Biouptake modelling

KEY FACTORS AND CHALLENGES FOR FUTURE RESEARCH IN BIOUPTAKE MODELLING... 

The preceding sections have demonstrated the considerable quantitative understanding of biouptake that can be attained by models with a sound theoretical basis. We have shown solutions for a range of conditions, ranging from relatively simple limiting cases to more involved situations involving kinetically limited metal complex dissociation fluxes. In this section, we highlight key points that should be considered in future refinements of biouptake models. 

The finite kinetics of the adsorption/desorption steps at the interface have been extensively studied by Hudson and Morel [13,15]. A wealth of literature is available on dealing with such interfacial processes [94-96] and its inclusion in the biouptake model should be implemented when experimental evidence of its necessity arises. 

Modelling biouptake processes helps in the understanding of the key factors involved and their interconnection [1]. In this chapter, uptake is considered in a general sense, without distinction between nutrition or toxicity, in which several elementary processes come together, and among which we highlight diffusion, adsorption and internalisation [2-4], We show how the combination of the equations corresponding with a few elementary physical laws leads to a complex behaviour which can be physically relevant. Some reviews on the subject, from different perspectives, are available in the literature [2,5-7]. 

In principle, any kind of limitation of the medium (e.g. due to some kind of clustering in a zone) tends to diminish the individual uptake rate [31]. From the point of view of modelling, the breaking of the symmetry rapidly complicates the problem (see Chapter 3 in this volume). As an exception to the general rule of decreased uptake due to inter-cell competition, it has been shown [49] that biouptake through siderophore excretion is only viable for nonisolated cells. 

Modelling biouptake requires the judicious consideration and selection of the underlying physical phenomena responsible for the experimental observations. We have seen that three fundamental phenomena may play a key role in biouptake mass transfer, adsorption, and internalisation. The inclusion of additional phenomena or refinements (such as nonexcess ligand complexation, non-first-order kinetics, nonlinear isotherms, etc.) may be essential to describe certain cases, but they have handicaps, such as ... 

It should be stressed that it is at least theoretically possible to model concentrations of substances in abiotic compartments like sediments and water in a rather straightforward manner. It is often much more difficult to apply causal models for biological variables and predict biouptake and concentrations in plankton and fish, and it is very difficult indeed to model, especially to have good, validated... 

All of the factors listed in Fig. 9.4 (and many more) could, potentially, influence the spread and biouptake of a metal. A central problem in predictive modeling is to quantitatively rank the importance of such factors and derive models that enable predictions of the y-variable, which in this example represents the metal content in top predator, from as few as easily obtainable and as relevant x-vari-ables as possible. 

In more traditional ecosystem modeling, it is often a goal to include as many relationships (fluxes and compartments) as possible and describe the complex relationships in a logical, causal manner. If, on the contrary, one would like to predict about one or a few y-variables, it is evident that it may be very impractical, costly and laborious to use very big ecosystem models. This mixed model has been constructed first of all to interpret the results presented for Hg and Cs. It may also be used as a tool to simulate the spread and biouptake of metals in lake ecosystems more generally. The idea is not to include every possible process, but the crucial processes. Mixed models in this context are models that are based on both dynamic characteristics and empirical relationships (Hakanson 1991). There are several ways to link these two fundamentally different model approaches, and here we will give some examples. 

Fig. 9.4. The new mixed model for metals in lakes. Load (or dose) parameters are related to the input of metals to the lake (direct load and load from the catchment), the metal amount in the lake water is distributed into dissolved and particulate phases by the partition coefficient (Kd). Sedimentation is net sedimentation per unit of time (the calculation unit is set to 1 year for Hg and 1 month for Cs). The sensitivity parameters influence biouptake of metals from water to phytoplankton (but they may also be used in other contexts, e.g., to influence the Kd-values, as illustrated by the dotted line, or the rate of sedimentation). The biological or ecosystem variables include pelagic and benthic uptake, bioaccumulation and retention time in the five compartments (lake water, active sediments, phytoplankton, prey and predator fish). The ejfect parameter is the concentration of the metal in predatory fish (used for human consumption). One panel gives the calculation of concentrations, another the driving parameters (model variables should, preferably, not be altered for different lakes, while environmental variables must be altered for each lake). The arrows between these two panels illustrate the phytoplankton biomass submodel...

The focus will now be set on the role of (1) the partition coefficient, (2) a changing pH (related to liming), (3) differences in biouptake pattern (pelagic or benthic) and (4) differences in retention (turnover) in the biological compartments (a slower retention for Hg and a faster retention for Cs). All data on rates and model variables are given in Table 9.5, and interesting data on amounts and fluxes in Table 9.7. 

In the following simulations, the other sensitivity factors (color, total-P and morphometry) were kept constant and pH varied to simulate effects of limings on the biouptake of the two test substances, Hg and Cs. It is possible to apply a given dimensionless moderator on many rates and model variables. This is schematically illustrated in Fig. 9.6 by the dotted arrow from YpH to the partition coefficient, since the water chemical conditions (pH, alkalinity, etc.) could influence the way metals are bound to carrier particles. 

Figure 9.11 presents sensitivity tests to give further insights into how the model works. Figure 9.11 A and B show that the conditions during fallout are of crucial importance for the biouptake of Cs in fish, and that it is inefficient to reduce the Cs-concentration in fish by applying remedies after the fallout. In these simulations, this has been tested by increasing pH from 6.0 to 6.7 at month 36 (1 year after the fallout), month 30 and month 27.

There are great uncertainties concerning most biouptake and retention rates in dynamic models for metals in most types of aquatic environments. 

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