Plasticity of circadian clocks and consequences for metabolism.

The increased prevalence of metabolic disorders and obesity in modern society, together with the widespread use of artificial light at night, have led researchers to investigate whether altered patterns of light exposure contribute to metabolic disorders. This article discusses the experimental evidence that perturbed environmental cycles induce rhythm disorders in the circadian system, thus leading to metabolic disorders. This notion is generally supported by animal studies. Distorted environmental cycles, including continuous exposure to light, affect the neuronal organization of the central circadian pacemaker in the suprachiasmatic nucleus (SCN), its waveform and amplitude of the rhythm in electrical activity. Moreover, repeated exposure to a shifted light cycle or the application of dim light at night are environmental cues that cause a change in SCN function. The effects on the SCN waveform are the result of changes in synchronization among the SCN's neuronal cell population, which lead consistently to metabolic disturbances. Furthermore, we discuss the effects of sleep deprivation and the time of feeding on metabolism, as these factors are associated with exposure to disturbed environmental cycles. Finally, we suggest that these experimental studies reveal a causal relationship between the rhythm disorders and the metabolic disorders observed in epidemiological studies performed in humans.

BDNF Val66Met genotype modulates the effect of childhood adversity on subgenual anterior cingulate cortex volume in healthy subjects.

According to the neurotrophic hypothesis of depression, stress can lead to brain atrophy by modifying brain-derived neurotrophic factor (BDNF) levels. Given that BDNF secretion is affected by a common polymorphism (rs6265, Val66Met), which also is associated with depression, we investigated whether this polymorphism modifies the effect of childhood adversity (CA) on local gray matter (GM) volume in depression-relevant brain regions, using data from two large cohorts of healthy subjects. We included 568 healthy volunteers (aged 18-50 years, 63% female) in our study, for whom complete data were available, with magnetic resonance imaging data at 1.5 Tesla (N=275) or 3 Tesla (N=293). We used a whole brain optimized voxel-based morphometry (VBM) approach assessing genotype-dependent GM differences, with focus on the amygdala, hippocampus and medial prefrontal cortex (PFC; including anterior cingulate cortex (ACC) and orbitomedial PFC). CA was assessed using a validated questionnaire. In both cohorts, we found that BDNF methionine (Met)-allele carriers with a history of CA had significantly less GM in subgenual ACC (P<0.05) compared with Met-allele carriers without CA and Val/Val homozygotes with CA. No differences were found in hippocampus, amygdala and orbitomedial PFC. On the basis of our findings, we conclude that BDNF Met-allele carriers are particularly sensitive to CA. Given the key role of the subgenual ACC in emotion regulation, this finding provides an important mechanistic link between stress and BDNF on one hand and mood impairments on the other hand.

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.

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.

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.

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.

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.

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.

Hematopoietic α7 nicotinic acetylcholine receptor deficiency increases inflammation and platelet activation status, but does not aggravate atherosclerosis.

BACKGROUND: The autonomic nervous system attenuates inflammation through activation of the α7 nicotinic acetylcholine receptor (α7nAChR), a pathway termed the cholinergic anti-inflammatory reflex. Interestingly, α7nAChR is expressed on immune cells and platelets, both of which play a crucial role in the development of atherosclerosis. OBJECTIVE: To investigate the role of hematopoietic α7nAChR in inflammation and platelet function in atherosclerotic ldlr(-/-) mice and to identify its consequences for atherosclerotic lesion development. METHODS: Bone marrow from α7nAChR(-/-) mice or wild-type littermates was transplanted into irradiated ldlr(-/-) mice. After a recovery period of 8 weeks, the mice were fed an atherogenic Western-type diet for 7 weeks. RESULTS: Hematopoietic α7nAChR deficiency clearly increased the number of leukocytes in the peritoneum (2.6-fold, P < 0.001), blood (2.9-fold; P < 0.01), mesenteric lymph nodes (2.0-fold; P < 0.001) and spleen (2.2-fold; P < 0.01), indicative of an increased inflammatory status. Additionally, expression of inflammatory mediators was increased in peritoneal leukocytes (TNFα, 1.6-fold, P < 0.01; CRP, 1.8-fold, P < 0.01) as well as in the spleen (TNFα, 1.6-fold, P < 0.01). The lack of α7nAChR on platelets from these mice increased the expression of active integrin αIIb ß3 upon stimulation by ADP (1.9-fold, P < 0.01), indicating increased activation status, while incubation of human platelets with an α7nAChR agonist decreased aggregation (-35%, P < 0.05). Despite the large effects of hematopoietic α7nAChR deficiency on inflammatory status and platelet function, it did not affect atherosclerosis development or composition of lesions. CONCLUSIONS: Hematopoietic α7nAChR is important for attenuation of inflammatory responses and maintaining normal platelet reactivity, but loss of hematopoietic α7nAChR does not aggravate development of atherosclerosis.

Evoked potential measures of auditory cortical function and auditory comprehension in aphasia.

This study investigated the relation between severity of auditory comprehension impairment in aphasia and the functional integrity of the posterior superior temporal region as evaluated by middle- and long-latency auditory evoked potentials and dipole source analysis. AEPs were studied in 20 stroke patients and in age-matched controls. AEPs and language data were collected 1 year or more post onset, and were compared to performance early after onset. Patients were differentiated in a group with severe and a group with moderate to recovered auditory comprehension impairment. Significant asymmetries of auditory evoked dipole source potentials were more frequent in the severely impaired group. However, a severe auditory comprehension deficit was not incompatible with normal AEPs. The results confirm the importance of the posterior superior temporal region for auditory language comprehension, but the correlation between AEP asymmetry and auditory comprehension seems due to the close spatial relation of AEP generating substrate and posterior language area rather than to partial overlap. Dipole source analysis of AEPs proved to be a valuable method for the assessment of interhemispheric asymmetries, enhancing the sensitivity of AEPs to unilateral damage of auditory cortex.

The Synthesizing Unit as model for the stoichiometric fusion and branching of metabolic fluxes.

The Synthesizing Unit (SU) binds given numbers of substrate molecules of several types of substrate to produce a product molecule or set of product molecules. Irreversible binding results in relatively simple and explicit expressions for the rate of product formation. Reversible binding can be implemented with relative ease in the carrier-SU complex, where the products of a set of carriers (a special type of SU) serve as substrate for an SU or set of SUs. A simple and parameter sparse approximation is presented for the production rate of a generalized compound, i.e. a rich mixture of compounds that does not change in composition. An analysis of Droop's data on the growth of a haptophyte on phosphate and vitamin B(12) reserves illustrates the application of SUs.

Salmonella test: relation between mutagenicity and number of revertant colonies.

This paper describes a model that relates the actual effect measured in the Salmonella test, i.e., the number of revertant colonies, to the mutation rate induced by a stable test compound having no side effects and acting without a time-lag. A maximum-likelihood estimator for the mutation rate is derived. Furthermore some side effects (mortality, increase in generation time, other mutations) are included in more extensive models. Side effects can cause a non-linear dose-response relation. Factors delaying the effect of the compound lead to an apparently higher mutation rate if a higher histidine dose is applied or a smaller inoculum is used. Factors slowly decreasing the effect of the compound reverse this result. Secondary effects of the test compound on the bacteria result in a non-linear dose-response relationship.

Analysis of bioassays with time-varying concentrations.

In the analysis of ecotoxicological bioassays the concentration of the test compounds is assumed to be constant. In many situations this assumption is questionable, as various processes may cause a substantial decline in the concentration during exposure. This leads to difficulties in the estimation of parameters that characterise the toxicity of the test compound. As a solution to this problem, time-varying concentrations are often replaced by their mean values for the estimation of toxicity parameters. However, Monte-Carlo simulations show that this approach results in biased estimates of the toxicity parameters. As an alternative approach, we propose models to estimate one important toxicity parameter, the no effect concentration, in situations where the concentration of the compound varies in time. These models are extensions of the DEBtox model (Kooijman and Bedaux, 1996) which is based on biological assumptions about toxicokinetics and toxic effects. We also propose a new approach for the estimation of toxicity parameters for strongly accumulating non-metabolisable compounds. This approach does not require any kinetics assumption. Computer simulation and experimental data confirm the relevance of the different proposals.

Consequences of population models for the dynamics of food chains.

A class of bioenergetic ecological models is studied for the dynamics of food chains with a nutrient at the base. A constant influx rate of the nutrient and a constant efflux rate for all trophic levels is assumed. Starting point is a simple model where prey is converted into predator with a fixed efficiency. This model is extended by the introduction of maintenance and energy reserves at all trophic levels, with two state variables for each trophic level, biomass and reserve energy. Then the dynamics of each population are described by two ordinary differential equations. For all models the bifurcation diagram for the bi-trophic food chain is simple. There are three important regions; a region where the predator goes to extinction, a region where there is a stable equilibrium and a region where a stable limit cycle exists. Bifurcation diagrams for tritrophic food chains are more complicated. Flip bifurcation curves mark regions where complex dynamic behaviour (higher periodic limit cycles as well as chaotic attractors) can occur. We show numerically that Shil'nikov homoclinic orbits to saddle-focus equilibria exists. The codimension 1 continuations of these orbits form a 'skeleton' for a cascade of flip and tangent bifurcations. The bifurcation analysis facilitates the study of the consequences of the population model for the dynamic behaviour of a food chain. Although the predicted transient dynamics of a food chain may depend sensitively on the underlying model for the populations, the global picture of the bifurcation diagram for the different models is about the same.

Resistance of a food chain to invasion by a top predator.

We study the invasion of a top predator into a food chain in a chemostat. For each trophic level, a bioenergetic model is used in which maintenance and energy reserves are taken into account. Bifurcation analysis is performed on the set of nonlinear ordinary differential equations which describe the dynamic behaviour of the food chain. In this paper, we analyse how the ability of a top predator to invade the food chain depends on the values of two control parameters: the dilution rate and the concentration of the substrate in the input. We investigate invasion by studying the long-term behaviour after introduction of a small amount of top predator. To that end we look at the stability of the boundary attractors; equilibria, limit cycles as well as chaotic attractors using bifurcation analysis. It will be shown that the invasibility criterion is the positiveness of the Lyapunov exponent associated with the change of the biomass of the top predator. It appears that the region in the control parameter space where a predator can invade increases with its growth rate. The resulting system becomes more resistant to further invasion when the top predator grows faster. This implies that short food chains with moderate growth rate of the top predator are liable to be invaded by fast growing invaders which consume the top predator. There may be, however, biological constraints on the top predator's growth rate. Predators are generally larger than prey while larger organisms commonly grow slower. As a result, the growth rate generally decreases with the trophic level. This may enable short food chains to be resistant to invaders. We will relate these results to ecological community assembly and the debate on the length of food chains in nature.

Food chain dynamics in the chemostat.

The asymptotic behavior of a tri-trophic food chain model in the chemostat is studied. The Monod-Herbert growth model is used for all trophic levels. The analysis is carried out numerically, by finding both local and global bifurcations of equilibria and of limit cycles with respect to two chemostat control parameters: the dilution rate of the chemostat and the concentration of input substrate. It is shown that the bifurcation structure of the food chain model has much in common with the bifurcation structure of a one-dimensional map with two turning points. This map is used to explain how attractors are created and destroyed under variation of the bifurcation parameters. It is shown that low as well as high concentration of input substrate can lead to extinction of the highest trophic level.

Multiple attractors and boundary crises in a tri-trophic food chain.

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed also by relating them to their counterparts for a two-dimensional map which is invertible like the next-return map. In the global bifurcations two homoclinic or two heteroclinic orbits collide and disappear. In the food chain model two attractors coexist; a stable limit cycle where the top-predator is absent and an interior attractor. In addition there is a saddle cycle. The stable manifold of this limit cycle forms the basin boundary of the interior attractor. We will show that this boundary has a complicated structure when there are heteroclinic orbits from a saddle equilibrium to this saddle limit cycle. A homoclinic bifurcation to a saddle limit cycle will be associated with a boundary crisis where the chaotic attractor disappears suddenly when a bifurcation parameter is varied. Thus, similar to a tangent local bifurcation for equilibria or limit cycles, this homoclinic global bifurcation marks a region in the parameter space where the top-predator goes extinct. The 'Paradox of Enrichment' says that increasing the concentration of nutrient input can cause destabilization of the otherwise stable interior equilibrium of a bi-trophic food chain. For a tri-trophic food chain enrichment of the environment can even lead to extinction of the highest trophic level.

Numerical bifurcation analysis of a tri-trophic food web with omnivory.

We study the consequences of omnivory on the dynamic behaviour of a three species food web under chemostat conditions. The food web consists of a prey consuming a nutrient, a predator consuming a prey and an omnivore which preys on the predator and the prey. For each trophic level an ordinary differential equation describes the biomass density in the reactor. The hyperbolic functional response for single and multi prey species figures in the description of the trophic interactions. There are two limiting cases where the omnivore is a specialist; a food chain where the omnivore does not consume the prey and competition where the omnivore does not prey on the predator. We use bifurcation analysis to study the long-term dynamic behaviour for various degrees of omnivory. Attractors can be equilibria, limit cycles or chaotic behaviour depending on the control parameters of the chemostat. Often multiple attractor occur. In this paper we will discuss community assembly. That is, we analyze how the trophic structure of the food web evolves following invasion where a new invader is introduced one at the time. Generally, with an invasion, the invader settles itself and persists with all other species, however, the invader may also replace another species. We will show that the food web model has a global bifurcation, being a heteroclinic connection from a saddle equilibrium to a limit cycle of saddle type. This global bifurcation separates regions in the bifurcation diagram with different attractors to which the system evolves after invasion. To investigate the consequences of omnivory we will focus on invasion of the omnivore. This simplifies the analysis considerably, for the end-point of the assembly sequence is then unique. A weak interaction of the omnivore with the prey combined with a stronger interaction with the predator seems advantageous.