Simulation of the dynamics of nitrogen metabolism in sheep
British Journal of Nutrition
I . The results of isotope tracer studies of the dynamics of nitrogen metabolism in mature sheep were used to construct a seven-pool mathematical model. 2. The model was extended to a nine-pool model, which incorporates lags describing the time taken for the passage of digesta through the gut of sheep. 3. Simulation studies using these models satisfactorily predicted results of independent experiments. 4. The dynamics of N metabolism in sheep appear to be best approximated by first-order
... first-order kinetics; that is, many of the important N transport processes are substantially linear orconcentration-dependent. This paper reports the development of a linear, multi-pool model of the dynamics of nitrogen metabolism in sheep. The model has some variable coefficients and time delays. Variable coefficients were required because of the necessary over-simplifications in little-understood aspects of N metabolism in sheep. Delays were incorporated into the model in order to describe the time taken for digesta to move through the gut. Experimental results used in both the construction and validation of the model reported here were based on, and therefore strictly applicable to, forage diets. Energy availability is known to be highly correlated with protein intake in sheep consuming dried, forage-based diets. For example, r2 = 0.8 when digestible crude protein (DCP) is correlated with metabolizable energy (ME; MJ/kg) for forage diets fed to ruminants. This value for r2 was calculated using values selected from Table I of McDonald, Edwards & Greenhalgh (1973) . Therefore, the ratio, available energy: N in the material undergoing rumen fermentation was assumed to be constant. Similarly, since only forage diets were considered, essential amino acids and dietary constituents other than N were assumed to be non-limiting in sheep given these diets. Flows of N between biologically important pools in sheep given a range of forage diets were well predicted by the model for a number of studies, both in these laboratories and elsewhere. A similar seven-pool model was constructed for sheep given a diet of (g/d) 500 wheaten chaff, roo Solka floc, 20 dried molasses. This diet provided an average intake of 4.9 g N/d but, for precise model balance, the input and the sum of losses were both assumed to be 491 g N/d in the model for the 'low-N ' diet. Identical pathways to those used in the 'high-" model were assumed for the '1ow-N' model and N flows were estimated by incorporating the results reported in Nolan (1971) and by subsequently balancing the flows to and from each pool, as well as for the whole model ( Table 2 ). The final, mean, seven-pool model that was assumed to be characteristic of the dynamics of N metabolism in sheep consuming forage diets containing between 4-9 and 23.4 g N/d is shown in Fig.