Research Summary:

Toxic compounds may reduce the fecundity, development rate, and/or survival probability of individual organisms. A large body of literature models the accumulation of toxic compounds in terms of exchange between organism and environment. These models range in sophistication from simple one-compartment models to more detailed descriptions where a growth model plays a role in determining toxicant uptake (Eby et al. 1997; Jackson 1997; Landrum et al. 1992). However, most bioaccumulation models have no feedback term through which toxicants affect organismal performance. One important mechanism for this feedback is that toxicants may cause a reduction in feeding and an increase in respiration. Such effects have been described in terms of scope for growth, defined as the excess of energy assimilation rate over respiration rate (Donkin et al. 1989; Widdows and Donkin 1991). Scope for growth is a particularly appealing concept for ecological applications, as it sidesteps the issue of chemical cause, and focuses directly on physiological effect. However, predicting the consequences of changes in scope for growth requires coupling a growth model with a dynamic model for toxicant exchange and physiological effects. We study these consequences with dynamic energy budget (DEB) models of the physiology of individuals.

DEB models use differential equations to describe the rates at which individual organisms assimilate and utilize energy from food for maintenance, growth, reproduction and development. These rates depend on the state of the organism (age, size, sex , nutritional status, etc.) and the state of its environment, (food density, temperature, toxicant levels, etc.). Solutions of the model equations represent the life history of individual organisms in a potentially variable environment.

One important use of DEB models is to relate observed patterns of growth, development, reproduction and mortality in a particular organism to empirical information on feeding rates and maintenance requirements, the goal of such studies being to get a close match between data and model descriptions for a particular species (McCauley et al. 1990). A second use, which we use in our research, takes a single, parameter- sparse, mechanistic model, and describes a broad spectrum of biological phenomena and life forms. Species differ only in their parameter values. A well-known example of this approach is the von Bertalanffy theory of growth, which with only two parameters fits the growth of many organisms very well (Kooijman 1993). The attractiveness of such parameter sparse, 'general' models is that they are relatively simple, yet they are based on physiological mechanisms. This combination warrants that these models are both testable and practicable for use at higher levels of biological organization.

We use two families of DEB models, that differ in their assumptions on priorities for energy allocation (see Gurney and Nisbet 1998, chapter 4). The first group, "net assimilation" models is represented by a thoroughly studied model developed by Kooijman (1993). The second group, "net production" models are represented by a model of Ross and Nisbet (1990) and by a more recent model of Lika and Nisbet (1998). There are a few situations where the differences between the models are important (see Nisbet et al. 1996; Gurney et al. 1996), but commonly, both models give equally good fits to limited data. Kooijman's (1993) model is currently our default choice; use of the other models allows us to explore the sensitivity of our conclusions to particular model assumptions. Kooijman (1993) discusses the physiological and physico-chemical rationale for the model assumptions and equations, which are listed in Tables 1 and 2.

• There are two state variables: structural body volume and energy reserve density.
• There are six energy fluxes: assimilation; somatic maintenance; somatic growth; maturation; maintenance of the state of maturity; and reproduction. These energy fluxes are irreversible.
• There are maximally three life stages: embryo's, which neither feed nor reproduce; juveniles, which may feed but do not reproduce; and adults, which may feed and reproduce.
• The rate of food uptake is proportional to the surface area of an organism, and is a hyperbolic function of the food density.
• Energy assimilated from food becomes part of the reserves. The dynamics of the energy reserve density are first order, with a rate that is inversely proportional to the length of an organism.
• A fixed fraction of the energy flowing out of the reserves is used by somatic tissue (somatic maintenance and growth), and the remainder is used for maturity maintenance, and maturation or reproduction (stored until reproductive event); maintenance demands have priority. This partitioning of energy cancels when somatic maintenance needs cannot be fulfilled; then somatic maintenance demands have priority.
• The chemical compositions of structure and reserves are constant. Thus, the following are constant:
  • the conversion efficiency of food into energy;
  • the cost to maintain a unit of structure;
  • the cost to form a unit of structure;
  • the cost to maintain the acquired state of maturity;
  • the cost to mature a unit of structure;
  • the cost to form a unit of reproductive matter.
• Life stage transitions occur when the cumulative amount of energy that is spent on maturation exceeds a threshold. An embryo initially has a negligibly amount of structure. With eggs, the energy reserve density of the embryo at hatching equals that of its mother during egg formation. A foetus develops at a rate that is independent of the reserve density of the mother; at birth, its energy reserve density equals that of the mother. Micro-organisms divide into daughter cells a constant interval after the initiation of DNA replication; replication starts at a threshold size.
• There is one state variable for each toxic compound: the density of that toxicant in the aqueous fraction of structure.
• There is one independent compartment: the aqueous fraction of structure. The density of toxicant in the aqueous fraction of structure is always in equilibrium with the toxicant density in other parts of the body (dry fraction of structure, reserves and stored resources for reproduction). Toxicants are exchanged with the ambient through the aqueous fraction of structure.
• Toxicants in ingested food are assimilated with a constant efficiency. Other toxicants in the environment are taken up at a rate that is proportional to the surface are of an organism and the ambient toxicant concentration.
• The rate of toxicant removal (excluding the release of reproductive matter) is proportional to the surface area of an organism and the toxicant density in the aqueous fraction of structure.
• Toxicants do not affect energy budgets when their density in the aqueous fraction of structure is below a fixed value, the no-effect concentration (NEC). At higher levels, the effective toxicant concentration is proportional to the density in the aqueous fraction of structure corrected for the NEC.
• The flow of energy declines as a hyperbolic function of the effective toxicant density. Demand driven fluxes (maintenance demands) are compensated such that the net commitment to maintenance increases linearly with the effective toxicant concentration.
• Toxicants act on different energy fluxes with equal strength.

reserve dynamics:
growth:
reproduction while growing:
reproduction without growth:
toxicant exchange:
toxic effect functions:

Cd	toxicant concentration in ambient	kxa	rate of toxicant uptake from food
Cx	toxicant concentration in food	m	maintenance rate
De	coefficient for partitioning toxicants between aquous fraction and reserves	m0	maintenance rate in absence of toxicants
Dy	coefficient for partitioning toxicants between aquous fraction and dry structure	[Q]	effective toxicant concentration
E	scaled energy reserves density	[Qnec]	no-effect concentration
Er	scaled density of energy reserved for reproduction	t	time
F	food (scaled density)	V	structural biovolume
Gr	growth investment	Vp	structural biovolume of maturing juvenile
Ki	Toxicity scaling factor	K	coefficient for partitioning energy between somatic and reproductive tissues
Kad	rate of toxicant uptake from ambient	U	energy conductance rate
Kda	rate of toxicant removal	U0	energy conductance rate in absence of toxicants

Ecotoxicological applications of DEB models require additional assumptions that describe the uptake, release and metabolism of toxic compounds, and the effects of toxicants on the organism's physiology. These are discussed in detail by Muller and Nisbet (1998) who argue that the DEB model must be supplemented by both a toxicokinetic model and a toxic effect model. The toxicokinetic model describes changes in the body burden of toxicant in relation to the state variables describing size and storage, characteristics that determine the rates of toxicant exchange and the potential for toxicant accumulation (Kooijman and Vanharen 1990; Lassiter and Hallam 1990; Van Haren et al. 1994). The toxic effect model specifies how DEB model parameters change in response to body burden of toxicant.

Growth of larvae of Crassostrea gigas at nominal mercury concentrations of 0 (), 5 (), 10 (), 20 (), and 40 () nM. Model fits represent fast exchange of mercury between larva and ambient (solid line) or slow exchange (broken line); see text for details. Parameter with rapid mercury exchange are: ultimate height 350 µm; initial height 63.3 (± 3.9) µm; von Bertalanffy growth rate 55.7 (± 1.7) 10-3 day-1; toxicity scaling 72.2 (± 6.5) nM; no-effect concentration in ambient 7.4 (± 1.7) nM; and development delay 1.8 (± 0.3) day (data from Beiras and His 1995).

The generality of the DEB-based approach relieves us from the impossible requirement of modeling every combination of toxicant and organism separately. While different toxicants may induce different biochemical responses in an organism, these responses translate into an effect on a small number of energy fluxes. Our formalism allows many possible assumptions on the precise form of this toxic effect; the simplest is that toxicants affect energy transduction in a hyperbolic way (resembling the way non-competitive inhibitors reduce the rate of simple Michaelis-Menten enzyme kinetics). As a result, toxicants directly affect parameters that specify the rates of feeding, assimilation and maintenance, and thereby indirectly reduce growth and reproduction rates (see Table 2 for equations).

Our default model successfully describes how various lipophilic (PAH's) and metallic (copper, cadmium, mercury) compounds, either added singly or in the form of a mixture, change the rates of feeding, respiration and growth in several animal species. Figure 1 shows an example, larval growth of the oyster Crassostrea gigas in the presence of mercury (data from Beiras and His 1995). Because the authors did not measure tissue levels of mercury (unfortunately, experimental studies tend to focus on either bioaccumulation or toxic effects, but rarely both), we fitted the data with our toxic effect model assuming the two extreme possibilities for mercury exchange: very rapid and very slow exchange. Both extremes yield acceptable fits, which shows that the toxic effect model is relatively insensitive to details of toxicant accumulation.

Figure 2. Peak values of reserves in full-grown Mytilus edulis as a function of fluctuations in food availability. The dampening effect of reserves on its dynamics strongly depends on the period at which food availability changes. When this rate is relatively high, the peak value will be low, implying that the reserve density will be cycling with a small amplitude. When the food scaled food density is fluctuating around 0.5, a typical mussel will always survive if the amplitude of the fluctuations in food is less than 0.17; beyond that, survival is a function of the periodicity.

In most natural environments organisms need to cope with temporary shortages of food. Toxicants aggravate the condition of starving organisms, and may accelerate death due to starvation. This mortality factor is a part of our model through mechanisms of 'sublethal' toxic effects, which include a reduction in feeding and an increase in maintenance requirements. In order to quantify this mortality factor, we need to model starvation strategies and specify the condition for death due to starvation in absence of toxicants.

The model we are using assumes that an organism dies when it cannot fulfill its maintenance demands, which happens when energy is released from reserves at an insufficiently rapid rate. The organism is neither supposed to regulate this mobilization rate, nor does it modify its maintenance requirements during periods of starvation. This constrains the survival potential of organisms in variable food environments, and this constraint may be unduly strong. We have conducted a few simulation studies assuming a periodically fluctuating food environment, and found that survival is a function of the period and amplitude. The results indicate that the margins for these parameters are unrealistically small.

Currently, we are studying the behavior of the DEB model with a periodically variable food environment in a systematical way. We use a few target species, among which is the marine mussel Mytilus edulis, that have been properly parameterized, and will study other species through body size scaling relationships, which are part of the model. For a singularly periodically variable food environment, we have been able to derive the environmental conditions granting long-term survival from food shortage, and we have also derived analytical solutions of the long-term dynamics of the state equations. Figure 2 exemplifies some of the model's behavior in a periodically variable food environment. It shows how ultimate peak values of energy reserves depend on the period and the amplitude of food fluctuations. It also shows the boundary conditions for long-term survival from starvation.

In the future, we plan to study starvation behavior in an environment in which food fluctuates stochastically. We expect that model organisms in a stochastically variable environment will be more vulnerable than organisms in a periodic environment. Due to its complexity, this part will be analyzed mostly with numerical studies.

Subsequently, depending on the outcomes of research, we will formulate and test alternative assumptions about energy expenditures during starvation conditions. An organism has in principle two options in order to increase its survival potential during starvation: it can regulate the mobilization of energy from reserves such that maintenance demands can be fulfilled; and it can reduce the requirements for maintenance by closing part of its physiological functions. Both options will potentially improve the realism of the model. The first option prevents a relatively fat animal from dying just because it has insufficient access to its reserves, a consequence of the model we have observed in our simulations. The second option acknowledges that many organisms have a resting stage in which part of the metabolic machinery has been shut down.

In addition to model refinements, we are investigating how toxicological parameters for different compounds can be related. Quantitative Structure Activity Relationship (QSAR) studies establish that factors influencing both toxicant accumulation and toxicant induced mortality depend on physical and chemical properties of a compound. Thus, if one compound shows a stronger effect than another, this may be because it accumulates easier, it is better retained in the animal, it is more toxic, or any combination of the above. In terms of our model, parameters for toxicant exchange and/or toxicity may be a function of physico-chemical properties of a toxicant. Currently we are exploring the uptake process. The system we are analyzing consists of mussels that take up PCBs via food and directly from the ambient. Variables are species of PCB and the fraction taken up with food. The results show a clear dependency between both variables and the octanol-water partitioning coefficient, but we have not yet modeled this dependency successfully. When we will have completed this analysis, we will study the dependency between the toxicity parameters and octanol-water partitioning coefficient, for which (again) the mussel Mytilus edulis will serve as model organism.