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 (PHE) and tyrosine (TYR) 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 PHE and TYR from the liver via the portal vein and hepatic artery. In addition, the exchange of free PHE and TYR between extracellular and intracellular pools was explained and the hydroxylation of PHE to TYR was estimated. The model was effective in providing information about the fates of PHE and TYR 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

The role of dynamic modelling in understanding the microbial contribution to rumen function

Mechanistic models of microbial metabolism in the rumen aim at an improved understanding and integration for research purposes or at an improved prediction for practical purposes. The standard way of representing such models is the rate: state formalism. The system is defined by a number of state variables and a set of differential equations describe the change of the state variables with time. Three different types of solution to these dynamic models are distinguished, and examples of these solutions are described to illustrate the applications and contributions of dynamic modelling in the study of the rumen microbial ecosystem. Type I solutions are obtained when the system is in steady state and the differential equations are solved by setting the differentials to zero. An application of the type I solution is the indirect approach to quantifying the fibrolytic anaerobic fungi in the rumen. The solutions of the model describing the alternate life cycle of rumen fungi, with its free-swimming dispersal and particle-attached stages, appear to be consistent with ruminal and faecal observations. Type II solutions are obtained when the system is not in steady state but the differential equations can be integrated analytically. An application of this type of solution is the quantification of the growth and growth yield in batch cultures. Such models help to quantify the degradation of substrates in the rumen and to elucidate the interactions between groups of rumen micro-organisms. Type III solutions are obtained when the system is not in steady state and when the differential equations have to be solved numerically. Applications of the type III solutions are the rumen simulation models that describe substrate degradation, endproduct formation and microbial metabolism in an integrated manner. To illustrate this type III solution, a model of lactic acid metabolism in the rumen is defined, and its contribution to understanding of the paths and rates of lactic acid disappearance described. It is essential that the models are based on sound mathematical and biological principles. However, the various applications described in the paper show that models need not necessarily be complex and very detailed to contribute to better understanding