Nutrient rational polynomials

There has been significant speculation on the reason why nutrient-response curves appear to be described by rational polynomials. It has been... 

FIG. 1. Possible shapes of nutrient-response curves and the parameter constraints which allow these curves to be described by a 2 2 rational polynomial. 

It is not surprising that the nutrient-response relationship is described by a rational polynomial for the rate of most biological reactions are described by this type of equation. The dimensions of the parameters in the general equation for nutrient-response are... 

Thus, the numerator terms are amplitude factors and the denominator polynomial represents the total nutrient processed by the organism. This allows partitioning the nutrient processed into a number of grossly defined pools. The number of pools is determined by the number of the denominator terms. This is entirely analogous to the rational polynomial which describes the steady state rate of an enzyme-catalyzed reaction in which the denominator consists of the enzyme species and the numerator contains amplitude terms. 

Estimates of the parameters of the equation for the nutrient-response curve can be obtained by graphical analysis (Schulz, 1987) or by statistical analysis of the rational polynomial (Press et al, 1992). Figure 4 shows the response of rats in terms of accumulation of body nitrogen to three different sources of dietary protein (Phillips, 1981). The sources of dietary protein were casein, peanut protein, and wheat gluten. The parameters were estimated graphically, and these estimates were fine tuned by simulation... 

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