of perturbation, with an average coefficient of determination of 0.99, and a concordance correlation coefficient of 0.99. The utility of the model is that it provides biologically meaningful parameters that inform on the amplitude and length of perturbation, and the rate of animal recovery. Our rationale is that the dynamics of weight inform on the capability of the animal to cope with the weaning disturbance. Indeed, there were significant correlations between model parameters and individual diarrhoea scores and haematological traits. Overall, the parameters of our model can be useful for constructing weaning robustness indexes by using exclusively the growth curves. We foresee that this modelling approach will provide a step forward in the quantitative characterisation of robustness.

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.

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.