A simple mechanistic model to interpret the effects of narcotics.

In this research we will show the advantages of using a time-independent dose metric in a mechanistic model to evaluate toxic effects for different narcotic compounds on different species. We will show how different already existing QSARs can be combined within a mechanistic framework to 1) make predictions of lethal thresholds; 2) show some limitations in the use of existing QSARs; 3) show how a mechanistic framework solves some conceptual problems in current approaches and 4) show how such a framework can be used to be of aid in an experimental setup in predicting the outcome of a survival experiment. The approach we chose is based on the simplest mechanistic model available, a scaled one-compartment model to describe uptake and elimination and hazard model to link the exposure to effects on survival. Within this theoretical framework a prediction for an internal threshold for effects on survival of 3 mmol/kg bw can be made, which should be similar for different species and independent of the partitioning characteristics of the toxicant. To demonstrate this, a threshold for 51 different species was derived, which indeed appeared to lie in a relatively small range, typically between 1 and 10 mmol/kg bw.

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

The LC(50) 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.