After a description of the historical roots, this text describes how the research program unfolded and matured into a program on the metabolic organisation of life in the scale-spectrum from molecules to system earth. Some concrete intriguing open DEB problems are listed separately.
Two questions. It all started with my attempt to find answers to two given simple concrete questions:
First principles. Since the two questions had an environmental risk assessment context, the ability to make predictions for potential effects of toxicants was essential for situations that have not been studied experimentally. This means that the standard empirical methods were useless, since they do not allow such extrapolations beyond the range of observed conditions. This constrained the quest for answers to methods that were based on first principles only.
Generalisations. It turned out that knowledge about energy budgets of individuals is essential to answer both questions, and that the way chemical compounds affect the budgets of individuals is vital for the evaluation of the consequences at higher levels of organisation. It appeared that many aspects of these energy budgets are not species-specific at all and apply to all species (micro-organisms, plants, animals). It also turned out that chemical compounds are just one of many factors (temperature, parasites) that modify properties of individuals * , and that there exists a unifying way to deal with such perturbations. Dynamic systems theory provided the proper context to capture how individuals cycle their way through life by changes in state variables, and how factors modify this by changes of individual-specific parameter values.
Extrapolations. The problem of specifying the model structure seems to be totally different from that of determining the values of its parameters. However, one of the most remarkable properties of the DEB theory is that the model structure has far-reaching implications for the co-variation of parameter values among species, especially if they belong to different species * . Similar rules also appeared to hold for the one-compartment model for toxico-kinetics and its modifications * * . These powerful rules are very useful for extrapolations of model predictions from one species of organism to another and from one chemical compound to another. The DEB theory may be unique in this respect.
Levels of organisation. By increasing the range of time-space scales that the theory covers, it became evident that each process has its characteristic scale at which it is most effective. In combination with the strategy to keep the models at the various time-space scales simple and consistent, a new research emphasis emerged of how to phase out particular processes and include other processes when walking up and down along the time-space scales. At both ends of the scale-spectrum hardly anything of the original model for individuals is visible, while it still plays a role in the background since individuals are the unit of selection in evolution and the survival machines of life.
Mathematical methodology. This quantitative research program required new mathematical and philosophical methodologies, and quite a few have been developed since its start, while many are still under development. Although the practical need for such methods has been the motivation to initiate their development, once brought into the beautiful abstract world of mathematics, they start an independent life in their own right and might get very different applications in the future.
Standard model. The simple situation of an isomorph with three life stages (embryo, juvenile, adult), one type of reserve, one type of structure that feeds on one type of food/resource is called the standard DEB model. Although its structure is now well established, recent conceptual progress has been made in finding a mechanism for the reserve dynamics * , which drives metabolism. We also found a simpler derivation of these kinetics and we can now obtain it as a consequence of the weak homeostasis assumption * . A formal reconstruction of the theory is now developed * , which will facilitate future extensions footed on a solid basis and improve the accessibility of the theory by people with other backgrounds. Last but but least, we developed a new non-destructive method to determine the entropy of living biomass *, , i.e. reserve and structure. This will enable us to test popular but wild claims as "life tends to maximise entropy production".
Auxiliary theory. Apart from progress in the core theory, we made progress * in auxiliary theory that links quantities that are easy to measure to DEB parameters. Most of the quantities that are easy to measure, such as body weight and respiration rates, have contributions from several processes, and are, therefore, not variables in explanatory models, such as the DEB model. Its variables and parameters, however, cannot be measured directly, which generates the need for auxiliary theory. Testing all possible aspects of the DEB theory to experimental data has always been a core topic. Since many popular empirical models turn out to be special cases of the DEB theory for particular situations, DEB theory has a substantial empirical support. However, the need for continued testing can never be completely satisfied.
Extended models for individuals. Meanwhile many extensions of the standard model have been developed, and some of them have matured as well. This includes
Classification. The newly developed theory for synthesizing units * classifies chemical compounds as substitutable or complementary, and transformations as sequential or parallel. Mixtures of these four classes turn out to be required to understand evolutionary aspects of symbiogenesis * and other complex transformations, such as co-metabolism in the biodegradation of mixtures of organic compounds * * .
Inhibition. By allowing binding probabilities to depend on what is already bound to synthesizing units, or replacing bounded substrates by newly arriving substrates, inhibition phenomena can be captured for application in adaptation and co-metabolism. These phenomena are of importance for e.g. remineralisation, the degradation of toxic compounds and the competition between substrates to partake in a transformation (think for instance of the use of reserve and structure for maintenance purposes * * ).
Handshaking. Within the context of DEB theory it does not make sense to model cellular metabolism directly in terms of interactions of all chemical compounds within the cell for the simple reason that that are too many of them. The strategy is to insert more layers of organisation first by delineating a limited number of metabolic modules (such as the tricarboxylic acid (TCA) cycle, or the glycolysis), with limited interactions. What happens within these modules is then linked to the communication between the modules via handshaking protocols. It turned out that a simple handshaking protocol for the communication of the enzymes of the TCA cycle is sufficient to cover exactly the varying needs of the cell for building-blocks-providing intermediary metabolites and energy-providing ATP * .
Animal behaviour. From an abstract point of view, enzyme-mediated transformation rates of chemical compounds are dominated by the time budget of enzyme molecules and their ability to parallelize several types of behaviour, such as binding various substrates simultaneously. This problem has abstract similarities with modelling the behaviour of organisms, which offers the possibility to use the theory of synthesizing units for animal behaviour, and study e.g. how social interactions affect feeding * . It is no coincidence that the Michaelis-Menten expression for simple enzyme-mediated transformations is identical to the Holling type II functional response for animal feeding. A richer behavioural repertoire modifies these simple expressions. Several of these extensions have been developed, and many more become available in the near future.
Stochasticity. Behaviour is an important source of stochasticity of biological systems, which combines nicely with the setup of theory for synthesizing units in terms of stochastic processes * . This is especially important for small numbers * . The density of both molecules of any particular chemical species in a cell, and individuals of any particular type (species, age, gender) is typically low, which calls for the inclusion of stochasticity. We only started to explore this line of reasoning. It typically requires a complete reformulation of existing stochastic models, because they are inconsistent with DEB theory, and e.g. ignore energy and mass conservation, or dependences between difference processes that complicate model properties.
System earth. The ultimate goal of the DEB research program is to link phenomena at system earth level to that at the molecular level via a long chain of intermediate levels of organisation. Climate change provides some motivation to study this level of organisation, but it is also of fundamental interest in itself. Since the dynamics of green-house gasses relate to the water and carbon cycles * * , and these cycles are linked to the various nutrient cycles, this calls for the development of an integrated biogeochemical climate modelling, where transport processes play an important role. The role of calcification * * , the rock cycle and continental drift in nutrient recycling brings in geological and biological components in climate models at an evolutionary time scale. Although the DEB model of individuals plays no direct role at this level, it still does do indirectly by specifying the activity of organisms in a varying environment, and in the coupling of the various cycles. Moreover, quite a few of its basic principles, such as mass and energy conservation and surface area-volume interactions equally apply at system earth level. This makes it interesting to study how the DEB theory can contribute to this level of organisation.
Evolution. The increase in spatial scale to the system earth level comes with an increase of time scale to that at which evolutionary change is operative. Adaptive dynamics provides a useful context to study speciation and self-organisation at the ecosystem level * * . The art of science here is to simplify DEB-based model formulations enough and/or to develop the methodology of adaptive dynamics enough to link these complementary two lines of reasoning. Spatial structure turned out to play a crucial role here * * * not by providing barriers in genetic exchange, however, but by creating differences in local environmental conditions. Many traditionally studied phenomena, such at the optimisation of life history traits * * * , the evolutionary increase of body size in animals, and the link between body size and geographical distribution * ask for a planetary context. I expect further progress in the contribution of DEB theory in this field.
Ecotoxicology. Applications in ecotoxicity remained on the agenda since the start of the DEB program; they all rest on the idea that effects relate to internal concentrations of compounds (so we have to consider availability, toxico-kinetic and transformation modules * * ), and the DEB model specifies the parameters that can potentially be affected by the compound * . The analysis of results of standardised bioassays is a basic result * * * * , but where the applications really become powerful is in the evaluation of effects when concentrations of toxicants vary in time * * , when compounds interact with the physiology of the organism * * , when we have mixtures of compounds * or want to make the step from effects on individuals to that on populations * * * or other types of extrapolation * . We started to study effects at the ecosystem level * . The availability of the required experimental data is here a limiting factor in the further development.
Fisheries/aquaculture. A very nice recent development in the application of DEB theory is by a group of people that is active in fisheries * * * * * and aquaculture: Aquadeb. Their primary focus is on the eco-physiology of fish and molluscs, both in aquaculture and in natural environments. This includes fundamental as well as ecotoxicological aspects. The group produced a special issue 2 of J. Sea Res. 56 (2006) on DEB applications, and plans for other special issue in 2009. They made remarkable progress in testing the applicability of DEB theory, estimate parameter values, evaluate factors that modify performance in field (e.g. seasonal changes), work out species-specific rules for the handling of the reproduction buffer (which is linked to seasonal effects on body composition). The systematic build-up of parameter estimates for a variety of species will stimulate further theory on parameter values. E.g. do species that live in fresh-water have higher maintenance costs than those in seawater, because of the osmotic work they have to do?
Economics/sustainable developments. Economic systems share many features with biological systems, and quite a few DEB concepts turned out to be applicable in this context * . The similarities includes the interaction between the various levels of organisation, from firms and households, to national and supra-national economies. This development potentially leads to mechanistic models for economic phenomena. Agricultural applications, and optimisation of bio-production include more direct application of DEB theory, which links up to some applications in aquaculture. From a theoretical perspective it is nice to see how problems of optimizing bio-production have many similarities with that of minimizing sludge-production in sewage treatment plants, for instance.