Biochemical Bases Needed for the Mathematical Representation of Whole Animal Metabolism

A review of key microbial and nutritional elements for mechanistic modeling of rumen fermentation in cattle under methane-inhibition

The environmental impacts of livestock agriculture include the production of greenhouse gasses (GHG) such as methane (CH4) through enteric fermentation. Recent advances in our understanding of methanogenesis have led to the development of animal feed additives (AFA) that can reduce enteric CH4 emissions. However, many interacting factors impact hydrogen (H2) and CH4 production and AFA efficacy, including animal factors, basal diet, particle and fluid outflow, microbial populations, rumen fluid pH, and fermentative cofactor dynamics. Characterizing the response of rumen fermentation to AFA is essential for optimizing AFA implementation. Mechanistic models of enteric fermentation are constructed to represent physiological and microbial processes in the rumen and can be updated to characterize the dependency of AFA efficacy on basal diet and the impacts of AFA on fermentation. The objective of this article is to review the current state of rumen mechanistic modeling, contrasting the representation of key pools in extant models with a particular emphasis on representation of CH4 production. Additionally, we discuss the first rumen mechanistic models to include AFA and emphasize future model needs for improved representation of rumen dynamics under CH4-inhibition due to AFA supplementation, including the representation of microbial populations, rumen pH, fractional outflow rates, and thermodynamic control of fermentative pathways.

Predicting fat cover in beef cattle to make on-farm management decisions: a review of assessing fat and of modeling fat deposition

Demands of domestic and foreign market specifications of carcass weight and fat cover, of beef cattle, have led to the development of cattle growth models that predict fat cover to assist on-farm managers make management decisions. The objectives of this paper are 4-fold: 1) conduct a brief review of the biological basis of adipose tissue accretion, 2) briefly review live and carcass assessments of beef cattle, and carcass grading systems used to develop quantitative compositional and quality indices, 3) review fat deposition models: Davis growth model (DGM), French National Institute for Agricultural Research growth model (IGM), Cornell Value Discovery System (CVDS), and BeefSpecs drafting tool (BeefSpecsDT), and 4) appraise the process of translating science and practical skills into research/decision support tools that assist the Beef industry improve profitability. The r2 for live and carcass animal assessments, using several techniques across a range of species and traits, ranged from 0.61 to 0.99 and from 0.52 to 0.99, respectively. Model evaluations of DGM and IGM were conducted using Salers heifers (n = 24) and Angus-Hereford steers (n = 15) from an existing publication and model evaluations of CVDS and BeefSpecsDT were conducted using Angus steers (n = 33) from a research trial where steers were grain finished for 101 d in a commercial feedlot. Evaluating the observed and predicted fat mass (FM) is the focus of this review. The FM mean bias for Salers heifers were 7.5 and 1.3 kg and the root mean square error of prediction (RMSEP) were 31.2 and 27.8 kg and for Angus-Hereford steers the mean bias were -4.0 and -10.5 kg and the RMSEP were 9.14 and 21.5 kg for DGM and IGM, respectively. The FM mean bias for Angus steers were -5.61 and -2.93 kg and the RMSEP were 12.3 and 13.4 kg for CVDS and BeefSpecsDT, respectively. The decomposition for bias, slope, and deviance were 21%, 12%, and 68% and 5%, 4%, and 91% for CVDS and BeefSpecsDT, respectively. The modeling efficiencies were 0.38 and 0.27 and the models were within a 20 kg level of tolerance 91% and 88% for CVDS and BeefSpecsDT, respectively. Fat deposition models reported in this review have the potential to assist the beef industry make on-farm management decisions on live cattle before slaughter and improve profitability. Modelers need to continually assess and improve their models but with a caveat of 1) striving to minimize inputs, and 2) choosing on-farm inputs that are readily available.

Review: Harnessing extant energy and protein requirement modeling for sustainable beef production

Numerous mathematical nutrition models have been developed in the last sixty years to predict the dietary supply and requirement of farm animals' energy and protein. Although these models, usually developed by different groups, share similar concepts and data, their calculation routines (i.e., submodels) have rarely been combined into generalized models. This lack of mixing submodels is partly because different models have different attributes, including paradigms, structural decisions, inputs/outputs, and parameterization processes that could render them incompatible for merging. Another reason is that predictability might increase due to offsetting errors that cannot be thoroughly studied. Alternatively, combining concepts might be more accessible and safer than combining models' calculation routines because concepts can be incorporated into existing models without changing the modeling structure and calculation logic, though additional inputs might be needed. Instead of developing new models, improving the merging of extant models' concepts might curtail the time and effort needed to develop models capable of evaluating aspects of sustainability. Two areas of beef production research that are needed to ensure adequate diet formulation include accurate energy requirements of grazing animals (decrease methane emissions) and efficiency of energy use (reduce carcass waste and resource use) by growing cattle. A revised model for energy expenditure of grazing animals was proposed to incorporate the energy needed for physical activity, as the British feeding system recommended, and eating and rumination (HjEer) into the total energy requirement. Unfortunately, the proposed equation can only be solved iteratively through optimization because HjEer requires metabolizable energy (ME) intake. The other revised model expanded an existing model to estimate the partial efficiency of using ME for growth (kg) from protein proportion in the retained energy by including an animal degree of maturity and average daily gain (ADG) as used in the Australian feeding system. The revised kg model uses carcass composition, and it is less dependent on dietary ME content, but still requires an accurate assessment of the degree of maturity and ADG, which in turn depends on the kg. Therefore, it needs to be solved iteratively or using one-step delayed continuous calculation (i.e., use the previous day's ADG to compute the current day's kg). We believe that generalized models developed by merging different models' concepts might improve our understanding of the relationships of existing variables that were known for their importance but not included in extant models because of the lack of proper information or confidence at that time.

Novel methodologies in marine fish larval nutrition

Major gaps in knowledge on fish larval nutritional requirements still remain. Small larval size, and difficulties in acceptance of inert microdiets, makes progress slow and cumbersome. This lack of knowledge in fish larval nutritional requirements is one of the causes of high mortalities and quality problems commonly observed in marine larviculture. In recent years, several novel methodologies have contributed to significant progress in fish larval nutrition. Others are emerging and are likely to bring further insight into larval nutritional physiology and requirements. This paper reviews a range of new tools and some examples of their present use, as well as potential future applications in the study of fish larvae nutrition. Tube-feeding and incorporation into Artemia of (14)C-amino acids and lipids allowed studying Artemia intake, digestion and absorption and utilisation of these nutrients. Diet selection by fish larvae has been studied with diets containing different natural stable isotope signatures or diets where different rare metal oxides were added. Mechanistic modelling has been used as a tool to integrate existing knowledge and reveal gaps, and also to better understand results obtained in tracer studies. Population genomics may assist in assessing genotype effects on nutritional requirements, by using progeny testing in fish reared in the same tanks, and also in identifying QTLs for larval stages. Functional genomics and proteomics enable the study of gene and protein expression under various dietary conditions, and thereby identify the metabolic pathways which are affected by a given nutrient. Promising results were obtained using the metabolic programming concept in early life to facilitate utilisation of certain nutrients at later stages. All together, these methodologies have made decisive contributions, and are expected to do even more in the near future, to build a knowledge basis for development of optimised diets and feeding regimes for different species of larval fish.

Modelling of nutrient partitioning in growing pigs to predict their anatomical body composition. 1. Model description

A dynamic mechanistic model was developed for growing and fattening pigs. The aim of the model was to predict growth rate and the chemical and anatomical body compositions from the digestible nutrient intake of gilts (20–105 kg live weight). The model represents the partitioning of digestible nutrients from intake through intermediary metabolism to body protein and body fat. State variables of the model were lysine, acetyl-CoA equivalents, glucose, volatile fatty acids and fatty acids as metabolite pools, and protein in muscle, hide–backfat, bone and viscera and body fat as body constituent pools. It was assumed that fluxes of metabolites follow saturation kinetics depending on metabolite concentrations. In the model, protein deposition rate depended on the availability of lysine and of acetyl-CoA. The anatomical body composition in terms of muscle, organs, hide–backfat and bone was predicted from the chemical body composition and accretion using allometric relationships. Partitioning of protein, fat, water and ash in muscle, organs, hide–backfat and bone fractions were driven by the rates of muscle protein and body fat deposition. Model parameters were adjusted to obtain a good fit of the experimental data from literature. Differential equations were solved numerically for a given set of initial conditions and parameter values. In the present paper, the model is presented, including its parameterisation. The evaluation of the model is described in a companion paper.

Comparison of mechanistic rumen models on mathematical formulation of extramicrobial and microbial processes

This study investigated the consequences of differences in applied concepts and individual mathematical formulations on steady-state behavior of three important mechanistic rumen models. In the models of Baldwin et al. (2) and Danfaer (6), the formulation of passage rate, nondietary inputs, defined rumen substrate pools, absorption rates, degradation rates, molecular weights, parameterization of VFA production, and physical compartmentalization were sequentially exchanged for the formulation of the model of Dijkstra et al. (9). Most of these adaptations had a considerable influence on model behavior, indicating large qualitative differences in formulation and sensitivity to concept choice. Because microbial substrate environments were similar after all adaptations, the microbial mechanisms could be compared objectively without being concealed by differences in extramicrobial formulation. None of the microbial functions were altered except for substrate degradation, which gave rise to a similar rate of substrate entrance to soluble rumen pools that are available for microbial utilization. Large differences remained in microbial functions of substrate fermentation, substrate incorporation, and microbial synthesis. Differences in extramicrobial rumen functions and microbial mechanisms had important consequences for simulated nutrient outputs from the rumen, illustrating the necessity for further validation of individual formulations.

Description of a model integrating protein and energy metabolism in preruminant calves

This paper describes the development of a mechanistic model integrating protein and energy metabolism in preruminant calves of 80-240 kg live weight. The objectives of the model are to gain insight into the partitioning of nutrients in the body of growing calves and to provide a tool for the development of feeding strategies for calves in this weight range. The model simulates the partitioning of nutrients from ingestion through intermediary metabolism to growth, consisting of accretions of protein, fat, ash and water. The model contains 10 state variables, comprising fatty acids, glucose, acetyl-CoA and amino acids as metabolite pools, and fat, ash and protein in muscle, hide, bone and viscera as body constituent pools. Turnover of protein and fat is represented. The model also includes a routine to check possible dietary amino acid imbalance and can be used to predict amino acid requirements on a theoretical basis. The model is based on two experiments, specifically designed for this purpose. Simulations of protein and fat accretion rates over a wide range of nutrient input suggest that the model is sound. In can be used as a research tool and for the development of feeding strategies for preruminant calves.

Simulation of the effects of diet on the contribution of rumen protozoa to degradation of fibre in the rumen

A previously described mathematical model, that stimulates the metabolic activities of rumen bacteria and protozoa, was used to examine the contribution of protozoa to neutral-detergent fibre (NDF) degradation in the rumen of cattle. Comparisons between predicted and experimentally observed NDF degradation showed general agreement. Further simulations were performed with diets containing variable proportions of concentrate (between 0 and 1 kg/kg diet DM) and at intake levels ranging between 5.3 and 21.0 kg DM/d. The simulated protozoal contribution to NDF degradation was 17-21% at the lowest intake level. Except for the all-concentrate diets, raising the feed intake level reduced this contribution to 5-13% at the highest intake level. The changes in contribution of protozoa to NDF degradation were related to variations in the fibrolytic bacteria: protozoa value and the NDF-degrading activities of protozoa predicted by the model. In simulations where dietary NDF levels were reduced and starch and sugar levels were increased independently, protozoal contribution to NDF degradation generally increased. These differences were reflected also in the generally increased protozoal contribution to NDF degradation predicted in response to a decreased roughage:concentrate value. The contribution of protozoa also generally declined in response to added N. These changes in predicted protozoal contribution to NDF degradation resulting from dietary variations provided possible explanations for the differences in rumen NDF degradation observed when animals are defaunated.

Simulation of the dynamics of protozoa in the rumen

A modified mathematical model is described that simulates the dynamics of rumen micro-organisms, with specific emphasis on the rumen protozoa. The model is driven by continuous inputs of nutrients and consists of nineteen state variables, which represent the N, carbohydrate, fatty acid and microbial pools in the rumen. Several protozoal characteristics were represented in the model, including preference for utilization of starch and sugars compared with fibre, and of insoluble compared with soluble protein; engulfment and storage of starch; no utilization of NH3 to synthesize amino acids; engulfment and digestion of bacteria and protozoa; selective retention within the rumen; death and lysis related to nutrient availability. Comparisons between model predictions and experimental observations showed reasonable agreement for protozoal biomass in the rumen, but protozoal turnover time was not predicted well. Sensitivity analyses highlighted the need for more reliable estimates of bacterial engulfment rate, protozoal maintenance requirement, and death rate. Simulated protozoal biomass was increased rapidly in response to increases in dietary starch content, but further increases in starch content of a high-concentrate diet caused protozoal mass to decline. Increasing the sugar content of a concentrate diet, decreased protozoa, while moderate elevations of the sugar content on a roughage diet increased protozoal biomass. Simulated protozoal biomass did not change in response to variations in dietary neutral-detergent fibre (NDF) content. Reductions in dietary N resulted in an increased protozoal biomass. Depending on the basal intake level and dietary composition, protozoal concentration in the rumen was either increased or decreased by changes in feed intake level. Such changes in relative amounts of protozoal and bacterial biomass markedly affected the supply of nutrients available for absorption. The integration of protozoal, bacterial and dietary characteristics through mathematical representation provided an improved understanding of mechanisms of protozoal responses to changes in dietary inputs.