The determination of nutritional requirements: A mathematical modeling approach

Abstract

The Saturation Kinetics Model (SKM) has been shown to describe the functional relationship between physiologic responses and nutrients fed in graded amounts. The SKM is based on the concept that an organism is characterized by a sequence of homeostatically constrained steady states. Responses are the result of a series of enzymatically mediated steps, one of which is rate limiting and displays saturation kinetics. The model is descriptive of a wide range of physiological responses and the model equation is continuous in its derivatives. This study examines the usefulness of the application of the SKM to the determination of nutritional requirement levels for growth in the young rat, and provides a basis for the rational formulation of complex mixtures of nutrients (diets) which are designed to optimize some measured performance characteristic in an animal. Using the model, theoretical response curves were constructed based on dietary nutrient concentration, daily weight gain (dW/dt) and daily food intake (dF/dt). Theoretical slopes (first derivative) and efficiency curves were also constructed. Parameters derived from the application of the SKM to rat growth experiments were used to formulate a complete dietary amino acid mix for weanling rats. Dietary ratios and concentrations for indispensable amino acids and arginine were calculated using the parameter K.5. A curve-shift technique was used to determine dietary concentrations for conditionally dispensable and dispensable amino acids. The model was also used to determine a dietary ratio of (IAA + Arg)/(CAA + DAA). Using the dietary amino acid concentrations suggested by the model and an (IAA + Arg)/(CAA + DAA) ratio of 1, a growth response curve was constructed and compared to a similar curve using the amino acid mix of Rogers and Harper. The modeling approach produced a 10–15% improvement in growth over the Rogers and Harper mix. The SKM is discussed in terms of calculating an ideal nutrient ratio and choosing of a desired response level. It was demonstrated that the model can rapidly produce accurate estimates for dietary amino acid levels, while minimizing required numbers of vertebrate animals.