An isotope dilution model for partitioning of phenylalanine and tyrosine uptake by the liver of lactating dairy cows.

An isotope dilution model to describe the partitioning of phenylalanine and tyrosine in the bovine liver was developed. The model comprises four intracellular and six extracellular pools and various flows connecting these pools and external blood. Conservation of mass principles were applied to generate the fundamental equations describing the behaviour of the system in the steady state. The model was applied to datasets from multi-catheterised dairy cattle during a constant infusion of [1-13C]phenylalanine and [2,3,5,6-2H]tyrosine tracers. Model solutions described the extraction of phenylalanine and tyrosine from the liver via the portal vein and hepatic artery. In addition, the exchange of free phenylalanine and tyrosine between extracellular and intracellular pools was explained and the hydroxylation of phenylalanine to tyrosine was estimated. The model was effective in providing information about the fates of phenylalanine and tyrosine in the liver and could be used as part of a more complex system describing amino acid metabolism in the whole animal.

A mechanistic model of small intestinal starch digestion and glucose uptake in the cow.

The high contribution of postruminal starch digestion (up to 50%) to total-tract starch digestion on energy-dense, starch-rich diets demands that limitations to small intestinal starch digestion be identified. A mechanistic model of the small intestine was described and evaluated with regard to its ability to simulate observations from abomasal carbohydrate infusions in the dairy cow. The 7 state variables represent starch, oligosaccharide, glucose, and pancreatic amylase in the intestinal lumen, oligosaccharide and glucose in the unstirred water layer at the intestinal wall, and intracellular glucose of the enterocyte. Enzymatic hydrolysis of starch was modeled as a 2-stage process involving the activity of pancreatic amylase in the lumen and of oligosaccharidase at the brush border of the enterocyte confined within the unstirred water layer. The Na+-dependent glucose transport into the enterocyte was represented along with a facilitative glucose transporter 2 transport system on the basolateral membrane. The small intestine is subdivided into 3 main sections, representing the duodenum, jejunum, and ileum for parameterization. Further subsections are defined between which continual digesta flow is represented. The model predicted nonstructural carbohydrate disappearance in the small intestine for cattle unadapted to duodenal infusion with a coefficient of determination of 0.92 and a root mean square prediction error of 25.4%. Simulation of glucose disappearance for mature Holstein heifers adapted to various levels of duodenal glucose infusion yielded a coefficient of determination of 0.81 and a root mean square prediction error of 38.6%. Analysis of model behavior identified limitations to the efficiency of small intestinal starch digestion with high levels of duodenal starch flow. Limitations to individual processes, particularly starch digestion in the proximal section of the intestine, can create asynchrony between starch hydrolysis and glucose uptake capacity.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of lactating dairy cows.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and phenylalanine hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant.

A dynamic mechanistic model of lactic acid metabolism in the rumen.

Current feed evaluation systems for ruminants are too imprecise to describe diets in terms of their acidosis risk. The dynamic mechanistic model described herein arises from the integration of a lactic acid (La) metabolism module into an extant model of whole-rumen function. The model was evaluated using published data from cows and sheep fed a range of diets or infused with various doses of La. The model performed well in simulating peak rumen La concentrations (coefficient of determination = 0.96; root mean square prediction error = 16.96% of observed mean), although frequency of sampling for the published data prevented a comprehensive comparison of prediction of time to peak La accumulation. The model showed a tendency for increased La accumulation following feeding of diets rich in nonstructural carbohydrates, although less-soluble starch sources such as corn tended to limit rumen La concentration. Simulated La absorption from the rumen remained low throughout the feeding cycle. The competition between bacteria and protozoa for rumen La suggests a variable contribution of protozoa to total La utilization. However, the model was unable to simulate the effects of defaunation on rumen La metabolism, indicating a need for a more detailed description of protozoal metabolism. The model could form the basis of a feed evaluation system with regard to rumen La metabolism.

A dynamic model of N metabolism in the lactating dairy cow and an assessment of impact of N excretion on the environment.

Improving N utilization in dairy cows and especially reducing N output in excreta is desirable due to global concerns of agricultural contribution of N to environmental pollution, particularly as ammonia. Data from five N balance experiments were used to develop a dynamic model that was evaluated with independent data. Model predictions of feces, urine, and milk outputs were close to observed values. Statistical analysis showed that 96% of mean square prediction error for feces and urine N output predictions was due to random variation. However, the model tends to overpredict milk N output, especially at higher N intake levels. Evaluation of model predictions for independent experimental observations from Agricultural Development Advisory Service at Bridgets (U.K.) showed good agreement between predicted and observed urine N output (95% due to random variation). However, there was a slight underprediction for fecal N output (14% mean square prediction error due to bias) and overprediction of milk N output (22% of mean square prediction error due to bias). The model predictions of N outputs in excreta were sensitive to changes in energy concentration of the diet. Dietary protein degradability had only a small influence on predicted fecal N output. However, the model was sensitive in its predictions of urine N when protein degradability was varied. Application of the model to assess reduction in ammonia emissions from dairy cows showed that increasing the energy concentration could potentially reduce ammonia emissions by up to 25% per cow. Similarly, reducing CP concentration in the diet to about 16% could reduce ammonia production by 20% and lower degradability of CP to match microbial requirement by 19% per cow. The model is a first step toward a mechanistic approach of nutrient modeling, and it is a valuable method for predicting N excretions and estimating N emissions from dairy systems.

Alternative approaches to predicting methane emissions from dairy cows.

Previous attempts to apply statistical models, which correlate nutrient intake with methane production, have been of limited value where predictions are obtained for nutrient intakes and diet types outside those used in model construction. Dynamic mechanistic models have proved more suitable for extrapolation, but they remain computationally expensive and are not applied easily in practical situations. The first objective of this research focused on employing conventional techniques to generate statistical models of methane production appropriate to United Kingdom dairy systems. The second objective was to evaluate these models and a model published previously using both United Kingdom and North American data sets. Thirdly, nonlinear models were considered as alternatives to the conventional linear regressions. The United Kingdom calorimetry data used to construct the linear models also were used to develop the three nonlinear alternatives that were all of modified Mitscherlich (monomolecular) form. Of the linear models tested, an equation from the literature proved most reliable across the full range of evaluation data (root mean square prediction error = 21.3%). However, the Mitscherlich models demonstrated the greatest degree of adaptability across diet types and intake level. The most successful model for simulating the independent data was a modified Mitscherlich equation with the steepness parameter set to represent dietary starch-to-ADF ratio (root mean square prediction error = 20.6%). However, when such data were unavailable, simpler Mitscherlich forms relating dry matter or metabolizable energy intake to methane production remained better alternatives relative to their linear counterparts.

Technical note: A proposed method to determine the extent of degradation of a feed in the rumen from the degradation profile obtained with the in vitro gas production technique using feces as the inoculum.

A method is proposed to determine the extent of degradation in the rumen involving a two-stage mathematical modeling process. In the first stage, a statistical model shifts (or maps) the gas accumulation profile obtained using a fecal inoculum to a ruminal gas profile. Then, a kinetic model determines the extent of degradation in the rumen from the shifted profile. The kinetic model is presented as a generalized mathematical function, allowing any one of a number of alternative equation forms to be selected. This method might allow the gas production technique to become an approach for determining extent of degradation in the rumen, decreasing the need for surgically modified animals while still maintaining the link with the animal. Further research is needed before the proposed methodology can be used as a standard method across a range of feeds.

Predicting the profile of nutrients available for absorption: from nutrient requirement to animal response and environmental impact.

Current feed evaluation systems for dairy cattle aim to match nutrient requirements with nutrient intake at pre-defined production levels. These systems were not developed to address, and are not suitable to predict, the responses to dietary changes in terms of production level and product composition, excretion of nutrients to the environment, and nutrition related disorders. The change from a requirement to a response system to meet the needs of various stakeholders requires prediction of the profile of absorbed nutrients and its subsequent utilisation for various purposes. This contribution examines the challenges to predicting the profile of nutrients available for absorption in dairy cattle and provides guidelines for further improved prediction with regard to animal production responses and environmental pollution.The profile of nutrients available for absorption comprises volatile fatty acids, long-chain fatty acids, amino acids and glucose. Thus the importance of processes in the reticulo-rumen is obvious. Much research into rumen fermentation is aimed at determination of substrate degradation rates. Quantitative knowledge on rates of passage of nutrients out of the rumen is rather limited compared with that on degradation rates, and thus should be an important theme in future research. Current systems largely ignore microbial metabolic variation, and extant mechanistic models of rumen fermentation give only limited attention to explicit representation of microbial metabolic activity. Recent molecular techniques indicate that knowledge on the presence and activity of various microbial species is far from complete. Such techniques may give a wealth of information, but to include such findings in systems predicting the nutrient profile requires close collaboration between molecular scientists and mathematical modellers on interpreting and evaluating quantitative data. Protozoal metabolism is of particular interest here given the paucity of quantitative data.Empirical models lack the biological basis necessary to evaluate mitigation strategies to reduce excretion of waste, including nitrogen, phosphorus and methane. Such models may have little predictive value when comparing various feeding strategies. Examples include the Intergovernmental Panel on Climate Change (IPCC) Tier II models to quantify methane emissions and current protein evaluation systems to evaluate low protein diets to reduce nitrogen losses to the environment. Nutrient based mechanistic models can address such issues. Since environmental issues generally attract more funding from governmental offices, further development of nutrient based models may well take place within an environmental framework.

Modelling mammary metabolism in the dairy cow to predict milk constituent yield, with emphasis on amino acid metabolism and milk protein production: model evaluation.

A model of mammary metabolism has been constructed and parameterized, with milk protein synthesis represented as a function of five essential amino acids (EAA) (Hanigan et al., 2001). Herein the model is evaluated using both the data used to construct the model (reference data) and an independent data set (literature data), and sensitivity to inputs and parameter estimates is assessed. The model predicted metabolite removal well for the reference data with exceptions for glutamate, glucose, and acetate. However, predictions of milk protein synthesis exhibited significant mean positive bias, which apparently was associated with the representation of milk protein synthesis. Adjustment of model parameters removed the mean bias, however, prediction accuracy was still inadequate. Simulation of the single reference experiment containing all critical inputs resulted in predictions of milk protein output that explained 53% of the observed variation, suggesting that the limited accuracy of the model when applied to the entire reference data set was due to assumptions regarding missing inputs. Mammary removal of glutamate, isoleucine, lysine, phenylalanine, tyrosine, valine, glycerol, beta -hydroxybutyrate (BHBA), and acetate were predicted less accurately when simulations of the independent data set were conducted. Twenty-five percent of the observed variation in milk protein yields for the independent data set was explained by the model. Refitting parameters for removal of isoleucine, lysine, phenylalanine, tyrosine, valine, glycerol, BHBA, and acetate raised the variation explained to 43%. Sensitivity analysis indicated that milk protein synthesis was responsive to only the five EAA used in its determination, with sensitivity to any single EAA falling to zero as supply of the EAA exceeded protein synthetic needs. Similarly, milk protein synthesis was readily affected by parameters associated with removal and metabolism of the five EAA. Milk lactose was found to be sensitive to glucose input as well as to similar parameters and inputs as milk protein. It is concluded that representation of the milk protein synthesis process as a function of a single limiting EAA may not be adequate and might be better represented by simultaneous consideration of multiple EAA. Additional work on the description of energy metabolism is also suggested.