### Scaling relationships based on partition coefficients and
body sizes have similarities and interactions

Kooijman, S. A. L. M., Baas, J., Bontje, D., Broerse, M., Jager, T., Gestel, C. van and Hattum, B. van 2007.

Scaling relationships on based on partition coefficients and
body sizes have similarities and interactions.

*SAR and QSAR in Environ. Res.* **18**: 315--330
#### Abstract

The LC50 of compounds with a similar biological effect, at a given
exposure period, is frequently plotted log-log against the
octanol-water partition coefficient and a straight line is fitted
for interpolation purposes. This is also frequently done for
physiological properties, such as the weight-specific respiration
rate, as function of the body weight of individuals. This paper
focuses on the remarkable observation that theoretical
explanations for these relationships also have strong
similarities. Both can be understood as result of the covariation
of the values of parameters of models of a particular type for the
underlying processes, while this covariation follows logically
from the model structure. The one-compartment model for the uptake
and elimination of compounds by organisms is basic to the
BioConcentration Factor (BCF), or the partition coefficient; the
standard Dynamic Energy Budget model is basic to the (ultimate)
body size. The BCF is the ratio of the uptake and the elimination
rates; the maximum body length is the ratio of the assimilation
(i.e. uptake of resources) and the maintenance (i.e. use of
resources) rates. This paper discusses some shortcomings of
descriptive approaches and conceptual aspects of theoretical
explanations. The strength of the theory is in the combination of
why metabolic transformation depends both on the BCF and the body
size. We illustrate the application of the theory with several
data sets from the literature.