Contributions to the Energetics of Animal Growth
121
the interaction between rather complicated exponential functions. Our
intellect is not able to understand such interactions of exponential functions.
All these problems require the use of mathematics.
We started with the allometric formula as an approach to the relative
growth in animals. It has been shown to be applicable in numerous examples
for the description of growth processes in morphology and physiology.
Thence it may be regarded as a highly secured biomathematical expression.
PUTTER [11] and BERTALANFFY [1] applied this allometric formulation to the
basic processes of growth: anabolism and catabolism. In this manner they
derived a very good formulation of the growth of animals as a function of
time. I could show that the PUTTER-BERTALANFFy-equation has to be
accomplished by a third term connecting the energetic output of anabolism
with the formation of living substance. This third term allowed the derivation of the "Struktur-Energie", which seems to me a very important
concept for the understanding of growth processes, as could be shown by
some examples.
By its mathematical relationship to the allometric formula, the growth
function which I proposed, was a further important tool; because of this
property it is possible to give an explanation for the parameters of the
allometry formula, so that they do no more remain pure numerical values.
In this manner it was possible to explain the exponent calculated from
respiration measurements as an energetic relation, and we gained further
insights into the energetics of growth. Here we see that it is very useful,
if we are able to establish mathematical connections between our formulations.
The new growth formula also includes the anabolism-catabolism concept of the PUTTER-BERTALANFFy-equation. According to this hypothesis
a part of the living matter continuously decays. The loss in mass caused by
catabolism disturbes the equilibrium between anabolism and catabolism
and is compensated by increased anabolism. This increase in the rate of
anabolism continues until the " Soll-Wert" is reached. This compensatory
growth is a well known fact in animals whose growth has been retarded
by illness or starvation. Here we have to assume regulatory mechanisms
between anabolism and catabolism linked together by metabolites. This
assumption would describe the pathological growth as a disengagement
of the anabolic and catabolic processes-each running without control.
In the course of normal growth anabolism only repairs the loss in mass
caused by catabolism. If the connection between anabolism and catabolism
is disturbed, living matter will be organized without limits. This seems to
me a very interesting aspect of the much discussed problem of pathological
growth, derived from the anabolism-catabolism concept of growth.
The allometric formula, the new growth formula and the completed
PUTTER-BERTALANFFy-equation seem to me useful tools for a further theo-
121
the interaction between rather complicated exponential functions. Our
intellect is not able to understand such interactions of exponential functions.
All these problems require the use of mathematics.
We started with the allometric formula as an approach to the relative
growth in animals. It has been shown to be applicable in numerous examples
for the description of growth processes in morphology and physiology.
Thence it may be regarded as a highly secured biomathematical expression.
PUTTER [11] and BERTALANFFY [1] applied this allometric formulation to the
basic processes of growth: anabolism and catabolism. In this manner they
derived a very good formulation of the growth of animals as a function of
time. I could show that the PUTTER-BERTALANFFy-equation has to be
accomplished by a third term connecting the energetic output of anabolism
with the formation of living substance. This third term allowed the derivation of the "Struktur-Energie", which seems to me a very important
concept for the understanding of growth processes, as could be shown by
some examples.
By its mathematical relationship to the allometric formula, the growth
function which I proposed, was a further important tool; because of this
property it is possible to give an explanation for the parameters of the
allometry formula, so that they do no more remain pure numerical values.
In this manner it was possible to explain the exponent calculated from
respiration measurements as an energetic relation, and we gained further
insights into the energetics of growth. Here we see that it is very useful,
if we are able to establish mathematical connections between our formulations.
The new growth formula also includes the anabolism-catabolism concept of the PUTTER-BERTALANFFy-equation. According to this hypothesis
a part of the living matter continuously decays. The loss in mass caused by
catabolism disturbes the equilibrium between anabolism and catabolism
and is compensated by increased anabolism. This increase in the rate of
anabolism continues until the " Soll-Wert" is reached. This compensatory
growth is a well known fact in animals whose growth has been retarded
by illness or starvation. Here we have to assume regulatory mechanisms
between anabolism and catabolism linked together by metabolites. This
assumption would describe the pathological growth as a disengagement
of the anabolic and catabolic processes-each running without control.
In the course of normal growth anabolism only repairs the loss in mass
caused by catabolism. If the connection between anabolism and catabolism
is disturbed, living matter will be organized without limits. This seems to
me a very interesting aspect of the much discussed problem of pathological
growth, derived from the anabolism-catabolism concept of growth.
The allometric formula, the new growth formula and the completed
PUTTER-BERTALANFFy-equation seem to me useful tools for a further theo-