When food protein is absorbed by a growing animal, a part of it is used in maintenance metabolism and the part utilized for increase of body protein is only a fraction of the rest. This fraction decreases with the increasing amount of absorbed. protein, since even in a grow-ing animal excretion of nitrogen rises parallel with increase in absorption of nitrogen Then the accumulation of body protein,
P, may be expressed as follows :
P=e
-a-bx(x-x
o) (1),
where
x is the amount of the absorbed protein, x
0 that of maintenance protein ;
u and
b are constants. The formula holds good only when the protein is normally metabolized. Hence
x should be greater than
x0 and the nutritive ratio of the diet should not be too small. Re-writing the equation (1), we obtain more easily provable from,
ln P/x-x
0 =-a-b
x (2).
With gold-fish kept on diets with equal caloric value but of different nutritive ratio, the formula was proved in the following manner. The amounts of absorbed and excreted nitrogen were estimated and the nitrogen retention
P was calculated, maintenance protein being as-sumed to be 9 mg/100g, 24 hrs. from the nitrogen excretion of the fish fed on high caloric but protein free diet. (Table 1).
The value of In P/
x-
x0 was plotted against
x and proved to settle on a straight line (Fig. 1).
The optimum quantity of absorbed nitrogen can be obtained from equation (3).
xmax=
bx0+1 b (3). Nitrogen accumulation of gold-fish under the conditions of our experiment is found to be P=e-0.54-0.0108 (x-9) where x is expressed in terms of mg of nitrogen per 100 g of body weight and 24 hours. The optimum quantity of absorbed nitrogen is 103 mg, which corresponds to a diet of protein con-tent ca. 64% and of nutritive ratio 0.75.
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