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Biomedical subjects

S A Kooijman

Publications and source records attributed to S A Kooijman.

At least 19 recordsLinked to original sources
PubMed2001

Quantitative aspects of metabolic organization: a discussion of concepts.

Metabolic organization of individual organisms follows simple quantitative rules that can be understood from basic physical chemical principles. Dynamic energy budget (DEB) theory identifies these rules, which quantify how individuals acquire and use energy and nutrients. The theory provides constraints on the metabolic organization of subcellular processes. Together with rules for interaction between individuals, it also provides a basis to understand population and ecosystem dynamics. The theory, therefore, links various levels of biological organization. It applies to all species of organisms and offers explanations for body-size scaling relationships of natural history parameters that are otherwise difficult to understand. A considerable number of popular empirical models turn out to be special cases of the DEB model, or very close numerical approximations. Strong and weak homeostasis and the partitionability of reserve kinetics are cornerstones of the theory and essential for understanding the evolution of metabolic organization.

Animals↗
PubMed2001

Iteroparous reproduction strategies and population dynamics.

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are derived for iteroparous populations. First, the governing equations are presented for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile period, and at specific equidistant ages, which are determined by the iteroparous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortality function. Mortality in the period between two reproductive events is assumed to be a continuous process where the death rate for the adults is a function of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the steady-state solution of the continuous-time formulation. Conclusions include that there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the ratio between the maximal age and the reproductive period) is fundamental to determining this convergence. When the vital ratio is rational, an equivalent discrete-time model for the population can be derived whose asymptotic dynamics are periodic and when there are a finite number of founder cohorts, the number of cohorts remains finite. When the ratio is an irrational number, effectively there is convergence to the steady-state age distribution. With a finite number of founder cohorts, the number of cohorts becomes countably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age distribution. The applicability in ecotoxicology of the population matrix model formulation for iteroparous populations is discussed.

Animals↗
PubMed2001

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.

Animals↗
PubMed2001

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.

Biological Assay↗
PubMed2000

Two parameters account for the flocculated growth of microbes in biodegradation assays.

Microbes in activated sludge tanks mostly occur in flocs rather than in cell suspensions. Flocculation results in a limited supply of substrate to the bacteria inside the flocs, which reduces the biodegradation rate of organic compounds by several orders of magnitude. This article presents a simple two-parameter extension of growth models for cell suspensions to account for the ensuing reduction of the degradation rate. The additional parameters represent floc size at division and diffusion length. The biomass of small flocs initially increases exponentially at a rate equal to that of cell suspensions. After this first phase, the growth rate gradually decreases and finally the radius becomes a linear function of time. At this time flocs are large and have a kernel of dead biomass. This kernel arises when the substrate concentration decreases below the threshold level at which cells are just able to pay their maintenance costs. We deduce an explicit approximative expression for the interdivision time of flocs, and thereby for the growth of flocculated microbial biomass at constant substrate concentrations. The model reveals that the effect of stirring on degradation rates occurs through a reduction of the floc size at division. The results can be applied in realistic biodegradation quantifications in activated sludge tanks as long as substrate concentrations change slowly.

Bioreactors↗
PubMed2000

A mathematical model for yeast respiro-fermentative physiology.

A mechanistic model is presented that describes the respiro-fermentative physiology of yeast. The model assumes the presence of multiple types of glucose carriers and multiple assimilation pathways. Respiro-fermentative physiology is explained by the mechanistic response of the different types of carriers and assimilation pathways on the substrate concentration. At low substrate concentrations, glucose is taken up mainly via a high affinity carrier with a low maximum uptake rate. At high substrate concentrations, this carrier becomes saturated and the main pathway for glucose uptake is via a low affinity carrier with a high maximum uptake rate. The price to pay for the high uptake rate is a lowered assimilation efficiency, resulting in a low biomass yield. Product formation occurs via the pathway with the high uptake rate. The model explains the link between substrate concentration and product formation generally observed in the literature on yeast and bacteria. Model parameter values are estimated by fitting data from the literature. The model distinguishes itself from other models in that it does not rely on the presence of switches, such as the 'critical dilution rate', or on the assumption that the respiratory capacity reaches its maximum during respiro-fermentative metabolism. The present theory is not designed exclusively for the phenomenon of respiro-fermentative physiology: it describes the degradation of substances by heterotrophic micro-organisms in general.

Carbon Dioxide↗
PubMed2000

The role of intracellular components in food chain dynamics.

The dynamics of a simple food web, including multiple substrates and predator-prey interactions, is studied. An individual-based model is presented that describes the intracellular composition of the biomass of each population with two components: reserves and structural biomass. The model describes the simultaneous uptake of multiple substrates via specific carriers and their assimilation into reserve energy via multiple assimilation pathways. The available energy is used for maintenance and growth. Parameters are estimated by curve-fitting data from the literature under the condition that the elemental balances and the enthalpy balances are met. The proposed model provides an adequate description of the macromolecular composition of biomass. The model is not too complicated to be of use in the study of food webs. The consequences of the presence of intracellular components in a food web on its long-term dynamics are investigated with bifurcation analysis.

Animals↗
PubMed1999

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.

Animals↗
PubMed1999

Discrete event versus continuous approach to reproduction in structured population dynamics.

The governing equations are derived for the dynamics of a population consisting of organisms which reproduce by laying one egg at the time, on the basis of a simple physiological model for the uptake and use of energy. Two life stages are assumed, the egg and the adult stage where the adults do not grow. These assumptions hold true, for instance, for rotifers. From the model for the life history of the individuals, a physiologically structured population model for a rotifer population is derived. On the basis of this discrete event reproduction population model a continuous reproduction population model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We show that for the calculation of the transient population dynamic behaviour after a step-wise change of the dilution rate, an age structure suffices, despite the size and energy structure used to describe the dynamics of the individuals. Aggregation of the continuous reproduction population model yields an approximate lumped parameter model in terms of delay differential equations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discuss the consequences of discrete event versus continuous reproduction. In both population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimentally observed lack of egg production shortly after the step change in the dilution rate of the chemostat.

Age Factors↗
PubMed1998

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.

Journal Article↗
PubMed1998

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.

Animals↗
PubMed1998

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.

Animals↗
PubMed1996

A generic toxicokinetic model for persistent lipophilic compounds in humans: an application to TCDD.

This paper discusses a toxicokinetic model describing the distribution of TCDD in the human body during a lifetime. The model divides the body into several physiological compartments, their weights being functions of age. Ingested TCDD is instantaneously distributed over all compartments according to their lipid content. The liver eliminates TCDD from the body by a first-order process. Intake depends on age, as estimated from food consumption survey data combined with data on TCDD concentrations in various foods. It is shown that historical changes in intake, due to changes in environmental concentrations and in dietary habits, should be taken into account as well. Elimination rate and bioavailability, the only unknown parameters in the model, were estimated by calibrating the model to human data on internal concentrations. The generic formulation of the model makes it suitable for slowly eliminated lipophilic compounds in general.

Aging↗
PubMed1993

Why it pays for bacteria to delete disused DNA and to maintain megaplasmids.

Genetic information for disused metabolic systems is easily lost. This can be understood on the basis of a mathematic model for the description of the growth of individual microbial cells. The essential features of the model are that the uptake of nutrients is proportional to the surface area of the cell and maintenance costs are proportional to the volume. This explains why disused genes are easily lost. Growth of the individual cell continues until DNA replication of the genome is completed. The consequence is that cells with a large genome size are bigger at the moment of cell division. This results in a less favourable surface to volume ratio, which has a negative influence on the population growth rate. This means that cells with a smaller genome size will have a selective advantage. In cells in which the total DNA is divided over several units which replicate simultaneously (e.g. a cell with more chromosomes or a cell with one chromosome and one or more megaplasmids) a high surface to volume ratio can be maintained. The great metabolic differences between phylogenetically strongly related bacteria are due to loss of genetic information for complex metabolic characters in order to maintain a small genome size and a favourable surface to volume ratio.

Bacteria↗
PubMed1993

Comparative kinetics of embryo development.

A model of embryo energetics was fitted to data from the literature for species as different as snails and mammals. The model is based on assumptions about energy uptake, storage and utilization. It describes the animal by two state variables: volume and energy storage. Embryo weight is taken to be proportional to volume, yolk weight to energy storage, and respiration rate to storage utilization rate. The fits were good, with minor deviations occurring only in the early phases of development. For altricial birds, good model fits were obtained, but the parameter values markedly differed from those of other species. We hypothesized that, due to an increase in energy utilization towards hatching, the temperature of the embryo increases. As a result, metabolic processes are accelerated. When this was taken into account, parameter values were obtained that correspond better with those of other animals.

Animals↗
PubMed1990

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.

Mathematics↗
PubMed1987

Concentrations of polycyclic hydrocarbons in airborne particles in The Netherlands and their correlation with mutagenicity.

The concentrations of 15 polycyclic aromatic hydrocarbons (PAH) were determined in ambient air particles sampled at four sites in an urban and industrialized area in The Netherlands, and at one site near the coast (generally upwind). The contributions of sources in the area to the background concentrations as measured at the coastal site, were investigated. The temporal and spatial variation of the PAH profile, i.e. the relative concentrations of the 15 individual PAH, were also investigated. Variation of the PAH profile was predominantly determined by volatility. The variation of the profile of the less-volatile PAH was small compared with the variation these PAH had in common. Slight indications for the influence of differing sources and chemical conversion on the profile were found. The role of chemical conversion was suggested by a linkage of the variation of the profile with differences in reactivity between the PAH. The similarity of the profiles at the background coastal site and at the sites influenced by local sources was striking. The PAH concentrations showed weak-to-moderate correlations with mutagenicity. The correlations increased if the results of samples taken during periods with wind from one sector were considered.

Air Pollutants↗