Ecotoxicity applications of DEB theory with AmP support

The motivation to develop DEB theory in 1979 originated from the (societal) need to quantify effects of chemicals on individuals and to work out the implications of such effects for populations and ecosystems. Since (energy) allocation rules determine whether or not effects on growth and reproduction depend on food availability, there was a need to study these allocation rules in more detail. It is part of the many complexities that are involved in translating results of bioassays under standardized laboratory conditions to expected effects under field conditions. Differences in exposure are another source of complexities in this context, involving environmental chemistry (ligand, pH, water hardness, soil chemistry), (bio)transformation and transport. Spatial (point or diffuse) and temporal scales (continuous or event) of emissions and ecosystem conditions ("virgin" or already disturbed, affecting re-inoculation potential from unaffected surrounding areas) further contribute to the complexity of this extrapolation step. Effect-studies of chemicals presently delineate toxicokinetic aspects, i.e. the link between external and internal concentrations of chemicals, and toxicodynamic aspects, i.e. the link between internal concentrations and effects on individuals.


DEB theory captures effects of chemicals on energetics via changes in parameter values, linked to internal concentrations. All DEB parameters are potentially affected. The hazard rate, also called instantaneous death rate, classifies as state (i.e. a function of other states and parameters) that is a target for aging and starvation, for instance. Lethal effects are captured via effects on the hazard rate; other effects are called sublethal effects. DEB parameters have been chosen such that each of them relates to a single metabolic flux, one parameter per flux, exposing the potential handles for chemicals to modify individual performance Three concentration ranges are delineated for each parameter: "too little", "enough" and "too much". Within the "enough"-range for a particular parameter, the parameter does not depend on the concentration. The boundaries of this parameter-specific range are called the (lower and upper) internal no-effect concentrations. Changes in parameter values are proportional to the difference between the internal concentration and the (relevant) no-effect concentration for small changes in parameter values, on the basis of Taylor's approximation. Small changes in parameter values can, however, result in large changes in measured quantities (i.e. growth or reproduction), which are called endpoints. Effects on several endpoints might be due to a change in single parameter. Toxicants are chemicals for which the "too little"-range is zero, i.e. the lower no-effect concentration is zero; the upper no-effect concentration then becomes THE no-effect concentration for that parameter. For some compounds, such as most mutagenic compounds, even the no-effect concentration is zero and all internal molecules have effects. For increasing internal concentrations of toxicants, first one, then more and more parameters become affected. If the concentration range for which a single parameter is affected, is rather large, this parameter represents the effective mode of action of the toxicant (in low concentrations). Effects on a single parameter can translate into effects on multiple endpoints. Toxicants with a similar biochemical mode of action, can have different effective modes of action and vice versa.

Cases where just a single toxicant is involved are rare, due to chemical and metabolic transformation, e.g. ionization. Lipophilic compounds are frequently transformed to more hydrophilic (and more toxic) ones, enhancing elimination. Toxicity studies are typically motivated by potential pollution or exposure scenarios, which usually involve mixtures directly. Theory has been developed for how mixtures of chemical compounds affect parameters. DEB theory also has modules for the growth of tumors in relation to the state of the individual, including the nutritional condition.


The basic toxicokinetic model is the one-compartment model, where uptake is proportional to the external concentration and elimination is proportional to the internal concentration. In a DEB context, these rates are also proportional to surface area, which links them to structural length of individuals; small individuals more rapidly equilibrate with the (changing) chemical environment, compared to bigger ones. Dilution by growth is easy to account for in a DEB context; even little growth can affect internal concentration-profiles substantially. Although this simple one-compartment model frequently captures the broad picture well, in practice deviations occur, for which variants of the basic model have been developed.

The most important variants of one-compartment models delineate several uptake and elimination routes. They account for uptake via food (especially for poorly soluble compounds), or directly from the environment (respiration, water for aquatic organisms, skin-contact for terrestrial ones), and elimination via feces, respiration, reproduction. Uptake can depend on nutritional condition via re-partitioning of the internal compound between reserve and structure (multi-compartment models), which helps to understand that effects of some toxicants only show up during starvation. Elimination is frequently an active metabolic process, involving chemical transformations and temperature-dependence. DEB theory specifies the network of interlinked metabolic processes, so concerning not only toxicodynamic, but also toxicokinetics processes.

From AmP entries to ecotoxicity

The AmPtox GitHub repository has a number of examples of analyses of effects of toxicants on various endpoints. The system is similar to that used for AmP entries, using 4 source-Matlab-files:
  • mydata_FileNm to specify data and relevant info
  • pars_init_FileNm to specify initial parameter values
  • predict_FileNm to specify predictions for all data sets
  • run_FileNm to set estimation options, run the estimation and report the results
where FileNm is replaced by a code-name for the data-sets, such as the OECD test number, followed by the compound name (see OECD221_Cd for example). The run-file in all examples directly writes a report after completing the estimation.

The examples presently include

test_compound species end point target
OECD201_LAS Isochrysis galbana optical density hazard rate, cost for structure
OECD202_dichromate Daphnia magna survival hazard rate
OECD203_dieldrin Poecilia reticulata survival hazard rate
OECD210_PAH Danio rerio body length spec assimilation
OECD221_Cd Daphnia magna cum # offspring embryo hazard
OECD222_Cu Lumbricus rubelles body weight hazard rate
OECD232_Cd_Cu Folsomia candida survival hazard rate
OECD232_Cd_Pb Folsomia candida survival hazard rate
OECD232_Cu_Pb Folsomia candida survival hazard rate
OECD232_Cd_Zn Folsomia candida survival hazard rate
OECD232_Zn_Cu Folsomia candida survival hazard rate
OECD232_Zn_Pb Folsomia candida survival hazard rate
OECD232_Cd_Cu_Pb_Zn Folsomia candida survival hazard rate
Notice that all stress parameters are specified at the current temperature, since toxicity tests are typically done at a single temperature only with no information about how to convert to other temperatures. The tests on survival show a case where the change in size during exposure can be ignored (OECD203_dieldrin) and a case where it cannot (OECD202_dichromate).

The DEB parameters for a particular existing entry can be found from running prt_report_my_pet('My_Pet'), where My_Pet is replaced by the name of the entry. This opens a searchable html-page that also shows the temperatures at which the values apply and info to convert to other temperatures.

If you run a run-file in any example, a report is produced and shown in your browser; use mat2pars_init (without input) to copy the results of the estimation into the pars_init file, which you can see in the Matlab editor. The production of the report runs BibTex (under Matlab), which can be downloaded freely, to produce an html with references; if not available, the bib-file is shown. Tri-variate data, like in the toxicity tests of mixtures (OECD232-tests), requires the code "animated png assembler" apngasm64.exe to generate the resulting animated png-file. Please make sure that your system can find this code by setting a path to it in the environmental variables.

Multiple entries

The AmP setup for parameter estimation can handle multiple entries to accomodate the fact that some parameters differ between species, but others are the same. This setup also applies to the AmPtox module. The test OECD232_Cd_Cu_Pb_Zn with 4 metals, combines the 6 binary mixtures with a reduced number of parameters, exploiting the notion that each metal was tested 3 times. The pars_init_group_d0 file in this entry shows the results, given no interaction-toxicity of the binary mixtures, while the pars_init_group file includes these interactions. The conclusion must be that the interactions are weak only. The resulting parameter estimates were used as initial values for the 6 binary-mixture tests, allowing variations in toxicity of each metal between tests.

A useful application of the multiple-entry case is to combine an existing AmP entry with the data of the toxicity test. The underlying idea is that test-conditions typically differ from the conditions that apply to the data in the AmP entry (temperature, food, housing). This might result in deviating values of one or more parameters. Only a few species can be kept successfully under laboratory conditions. Knowledge of where and how the test-species differs from the data in the AmP entry is important for the interpretation of the effects of toxicants.