Contributions to the Energetics of Animal Growth
125
KRUGER:
(1) My derivations are based on the PUTTER-BERTALANFFY equation. It is
unwarranted to call it "obsolete", since no other useful concept has yet been
proposed. Both authors have derived the mathematical expression for catabolism from the loss in weight on starving animals and the expression for
anabolism from experiments on heat production. It is therefore a fact that the
BERTALANFFY equation uses for both terms physically different dimensions. If
we use caloric values for both terms, we find a higher value for the anabolism
than for the catabolism, and meet the same difficulty. If Dr. LOCKER defines
"catabolism as the heat produced by the organism", catabolism would stand
in an exponential relation to body weight, and this would mean that the BERT ALANFFY equation is no longer valid. (2) I have never said that we measure
the anabolism in respiration measurements. I derived only from the BERTALANFFY equation the fact that we measure the exponent of the allometric
formula in those experiments. The literature cited by Dr. LOCKER is not at
my disposal at the moment. Therefore I do not know in what manner catabolism was estimated by these authors. I am however convinced that the earlier
observations of PUTTER and other authors are reliable. The reputed mistake
in my derivations from the results of P AN DIAN would need an accurate exposition to give an answer. (3) Dr. LOCKER'S objection against my hypothesis
of the structural energy as an entropy is not convincing. I derived this concept
from the BERTALANFFY equation completed by the conversion term. I shall try
to clarifv mv concept: The animal needs much more food than is formed into
body substance. XX/hat is the fate of energy consumed with the food? Naturally
it is partly used fur physical and chemical work, but it is my opinion that the
construction of any order also needs energy and that the energy expended for
this aim is no longer freely convertible. Not suppositions, only experiments
may confirm or disprove mv ideas.
LOCKER:
In Prof. KRUGER'S paper has been neglected the distinction between physical
and informational entropy; only the former bears physical dimensions, viz.
erg/degr., while the latter does not. An equivalence, however, between the
two can be accomplished in the form of H = -as, by concerning physical
entropy with the total number of ways of which a structure can be assembled.
Then a =c 0.73. For the production of information in an organism a conservation law holds, namely that it is equal to the rate of information leaving the
system (by performing functions) plus the rate of storage (e. g. for growth)
and for maintenance and repair. Since in the organism LIS = Swaste-Sfood,
the net entropy in the organism can be transformed to information (or
Hfood-Hwaste = H orz')' During growth the increase of free energy in the
organism associated with the conversion of nutrient material into protoplasm
involves a heat and an entropy term. In case that no other work than protoplasm svnthesis is done
(LlH: heat absorbed by reactants from the environment; -LIH/T: entropy
change of environment; L1S: entropy change of reactants). LlSint. may thus be
obtained by experimental assessment of LlP~xt. (free energy of food ingested
and released as waste) and the addition of LlHint. (difference of heat content
between cell structure and a stoichiometrically equivalent amount of food;
125
KRUGER:
(1) My derivations are based on the PUTTER-BERTALANFFY equation. It is
unwarranted to call it "obsolete", since no other useful concept has yet been
proposed. Both authors have derived the mathematical expression for catabolism from the loss in weight on starving animals and the expression for
anabolism from experiments on heat production. It is therefore a fact that the
BERTALANFFY equation uses for both terms physically different dimensions. If
we use caloric values for both terms, we find a higher value for the anabolism
than for the catabolism, and meet the same difficulty. If Dr. LOCKER defines
"catabolism as the heat produced by the organism", catabolism would stand
in an exponential relation to body weight, and this would mean that the BERT ALANFFY equation is no longer valid. (2) I have never said that we measure
the anabolism in respiration measurements. I derived only from the BERTALANFFY equation the fact that we measure the exponent of the allometric
formula in those experiments. The literature cited by Dr. LOCKER is not at
my disposal at the moment. Therefore I do not know in what manner catabolism was estimated by these authors. I am however convinced that the earlier
observations of PUTTER and other authors are reliable. The reputed mistake
in my derivations from the results of P AN DIAN would need an accurate exposition to give an answer. (3) Dr. LOCKER'S objection against my hypothesis
of the structural energy as an entropy is not convincing. I derived this concept
from the BERTALANFFY equation completed by the conversion term. I shall try
to clarifv mv concept: The animal needs much more food than is formed into
body substance. XX/hat is the fate of energy consumed with the food? Naturally
it is partly used fur physical and chemical work, but it is my opinion that the
construction of any order also needs energy and that the energy expended for
this aim is no longer freely convertible. Not suppositions, only experiments
may confirm or disprove mv ideas.
LOCKER:
In Prof. KRUGER'S paper has been neglected the distinction between physical
and informational entropy; only the former bears physical dimensions, viz.
erg/degr., while the latter does not. An equivalence, however, between the
two can be accomplished in the form of H = -as, by concerning physical
entropy with the total number of ways of which a structure can be assembled.
Then a =c 0.73. For the production of information in an organism a conservation law holds, namely that it is equal to the rate of information leaving the
system (by performing functions) plus the rate of storage (e. g. for growth)
and for maintenance and repair. Since in the organism LIS = Swaste-Sfood,
the net entropy in the organism can be transformed to information (or
Hfood-Hwaste = H orz')' During growth the increase of free energy in the
organism associated with the conversion of nutrient material into protoplasm
involves a heat and an entropy term. In case that no other work than protoplasm svnthesis is done
(LlH: heat absorbed by reactants from the environment; -LIH/T: entropy
change of environment; L1S: entropy change of reactants). LlSint. may thus be
obtained by experimental assessment of LlP~xt. (free energy of food ingested
and released as waste) and the addition of LlHint. (difference of heat content
between cell structure and a stoichiometrically equivalent amount of food;