Review: to be or not to be an identifiable model. Is this a relevant question in animal science modelling?

International audienceWhat is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODE) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and highly informative experiments. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design

Prediction of the lifetime productive and reproductive performance of Holstein cows managed for different lactation durations, using a model of lifetime nutrient partitioning

The GARUNS model is a lifetime performance model taking into account the changing physiological priorities of an animal during its life and through repeated reproduction cycles. This dynamic and stochastic model has been previously used to predict the productive and reproductive performance of various genotypes of cows across feeding systems. In the present paper, we used this model to predict the lifetime productive and reproductive performance of Holstein cows for different lactation durations, with the aim of determining the lifetime scenario that optimizes cows’ performance defined by lifetime efficiency (ratio of total milk energy yield to total energy intake) and pregnancy rate. To evaluate the model, data from a 16-mo extended lactation experiment on Holstein cows were used. Generally, the model could consistently fit body weight, milk yield, and milk components of these cows, whereas the reproductive performance was overestimated. Cows managed for repeated 12-, 14-, or 16-mo lactation all their life were simulated and had the highest lifetime efficiency compared with shorter (repeated 10-mo lactations: scenario N-N) or longer lactations (repeated 18-, 20-, or 22-mo lactations). The pregnancy rates increased slightly from a 10-mo to a 16-mo lactation but not significantly. Cows managed for a 16-mo lactation during their first lactation, followed by 10-mo lactations for the rest of their lives (EL-N scenario), had a similar lifetime efficiency as cows managed for 16-mo lactation all of their lives (EL-EL scenario). Cows managed for a 10-mo lactation during their first lactation, followed by 16-mo lactations for the rest of their lives (N-EL scenario), had a similar lifetime efficiency as that of the N-N scenario. The pregnancy rates of these 4 scenarios (N-N, EL-EL, N-EL, and EL-N) were similar to one another. To conclude, the GARUNS model was able to fit and simulate the extended lactation of Holstein cows. The simulated outputs indicate that managing the primiparous cows with a 16-mo extended lactation, followed by 10-mo lactations, allows their lifetime efficiency to increase and become similar to cows managed for 16-mo lactation during their entire lives. Further work should include health incidence (i.e., diseases) in the prediction model to have more accurate and realistic predictions of lifetime efficiency

Transcriptome Profiling Of Feeding-To-Fasting Transition In Chicken Liver Using A Chicken 20K Oligo Microarray

International audienceStarvation triggers a complex array of adaptative metabolic responses including energy-metabolic responses, a process which must imply tissue specific alterations in gene expression profiles. In the chicken, liver is a major organ controlling energy metabolism. The present study aimed to describe the evolution of global gene expression profiles in chicken liver during a 48h fasting period. Liver RNA samples were collected from 4 weeks old broilers, fed ad libitum or fasted for 16h or 48h. Following reverse-transcription and Cy dye labelling, the samples were hybridized on chicken 20K oligochips (ARK-genomics) against a reference sample. The data were then normalized by “Lowess-fitness” and analyzed by analysis of variance using LIMMA package. The number of genes altered by fasting increased from 190 at 16h to 611 at 48h (p<0.0001 following Benjamini-Hochberg correction) showing a more important hepatic transcriptional activity modification when the fasting was extended. After 16h of fasting, several genes involved in mitochondrial or peroxisomal fatty acid beta-oxidation (eight of the nine genes), in ketogenesis (three genes) and gluconeogenesis (three genes) were up-regulated, whereas genes involved in fatty acid synthesis (five genes) were down-regulated. This is consistent with the known regulation of glucose and lipid metabolisms in response to nutritional deprivation, as documented in different species. Further analysis was focused on 600 genes, which were significantly differentially expressed between at least two nutritional groups and for which a human ortholog could be identified, thus allowing to collect functional informations. This allowed identifying Gene Ontology categories and metabolic pathways altered by fasting

Evaluating the ability of a lifetime nutrient-partitioning model for simulating the performance of Australian Holstein dairy cows

The present study determined the ability of a lifetime nutrient-partitioning model to simulate individual genetic potentials of Australian Holstein cows. The model was initially developed in France and has been shown to be able to accurately simulate performance of individual cows from various breeds. Generally, it assumes that the curves of cow performance differ only in terms of scaling, but the dynamic shape is universal. In other words, simulations of genetic variability in performance between cow genotypes can be performed using scaling parameters to simply scale the performance curves up or down. Validation of the model used performance data from 63 lactations of Australian Holstein cows offered lucerne cubes plus grain-based supplement. Individual cow records were used to derive genetic scaling parameters for each animal by calibrating the model to minimise root mean-square errors between observed and fitted values, cow by cow. The model was able to accurately fit the curves of bodyweight, milk fat concentration, milk protein concentration and milk lactose concentration with a high degree of accuracy (relative prediction error

Genetically regulated metabolic networks: Gale-Nikaido modules and differential inequalities

International audienceWe propose an approach to study static properties of metabolic networks with genetic regulation. We base our results on differential inequalities which are constraints on the values of the partial derivatives of the reaction rate functions. The approach uses an iterative elimination method for the steady state equations involving algebraic modules that satisfy the Gale-Nikaido global univalence property. The same method allows to find conditions for unique steady state. In the case of metabolic pathways, partial elimination of variables can produce several alternative models, allowing to compare steady state changes of metabolites with and without genetic regulation