The Determination of Nutritional Requirements in Rats: Mathematical Modeling of Sigmoidal, Inhibited Nutrient-Response Curves

Abstract

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 (Ks) 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 Ks (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.

Limits of adaptation to high dietary protein intakes

“…There is the need to determine the basic principles which underlie the de®nition of the upper limit of intake of protein or amino acids which can be metabolised effectively without adverse effect and how this might translate into patterns of food consumption. What is clear from the studies in humans is that we have only a rudimentary understanding of the nature of the dose response to variations in dietary protein or amino acids, from one situation to another, as needed to model the kind of mathematical analysis developed by Mercer (Mercer et al, 1989). In order to achieve their objective, to characterise a dose response curve, which identi®es levels that map to threshold, de®cient, adequate, optimal, and toxic levels of intake, there is the need for a limited range of outcome measures, which characterise desirable function.…”

Estimation of the tryptophan requirement in piglets by meta-analysis

“…Although it is difficult to precisely define the term 'requirement' (Mercer et al, 1989), for growing animals it is usually defined as the minimum supply of an AA that maximizes growth. For monogastric animals, AA requirements are often expressed based on the concept of ideal protein.…”

Redefining the requirement for total sulfur amino acids in the diet of barramundi (Lates calcarifer) including assessment of the cystine replacement value

“…Firstly, the one-slope break-point (broken-line model) analysis used by Coloso et al (1999) to estimate the requirement may have been inappropriate, resulting in underestimation of the requirement. Non-linear models, such as the four-and five-parameter saturation kinetics models, derived from the Michaelis-Menten model for enzyme-catalyzed reaction velocity (Michaelis and Menten, 1913) and developed and described by Mercer and others in a series of reports (Mercer et al, 1975;Mercer, 1980;Mercer et al, 1986;Mercer et al, 1989), are considered to be more accurate representations of biological responses compared with those which "force responses to conform to straight lines" (Pesti et al, 2009). …”

“…Broken line spline with ascending linear segment model (Robbins, 1986) Broken line spline with ascending quadratic segment model (Vedenov and Pesti, 2008) 4-Parameter Saturation Kinetics Model (Morgan et al, 1975) 5-Parameter Saturation Kinetics Model adapted from Mercer et al (1989) Three-parameter logistic model (SAS Institute Inc, 1990) Four-parameter logistic model (Gahl et al, 1991) Sigmoidal model (Robbins et al, 1979) Exponential model (Robbins et al, 1979) Compartmental model (Pesti et al, 2009) A C C E P T E D M A N U S C R I P T TSAA; 1.8-2.3% CP Met + 1.1% CP Cys).  Cystine can constitute at least 40% of the TSAA content of the diet of barramundi without significantly affecting growth.…”