Inferring physiological energetics of loggerhead turtle (Caretta caretta) from existing data using a general metabolic theory.

Loggerhead turtle is an endangered sea turtle species with a migratory lifestyle and worldwide distribution, experiencing markedly different habitats throughout its lifetime. Environmental conditions, especially food availability and temperature, constrain the acquisition and the use of available energy, thus affecting physiological processes such as growth, maturation, and reproduction. These physiological processes at the population level determine survival, fecundity, and ultimately the population growth rate-a key indicator of the success of conservation efforts. As a first step towards the comprehensive understanding of how environment shapes the physiology and the life cycle of a loggerhead turtle, we constructed a full life cycle model based on the principles of energy acquisition and utilization embedded in the Dynamic Energy Budget (DEB) theory. We adapted the standard DEB model using data from published and unpublished sources to obtain parameter estimates and model predictions that could be compared with data. The outcome was a successful mathematical description of ontogeny and life history traits of the loggerhead turtle. Some deviations between the model and the data existed (such as an earlier age at sexual maturity and faster growth of the post-hatchlings), yet probable causes for these deviations were found informative and discussed in great detail. Physiological traits such as the capacity to withstand starvation, trade-offs between reproduction and growth, and changes in the energy budget throughout the ontogeny were inferred from the model. The results offer new insights into physiology and ecology of loggerhead turtle with the potential to lead to novel approaches in conservation of this endangered species.

Yolky eggs prepare for metabolic acceleration.

Embryos convert some of their reserve into structure during development. At birth, enough must be left for further maturation, which implicitly defines the minimum amount of initial reserve. The maximum amount occurs if the mother is well-fed. Yolkiness is defined as the ratio of the maximum and the minimum amounts of initial reserve of an animal egg. Embryo development is frequently slower than can be expected on the basis of late juvenile and adult development. So development accelerates during the early juvenile stage, quantified as the ratio of the lengths at metamorphosis and at birth; during acceleration maximum specific assimilation and energy conductance increase with length. Parameters of the standard DEB model have now been estimated for some 165 species, and the goodness of fit with data is typically very good. These parameters have been used to quantify yolkiness and metabolic acceleration and a clear proportionality relationship resulted. I present some suggestions for explanations in the context of life histories.

Juvenile food limitation in standardized tests: a warning to ecotoxicologists.

Standard ecotoxicological tests are as simple as possible and food sources are mainly chosen for practical reasons. Since some organisms change their food preferences during the life-cycle, they might be food limited at some stage if we do not account for such a switch. As organisms tend to respond more sensitively to toxicant exposure under food limitation, the interpretation of test results may then be biased. Using a reformulation of the von Bertalanffy model to analyze growth data of the pond snail Lymnaea stagnalis, we detected food limitation in the early juvenile phase. The snails were held under conditions proposed for a standardized test protocol, which prescribes lettuce as food source. Additional experiments showed that juveniles grow considerably faster when fed with fish flakes. The model is based on Dynamic Energy Budget (DEB) theory, which allows for mechanistic interpretation of toxic effects in terms of changes in energy allocation. In a simulation study with the DEB model, we compared the effects of three hypothetical toxicants in different feeding situations. The initial food limitation when fed with lettuce always intensified the effect of the toxicants. When fed with fish flakes, the predicted effect of the toxicants was less pronounced. From this study, we conclude that (i) the proposed test conditions for L. stagnalis are not optimal, and require further investigation, (ii) fish flakes are a better food source for juvenile pond snails than lettuce, (iii) analyzing data with a mechanistic modeling approach such as DEB allows identifying deviations from constant conditions, (iv) being unaware of food limitation in the laboratory can lead to an overestimation of toxicity in ecotoxicological tests.

A full lifecycle bioenergetic model for bluefin tuna.

We formulated a full lifecycle bioenergetic model for bluefin tuna relying on the principles of Dynamic Energy Budget theory. Traditional bioenergetic models in fish research deduce energy input and utilization from observed growth and reproduction. In contrast, our model predicts growth and reproduction from food availability and temperature in the environment. We calibrated the model to emulate physiological characteristics of Pacific bluefin tuna (Thunnus orientalis, hereafter PBT), a species which has received considerable scientific attention due to its high economic value. Computer simulations suggest that (i) the main cause of different growth rates between cultivated and wild PBT is the difference in average body temperature of approximately 6.5°C, (ii) a well-fed PBT individual can spawn an average number of 9 batches per spawning season, (iii) food abundance experienced by wild PBT is rather constant and sufficiently high to provide energy for yearly reproductive cycle, (iv) energy in reserve is exceptionally small, causing the weight-length relationship of cultivated and wild PBT to be practically indistinguishable and suggesting that these fish are poorly equipped to deal with starvation, (v) accelerated growth rate of PBT larvae is connected to morphological changes prior to metamorphosis, while (vi) deceleration of growth rate in the early juvenile stage is related to efficiency of internal heat production. Based on these results, we discuss a number of physiological and ecological traits of PBT, including the reasons for high Feed Conversion Ratio recorded in bluefin tuna aquaculture.

Developmental energetics of zebrafish, Danio rerio.

Using zebrafish (Danio rerio) as a case study, we show that the maturity concept of Dynamic Energy Budget (DEB) theory is a useful metric for developmental state. Maturity does not depend on food or temperature contrary to age and to some extent length. We compile the maturity levels for each developmental milestone recorded in staging atlases. The analysis of feeding, growth, reproduction and aging patterns throughout the embryo, juvenile and adult life stages are well-captured by a simple extension of the standard DEB model and reveals that embryo development is slow relative to adults. A threefold acceleration of development occurs during the larval period. Moreover we demonstrate that growth and reproduction depend on food in predictable ways and their simultaneous observation is necessary to estimate parameters. We used data on diverse aspects of the energy budget simultaneously for parameter estimation using the covariation method. The lowest mean food intake level to initiate reproduction was found to be as high as 0.6 times the maximum level. The digestion efficiency for Tetramin™ was around 0.5, growth efficiency was just 0.7 and the value for the allocation fraction to soma (0.44) was close to the one that maximizes ultimate reproduction.

Dynamic energy budget theory restores coherence in biology.

We present the state of the art of the development of dynamic energy budget theory, and its expected developments in the near future within the molecular, physiological and ecological domains. The degree of formalization in the set-up of the theory, with its roots in chemistry, physics, thermodynamics, evolution and the consistent application of Occam's razor, is discussed. We place the various contributions in the theme issue within this theoretical setting, and sketch the scope of actual and potential applications.

Subcellular metabolic organization in the context of dynamic energy budget and biochemical systems theories.

The dynamic modelling of metabolic networks aims to describe the temporal evolution of metabolite concentrations in cells. This area has attracted increasing attention in recent years owing to the availability of high-throughput data and the general development of systems biology as a promising approach to study living organisms. Biochemical Systems Theory (BST) provides an accurate formalism to describe biological dynamic phenomena. However, knowledge about the molecular organization level, used in these models, is not enough to explain phenomena such as the driving forces of these metabolic networks. Dynamic Energy Budget (DEB) theory captures the quantitative aspects of the organization of metabolism at the organism level in a way that is non-species-specific. This imposes constraints on the sub-organismal organization that are not present in the bottom-up approach of systems biology. We use in vivo data of lactic acid bacteria under various conditions to compare some aspects of BST and DEB approaches. Due to the large number of parameters to be estimated in the BST model, we applied powerful parameter identification techniques. Both models fitted equally well, but the BST model employs more parameters. The DEB model uses similarities of processes under growth and no-growth conditions and under aerobic and anaerobic conditions, which reduce the number of parameters. This paper discusses some future directions for the integration of knowledge from these two rich and promising areas, working top-down and bottom-up simultaneously. This middle-out approach is expected to bring new ideas and insights to both areas in terms of describing how living organisms operate.

How far details are important in ecosystem modelling: the case of multi-limiting nutrients in phytoplankton-zooplankton interactions.

We try to answer the question of to what extent details in nutrient uptake and phytoplankton physiology matter for population and community dynamics. To this end, we study how two nutrients interact in limiting phytoplankton growth. A popular formulation uses a product-rule for nutrient uptake, which we compare with that on the basis of synthesizing units. We first fit different nutrient uptake models to a dataset and conclude that the quantitative differences between the models are small. Then we study the sensitivity of phytoplankton growth and zooplankton-phytoplankton interactions (ZPi) models to uptake formulations. Two population models are compared; they are based on different assumptions on the relation between nutrient uptake and phytoplankton growth. We find that the population and community models are sensitive to uptake formulations. According to the uptake formulation used in the ZPi models, qualitative differences can be observed. Indeed, although two models based on functions with similar shapes have close equilibria, these can differ in stability properties. Since stability involves the derivatives of formulas, even if two formulas provide close values, large numerical differences in the stability criterion may occur after derivation. We conclude that mechanistic details can be of importance for community modelling.

Stylized facts in microalgal growth: interpretation in a dynamic energy budget context.

A dynamic energy budget (DEB) model for microalgae is proposed. This model deviates from the standard DEB model as it needs more reserves to cope with the variation of assimilation pathways, requiring a different approach to growth based on the synthesizing unit (SU) theory for multiple substrates. It is shown that the model is able to accurately predict experimental data in constant and light-varying conditions with most of the parameter values taken directly from the literature. Also, model simulations are shown to be consistent with stylized facts (SFs) concerning NC ratio. These SFs are reinterpreted and the general conclusion is that all forcing variables (dilution rate, temperature and irradiance) impose changes in the nitrogen or carbon limitation status of the population, and consequently on reserve densities. Model predictions are also evaluated in comparison with SFs on chlorophyll concentration. It is proposed that an extra structure, more dependent on the nitrogen reserve, is required to accurately model chlorophyll dynamics. Finally, SFs concerning extracellular polymeric substances (EPSs) production by benthic diatoms are collected and interpreted and a formulation based on product synthesis and rejection flux is proposed for the EPSs production rate.

Prediction of daphnid survival after in situ exposure to complex mixtures.

We applied a mechanistically based model to predict the effects of complex mixtures as occurring in the field on the survival of Daphnia magna. We validated the model by comparing predicted survival with observed survival of in situ exposed laboratory cultured daphnids to polluted surface waters, in which over 90 chemical contaminants were measured. Using the chemical composition of the surface water at each sampling site, we calculated whether or not any of the individual or shared no effect concentrations were exceeded. If they were, we calculated the effect on survival. In 34 out of 37 cases (92%) we correctly predicted daphnid survival in surface waters. In the case of mortality we could also appoint the compound or group of compounds causing the effect. It is concluded that the proposed mechanistically based model accurately predicts effects on daphnids in the field, given the chemical composition of the water. Hence it is a powerful tool to link the chemical and ecological status of surface waters.

Modelling long-term ecotoxicological effects on an algal population under dynamic nutrient stress.

We study the effects of toxicants on the functioning of phototrophic unicellular organism (an algae) in a simple aquatic microcosm by applying a parameter-sparse model. The model allows us to study the interaction between ecological and toxicological effects. Nutrient stress and toxicant stress, together or alone, can cause extinction of the algal population. The modelled algae consume dissolved inorganic nitrogen (DIN) under surplus light and use it for growth and maintenance. Dead algal biomass is mineralized by bacterial activity, leading to nutrient recycling. The ecological model is coupled with a toxicity-module that describes the dependency of the algal growth and death rate on the toxicant concentration. Model parameter fitting is performed on experimental data from Liebig, M., Schmidt, G., Bontje, D., Kooi, B.W., Streck, G., Traunspurger, W., Knacker, T. [2008. Direct and indirect effects of pollutants on algae and algivorous ciliates in an aquatic indoor microcosm. Aquatic Toxicology 88, 102-110]. These experiments were especially designed to include nutrient limitation, nutrient recycling and long-term exposure to toxicants. The flagellate species Cryptomonas sp. was exposed to the herbicide prometryn and insecticide methyl parathion in semi-closed Erlenmeyers. Given the total limiting amount of nitrogen in the system, the estimated toxicant concentration at which a long-term steady population of algae goes extinct will be derived. We intend to use the results of this study to investigate the effects of ecological (environmental) and toxicological stresses on more realistic ecosystem structure and functioning.

What the egg can tell about its hen: embryonic development on the basis of dynamic energy budgets.

The energy cost of offspring is important in the conversion of resources allocated to reproduction to numbers of offspring, and in obtaining energy budget parameters from quantities that are easy to measure. An efficient numerical procedure is presented to obtain this cost for eggs and foetusses in the context of the dynamic energy budget theory, which specifies that birth occurs when maturity exceeds a threshold value and maternal effects determine the reserve density at birth. This paper extends previous work to arbitrary values of the ratio of the maturity and somatic maintenance costs. I discuss the body size scaling implications for the relative size and age at birth and conclude that the size at birth, contrary to the age at birth, covaries with the maintenance ratio. Apart from evolutionary adaptation of the maturity at birth, this covariation might explain some of the observed scatter in the relative length at birth. The theory can be used to evaluate the effects of the separation of cells in e.g. the two-cell stage of embryonic development, and of the removal of initial egg mass. If cell separation hardly affects energy parameters, body size scaling relationships imply that cell separation can only occur successfully in species with sufficiently large maximum body length (as adult); i.e. some two times that of Daphnia magna. Toxic compounds that increase the cost of synthesis of structure, decrease the allocation to reproduction indirectly via the life cycle, because food uptake is linked to size. They can also decrease the egg size, however, such that the reproduction rate is stimulated at low concentrations. The present theory offers a possible explanation for this well-known phenomenon.

A model to analyze effects of complex mixtures on survival.

In ecotoxicology there is a growing interest in effects of mixtures. The aim of this research was to develop a biology-based model that describes effects of mixtures on survival in time. The model works from the individual compounds in the mixture. Such an approach requires parameters for each individual compound in the mixture. For narcotic compounds we underpinned theoretical relations between the toxic parameters and the logK(ow) with experimental data by analyzing almost 300 datasets from the open literature, allowing a vast reduction in effort in the assessment of effects of mixtures. To illustrate the use of the model we simulated the effect of a mixture of 14 PAHs on the survival of Pimephales promelas. The simulation showed that due to the combined effect of the compounds in the mixture effects can be seen at very low concentrations.

From food-dependent statistics to metabolic parameters, a practical guide to the use of dynamic energy budget theory.

The standard model of the dynamic energy budget theory for metabolic organisation has variables and parameters that can be quantified using indirect methods only. We present new methods (and software) to extract food-independent parameter values of the energy budget from food-dependent quantities that are easy to observe, and so facilitate the practical application of the theory to enhance predictability and extrapolation. A natural sequence of 10 steps is discussed to obtain some compound parameters first, then the primary parameters, then the composition parameters and finally the thermodynamic parameters; this sequence matches a sequence of required data of increasing complexity which is discussed in detail. Many applications do not require knowledge of all parameters, and we discuss methods to extrapolate parameters from one species to another. The conversion of mass, volume and energy measures of biomass is discussed; these conversions are not trivial because biomass can change in chemical composition in particular ways thanks to different forms of homeostasis. We solve problems like "What would be the ultimate reproduction rate and the von Bertalanffy growth rate at a specific food level, given that we have measured these statistics at abundant food?" and "What would be the maximum incubation time, given the parameters of the von Bertalanffy growth curve?". We propose a new non-destructive method for quantifying the chemical potential and entropy of living reserve and structure, that can potentially change our ideas on the thermodynamic properties of life. We illustrate the methods using data on daphnids and molluscs.

Stabilization due to predator interference: comparison of different analysis approaches.

We study the influence of the particular form of the functional response in two-dimensional predator-prey models with respect to the stability of the nontrivial equilibrium. This equilibrium is stable between its appearance at a transcritical bifurcation and its destabilization at a Hopf bifurcation, giving rise to periodic behavior. Based on local bifurcation analysis, we introduce a classification of stabilizing effects. The classical Rosenzweig-MacArthur model can be classified as weakly stabilizing, undergoing the paradox of enrichment, while the well known Beddington-DeAngelis model can be classified as strongly stabilizing. Under certain conditions we obtain a complete stabilization, resulting in an avoidance of limit cycles. Both models, in their conventional formulation, are compared to a generalized, steady-state independent two-dimensional version of these models, based on a previously developed normalization method. We show explicitly how conventional and generalized models are related and how to interpret the results from the rather abstract stability analysis of generalized models.

From empirical patterns to theory: a formal metabolic theory of life.

The diversity of life on Earth raises the question of whether it is possible to have a single theoretical description of the quantitative aspects of the organization of metabolism for all organisms. However, similarities between organisms, such as von Bertalanffy's growth curve and Kleiber's law on metabolic rate, suggest that mechanisms that control the uptake and use of metabolites are common to all organisms. These and other widespread empirical patterns in biology should be the ultimate test for any metabolic theory that hopes for generality. The present study (i) collects empirical evidence on growth, stoichiometry, feeding, respiration and energy dissipation and exhibits it as stylized biological facts; (ii) formalizes assumptions and propositions in a metabolic theory that is fully consistent with the Dynamic Energy Budget theory; and (iii) proves that these assumptions and propositions are consistent with the stylized facts.

A new class of non-linear stochastic population models with mass conservation.

We study the effects of random feeding, growing and dying in a closed nutrient-limited producer/consumer system, in which nutrient is fully conserved, not only in the mean, but, most importantly, also across random events. More specifically, we relate these random effects to the closest deterministic models, and evaluate the importance of the various times scales that are involved. These stochastic models differ from deterministic ones not only in stochasticity, but they also have more details that involve shorter times scales. We tried to separate the effects of more detail from that of stochasticity. The producers have (nutrient) reserve and (body) structure, and so a variable chemical composition. The consumers have only structure, so a constant chemical composition. The conversion efficiency from producer to consumer, therefore, varies. The consumers use reserve and structure of the producers as complementary compounds, following the rules of Dynamic Energy Budget theory. Consumers die at constant specific rate and decompose instantaneously. Stochasticity is incorporated in the behaviour of the consumers, where the switches to handling and searching, as well as dying are Poissonian point events. We show that the stochastic model has one parameter more than the deterministic formulation without time scale separation for conversions between searching and handling consumers, which itself has one parameter more than the deterministic formulation with time scale separation for these conversions. These extra parameters are the contributions of a single individual producer and consumer to their densities, and the ratio of the two, respectively. The tendency to oscillate increases with the number of parameters. The focus bifurcation point has more relevance for the asymptotic behaviour of the stochastic model than the Hopf bifurcation point, since a randomly perturbed damped oscillation exhibits a behaviour similar to that of the stochastic limit cycle particularly near this bifurcation point. For total nutrient values below the focus bifurcation point, the system gradually becomes more confined to the direct neighbourhood of the isocline for which the producers do not change.

Scaling relationships based on partition coefficients and body sizes have similarities and interactions.

The LC(50) of compounds with a similar biological effect, at a given exposure period, is frequently plotted log-log against the octanol-water partition coefficient and a straight line is fitted for interpolation purposes. This is also frequently done for physiological properties, such as the weight-specific respiration rate, as function of the body weight of individuals. This paper focuses on the remarkable observation that theoretical explanations for these relationships also have strong similarities. Both can be understood as result of the covariation of the values of parameters of models of a particular type for the underlying processes, while this covariation follows logically from the model structure. The one-compartment model for the uptake and elimination of compounds by organisms is basic to the BioConcentration Factor (BCF), or the partition coefficient; the standard Dynamic Energy Budget model is basic to the (ultimate) body size. The BCF is the ratio of the uptake and the elimination rates; the maximum body length is the ratio of the assimilation (i.e. uptake of resources) and the maintenance (i.e. use of resources) rates. This paper discusses some shortcomings of descriptive approaches and conceptual aspects of theoretical explanations. The strength of the theory is in the combination of why metabolic transformation depends both on the BCF and the body size. We illustrate the application of the theory with several data sets from the literature.

Quantitative steps in the evolution of metabolic organisation as specified by the Dynamic Energy Budget theory.

The Dynamic Energy Budget (DEB) theory quantifies the metabolic organisation of organisms on the basis of mechanistically inspired assumptions. We here sketch a scenario for how its various modules, such as maintenance, storage dynamics, development, differentiation and life stages could have evolved since the beginning of life. We argue that the combination of homeostasis and maintenance induced the development of reserves and that subsequent increases in the maintenance costs came with increases of the reserve capacity. Life evolved from a multiple reserves - single structure system (prokaryotes, many protoctists) to systems with multiple reserves and two structures (plants) or single reserve and single structure (animals). This had profound consequences for the possible effects of temperature on rates. We present an alternative explanation for what became known as the down-regulation of maintenance at high growth rates in microorganisms; the density of the limiting reserve increases with the growth rate, and reserves do not require maintenance while structure-specific maintenance costs are independent of the growth rate. This is also the mechanism behind the variation of the respiration rate with body size among species. The DEB theory specifies reserve dynamics on the basis of the requirements of weak homeostasis and partitionability. We here present a new and simple mechanism for this dynamics which accounts for the rejection of mobilised reserve by busy maintenance/growth machinery. This module, like quite a few other modules of DEB theory, uses the theory of Synthesising Units; we review recent progress in this field. The plasticity of membranes that evolved in early eukaryotes is a major step forward in metabolic evolution; we discuss quantitative aspects of the efficiency of phagocytosis relative to the excretion of digestive enzymes to illustrate its importance. Some processes of adaptation and gene expression can be understood in terms of allocation linked to the relative workload of metabolic modules in (unicellular) prokaryotes and organs in (multicellular) eukaryotes. We argue that the evolution of demand systems can only be understood in the light of that of supply systems. We illustrate some important points with data from the literature.

Thermodynamics of organisms in the context of dynamic energy budget theory.

We carry out a thermodynamic analysis to an organism. It is applicable to any type of organism because (1) it is based on a thermodynamic formalism applicable to all open thermodynamic systems and (2) uses a general model to describe the internal structure of the organism--the dynamic energy budget (DEB) model. Our results on the thermodynamics of DEB organisms are the following. (1) Thermodynamic constraints for the following types of organisms: (a) aerobic and exothermic, (b) anaerobic and exothermic, and (c) anaerobic and endothermic; showing that anaerobic organisms have a higher thermodynamic flexibility. (2) A way to compute the changes in the enthalpy and in the entropy of living biomass that accompany changes in growth rate solving the problem of evaluating the thermodynamic properties of biomass as a function of the amount of reserves. (3) Two expressions for Thornton's coefficient that explain its experimental variability and theoretically underpin its use in metabolic studies. (4) A mechanism that organisms in non-steady-state use to rid themselves of internal entropy production: "dilution of entropy production by growth." To demonstrate the practical applicability of DEB theory to quantify thermodynamic changes in organisms we use published data on Klebsiella aerogenes growing aerobically in a continuous culture. We obtain different values for molar entropies of the reserve and the structure of Klebsiella aerogenes proving that the reserve density concept of DEB theory is essential in discussions concerning (a) the relationship between organization and entropy and (b) the mechanism of storing entropy in new biomass. Additionally, our results suggest that the entropy of dead biomass is significantly different from the entropy of living biomass.