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The Determination of Nutritional Requirements in Rats: Mathematical Modeling of Sigmoidal, Inhibited Nutrient-Response Curves^{1 ,2}

Department of Biochemistry, School of Medicine, Oral Roberts University, Tulsa, OK 74171

The Saturation Kinetics Model (SKM) is useful in describing many physiological responses as functions of a limiting dietary nutrient. However, as nutrients are fed at higher dietary concentrations, responses become inhibited and diminish from their usual plateaus. By adding an inhibition constant (K_s) to the SKM in a manner consistent with substrate inhibition (based on enzyme kinetics), it becomes possible to predict the inhibited portions of the nutrient-response curve. To test this, rats were fed diets of graded levels of casein (0–75%) or lysine (0–6.2%), and weight gains and food intakes were measured daily for up to 2 wk. The inhibition form of the SKM was able to predict the complete response range of each experiment, producing a K_s (weight gain) at a dietary level of 50.60% for casein and 7.56% for lysine. It was also possible to set up an upper and lower dietary nutrient concentration that encompassed the 100% response range for each response, thereby giving an inhibition or toxicity index of 2.02 for casein and 4.98 for lysine. This index allows one to set nutritional requirement levels precisely, optimizing responses without moving into inhibiting or toxic ranges of nutrients. Based on growth response curves, requirements were 25.61% for casein and 1.97% for lysine.

KEY WORDS: • mathematical model • nutritional requirement • toxicology

¹ Supported by an intramural grant from the School of Medicine, Oral Roberts University.

² Presented in part at the 1989 FASEB meeting, New Orleans, LA.

Manuscript received 28 November 1988. Revision accepted 22 June 1989.