Consequences of Energy Metabolism Impairments - Ecological Biomarkers: Indicators of Ecotoxicological Effects - page 320

12.3 Modeling of Effects Based on Impact of Energy
To model the effects of a chemical on energy, the first point is to examine the relationships
between its accumulation in the organisms and its effects to obtain a certain amount of
toxicological relevance. In general, only exposure concentration is available, whereas the
effect is mainly linked to the concentration at target level. Usually, a simple but realistic
toxicokinetic model, also called one-compartment linear model, is used. The absorption
rate of the compound is assumed to be proportional to exposure concentration, and its
elimination rate proportional to its internal concentration. The following equation is then
obtained, for nongrowing organisms:

d
d

C
t

i

() t =× −× kct kCt () () (12.2)

a e e i

where C i is the compound internal concentration, c e is its exposure concentration, and k a
and k e are its absorption and elimination rates, respectively. Taking compound kinetics
into account has the advantage of highlighting the temporal aspects of the exposure. In
effect models, the effect is directly linked to the internal concentration, the only time fac-
tor involved being the determination of the concentration using the kinetic model. As a
consequence, parameter estimates do not depend on test duration.
Energy-based models presuppose the existence of a no-effect concentration, i.e., that
organisms can tolerate a certain level of concentration of xenobiotics, either by inhibiting
them through various trap mechanisms, or because a sufficient number of functions are
operational in a normally functioning individual. Once organisms are unable to tolerate
the accumulated toxicant, proportionality exists between the observed effect and excess
toxin; we will call “toxicity rate” the proportionality factor k i between effects and threshold
excess.

Effect = k i ( C i − NEC ) (12.3)

The effect is a disruption of the parameters controlling energy in organisms and is rep-
resented by the Dynamic Energy Budget theory. This theory (Kooijman 2010) aims to pro-
vide a mathematical representation of the use of energy from food intake, shared among
four major physiological functions: growth, maintenance of vital functions, maintenance
of reproductive capacity, and reproduction. This theory was tested on roughly 270 verte-
brate and invertebrate species. The physiological action mechanism of the toxicant cor-
responds to the affected parameter. More specifically, regarding survival, the effect is an
increase in mortality rate. Regarding growth, the effect involves either a maintenance cost
increase, an increase in the synthesis cost of new tissues, or a decrease in the nutrition rate.
Regarding reproduction, the effect could either disturb growth and thus reduce reproduc-
tion, or involve a direct reduction in fecundity.
The accuracy of this approach to assess the dose-response relationships was verified
with several species of invertebrates and different types of toxicants (pesticides, metals,
PAHs, etc.), and the results obtained were often significantly different from those expected
with a more standard statistical approach (Kooijman and Bedaux 1996; Péry et al. 2003;
Ducrot et al. 2004; Alvarez et al. 2005). Similarly, the accuracy of the assessed toxicity
threshold was demonstrated in Chironomus riparius (Péry et al. 2008) for cadmium, copper,