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Colicins are toxins produced and released by Enterobacteriaceae to kill competitors in the gut. While group A colicins employ a division of labor strategy to liberate the toxin into the environment via colicin-specific lysis, group B colicin systems lack cognate lysis genes. In Salmonella enterica serovar Typhimurium ( S. Tm), the group B colicin Ib (ColIb) is released by temperate phage-mediated bacteriolysis. Phage-mediated ColIb release promotes S. Tm fitness against competing Escherichia coli It remained unclear how prophage-mediated lysis is realized in a clonal population of ColIb producers and if prophages contribute to evolutionary stability of toxin release in S. Tm. Here, we show that prophage-mediated lysis occurs in an S. Tm subpopulation only, thereby introducing phenotypic heterogeneity to the system. We established a mathematical model to study the dynamic interplay of S. Tm, ColIb, and a temperate phage in the presence of a competing species. Using this model, we studied long-term evolution of phage lysis rates in a fluctuating infection scenario. This revealed that phage lysis evolves as bet-hedging strategy that maximizes phage spread, regardless of whether colicin is present or not. We conclude that the ColIb system, lacking its own lysis gene, is making use of the evolutionary stable phage strategy to be released. Prophage lysis genes are highly prevalent in nontyphoidal Salmonella genomes. This suggests that the release of ColIb by temperate phages is widespread. In conclusion, our findings shed new light on the evolution and ecology of group B colicin systems. IMPORTANCE Bacteria are excellent model organisms to study mechanisms of social evolution. The production of public goods, e.g., toxin release by cell lysis in clonal bacterial populations, is a frequently studied example of cooperative behavior. Here, we analyze evolutionary stabilization of toxin release by the enteric pathogen Salmonella The release of colicin Ib (ColIb), which is used by Salmonella to gain an edge against competing microbiota following infection, is coupled to bacterial lysis mediated by temperate phages. Here, we show that phage-dependent lysis and subsequent release of colicin and phage particles occurs only in part of the ColIb-expressing Salmonella population. This phenotypic heterogeneity in lysis, which represents an essential step in the temperate phage life cycle, has evolved as a bet-hedging strategy under fluctuating environments such as the gastrointestinal tract. Our findings suggest that prophages can thereby evolutionarily stabilize costly toxin release in bacterial populations., (Copyright © 2020 Spriewald et al.)

We present a mathematical model of biofilm response to antibiotics, controlled by a quorum sensing system that confers increased resistance. The model is a highly nonlinear system of partial differential equations that we investigate in computer simulations. Our results suggest that an adaptive, quorum sensing-controlled, mechanism to switch between modes of fast growth with little protection and protective modes of slow growth may confer benefits to biofilm populations. It enhances the formation of micro-niches in the inner regions of the biofilm in which bacteria are not easily reached by antibiotics. Whereas quorum sensing inhibitors can delay the onset of increased resistance, their advantage is lost after up-regulation. This emphasizes the importance of timing for treatment of biofilms with antibiotics.

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Quorum sensing (QS) in Pseudomonas aeruginosa coordinates the expression of virulence factors, some of which are used as public goods. Since their production is a cooperative behavior, it is susceptible to social cheating in which non-cooperative QS deficient mutants use the resources without investing in their production. Nevertheless, functional QS systems are abundant; hence, mechanisms regulating the amount of cheating should exist. Evidence that demonstrates a tight relationship between QS and the susceptibility of bacteria against the attack of lytic phages is increasing; nevertheless, the relationship between temperate phages and QS has been much less explored. Therefore, in this work, we studied the effects of having a functional QS system on the susceptibility to temperate bacteriophages and how this affects the bacterial and phage dynamics. We find that both experimentally and using mathematical models, that the lysogenic bacteriophages D3112 and JBD30 select QS-proficient P. aeruginosa phenotypes as compared to the QS-deficient mutants during competition experiments with mixed strain populations in vitro and in vivo in Galleria mellonella , in spite of the fact that both phages replicate better in the wild-type background. We show that this phenomenon restricts social cheating, and we propose that temperate phages may constitute an important selective pressure toward the conservation of bacterial QS.

Cell-cell communication, also termed quorum sensing (QS), is a widespread process that coordinates gene expression in bacterial populations. The generally accepted view is that QS optimizes the cell density-dependent benefit attained from cooperative behaviors, often in the form of secreted products referred to as "public goods." This view is challenged by an increasing number of cell-associated products or "private goods" reported to be under QS-control for which a collective benefit is not apparent. A prominent example is nucleoside hydrolase from Pseudomonas aeruginosa , a periplasmic enzyme that catabolizes adenosine. Several recent studies have shown that private goods can function to stabilize cooperation by co-regulated public goods, seemingly explaining their control by QS. Here we argue that this property is a by-product of selection for other benefits rather than an adaptation. Emphasizing ecophysiological context, we propose alternative explanations for the QS control of private goods. We suggest that the benefit attained from private goods is associated with high cell density, either because a relevant ecological condition correlates with density, or because the private good is, directly or indirectly, involved in cooperative behavior. Our analysis helps guide a systems approach to QS, with implications for antivirulence drug design and synthetic biology.

Bacterial communication is enabled through the collective release and sensing of signalling molecules in a process called quorum sensing. Cooperative processes can easily be destabilized by the appearance of cheaters, who contribute little or nothing at all to the production of common goods. This especially applies for planktonic cultures. In this study, we analyse the dynamics of bacterial quorum sensing and its evolutionary stability under two levels of cooperation, namely signal and enzyme production. The model accounts for mutation rates and switches between planktonic and biofilm state of growth. We present a mathematical approach to model these dynamics using age-dependent colony models. We explore the conditions under which cooperation is stable and find that spatial structuring can lead to long-term scenarios such as coexistence or bistability, depending on the non-linear combination of different parameters like death rates and production costs., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Metformin (MET) as an emerging contaminant has been detected in surface water and wastewater in numerous countries, due to insufficient retention in classical waste water treatment plants. In order to characterize the uptake of the compound during phytotreatment of waste water, a short term Pitman chamber experiment was carried out to assess the characteristics of MET uptake and transport by roots. Three different concentrations (0.5, 1.0 and 2.0 mmol L(-)(1)) were applied to cattail (Typha latifolia) and reed (Phragmites australis) roots which were used to investigate the uptake mechanism because they are frequently utilized in phytoremediation. In addition, quinidine was used as an inhibitor to assess the role of organic cation transporters (OCTs) in the uptake of MET by T. latifolia. The transport process of MET is different from carbamazepine (CBZ) and caffeine (CFN). In both T. latifolia and P. australis, the uptake processes were independent of initial concentrations. Quinidine, a known inhibitor of organic cation transporters, can significantly affect MET uptake by T. latifolia roots with inhibition ratios of 70-74%. Uptake into the root could be characterized by a linear model with R(2) values in the range of 0.881-0.999. Overall, the present study provides evidence that MET is taken up by plant roots and has the potential for subsequent translocation. OCTs could be one of the important pathways for MET uptake into the plant., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Background: Cell dispersal (or detachment) is part of the developmental cycle of microbial biofilms. It can be externally or internally induced, and manifests itself in discrete sloughing events, whereby many cells disperse in an instance, or in continuous slower dispersal of single cells. One suggested trigger of cell dispersal is quorum sensing, a cell-cell communication mechanism used to coordinate gene expression and behavior in groups based on population densities., Method: To better understand the interplay of colony growth and cell dispersal, we develop a dynamic, spatially extended mathematical model that includes biofilm growth, production of quorum sensing molecules, cell dispersal triggered by quorum sensing molecules, and re-attachment of cells. This is a highly nonlinear system of diffusion-reaction equations that we study in computer simulations., Results: Our results show that quorum sensing induced cell dispersal can be an efficient mechanism for bacteria to control the size of a biofilm colony, and at the same time enhance its downstream colonization potential. In fact we find that over the lifetime of a biofilm colony the majority of cells produced are lost into the aqueous phase, supporting the notion of biofilms as cell nurseries. We find that a single quorum sensing based mechanism can explain both, discrete dispersal events and continuous shedding of cells from a colony. Moreover, quorum sensing induced cell dispersal affects the structure and architecture of the biofilm, for example it might lead to the formation of hollow inner regions in a biofilm colony.

Summary: Autoinduction (AI), the response to self-produced chemical signals, is widespread in the bacterial world. This process controls vastly different target functions, such as luminescence, nutrient acquisition, and biofilm formation, in different ways and integrates additional environmental and physiological cues. This diversity raises questions about unifying principles that underlie all AI systems. Here, we suggest that such core principles exist. We argue that the general purpose of AI systems is the homeostatic control of costly cooperative behaviors, including, but not limited to, secreted public goods. First, costly behaviors require preassessment of their efficiency by cheaper AI signals, which we encapsulate in a hybrid "push-pull" model. The "push" factors cell density, diffusion, and spatial clustering determine when a behavior becomes effective. The relative importance of each factor depends on each species' individual ecological context and life history. In turn, "pull" factors, often stress cues that reduce the activation threshold, determine the cellular demand for the target behavior. Second, control is homeostatic because AI systems, either themselves or through accessory mechanisms, not only initiate but also maintain the efficiency of target behaviors. Third, AI-controlled behaviors, even seemingly noncooperative ones, are generally cooperative in nature, when interpreted in the appropriate ecological context. The escape of individual cells from biofilms, for example, may be viewed as an altruistic behavior that increases the fitness of the resident population by reducing starvation stress. The framework proposed here helps appropriately categorize AI-controlled behaviors and allows for a deeper understanding of their ecological and evolutionary functions., (Copyright © 2015, American Society for Microbiology. All Rights Reserved.)

Quorum sensing, a special kind of cell-cell communication, has originally been described for well-mixed homogeneous bacterial cultures. However, recent perception supports its ecological relevance for spatially heterogeneous distributed cells, like colonies and biofilms. New experimental techniques allow for single cell analysis under these conditions, which is crucial to understanding the effect of chemical gradients and intercell variations. Based on a reaction-diffusion system, we develop a method that drastically reduces the computational complexity of the model. In comparison to similar former approaches, handling and scaling is much easier. Via a suitable scaling, this approach leads to approximative algebraic equations for the stationary case. This approach can be easily used for numerical situations.

Efficient adaptation strategies to changing environmental conditions are essential for bacteria to survive and grow. Fundamental restructuring of their metabolism is usually mediated by corresponding gene regulation. Here, often several different environmental stimuli have to be integrated into a reasonable, energy-efficient response. Fast fluctuations and overshooting have to be filtered out. The gene regulatory network for the anaerobic adaptation of the pathogenic bacterium Pseudomonas aeruginosa is organized as a feed-forward loop (FFL), which is a three-gene network motif composed of two transcription factors (Anr for oxygen, NarxL for nitrate) and one target (Nar for nitrate reductase). The upstream transcription factor (Anr) induces the downstream transcription factor (NarXL). Both regulators act together positively by inducing the target (Nar) via a direct and indirect regulation path (coherent type-1 FFL). Since full promoter activity is only achieved when both transcription factors are present the target operon is expressed with a delay. Thus, in response to environmental stimuli (oxygen, nitrate), signals are mediated and processed in a way that short pulses are filtered out. In this study we analyze a special kind of FFL called FFLk by means of a family of ordinary differential equation models. The secondary FFL regulator (NarXL) is expressed constitutively but further induced in the presence of the upstream stimuli. This FFL modification has substantial influence on the response time and cost-benefit ratio mediated by environmental fluctuations. In order to find conditions where this regulatory network motif might be beneficial, we analyzed various models and environments. We describe the observed evolutional advantage of FFLk and its role in environmental adaptation and pathogenicity., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

In this interdisciplinary approach, the dynamics of production and degradation of the quorum sensing signal 3-oxo-decanoylhomoserine lactone were studied for continuous cultures of Pseudomonas putida IsoF. The signal concentrations were quantified over time by use of monoclonal antibodies and ELISA. The results were verified by use of ultra-high-performance liquid chromatography. By use of a mathematical model we derived quantitative values for non-induced and induced signal production rate per cell. It is worthy of note that we found rather constant values for different rates of dilution in the chemostat, and the values seemed close to those reported for batch cultures. Thus, the quorum-sensing system in P. putida IsoF is remarkably stable under different environmental conditions. In all chemostat experiments, the signal concentration decreased strongly after a peak, because emerging lactonase activity led to a lower concentration under steady-state conditions. This lactonase activity probably is quorum sensing-regulated. The potential ecological implication of such unique regulation is discussed.

Populations of genetically identical Sinorhizobium fredii NGR234 cells differ significantly in their expression profiles of autoinducer (AI)-dependent and AI-independent genes. Promoter fusions of the NGR234 AI synthase genes traI and ngrI showed high levels of phenotypic heterogeneity during growth in TY medium on a single-cell level. However, adding very high concentrations of N-(3-oxooctanoyl-)-l-homoserine lactone resulted in a more homogeneous expression profile. Similarly, the lack of internally synthesized AIs in the background of the NGR234-ΔtraI or the NGR234-ΔngrI mutant resulted in a highly homogenous expression of the corresponding promoter fusions in the population. Expression studies with reporter fusions of the promoter regions of the quorum-quenching genes dlhR and qsdR1 and the type IV pilus gene cluster located on pNGR234b suggested that factors other than AI molecules affect NGR234 phenotypic heterogeneity. Further studies with root exudates and developing Arabidopsis thaliana seedlings provide the first evidence that plant root exudates have strong effects on the heterogeneity of AI synthase and quorum-quenching genes in NGR234. Therefore, plant-released octopine appears to play a key role in modulation of heterogeneous gene expression., (Copyright © 2014, American Society for Microbiology. All Rights Reserved.)

We consider the uptake of various carbon sources by microorganisms based on four fundamental assumptions: (1) the uptake of nutrient follows a saturation characteristics (2) substrate processing has a benefit but comes at costs of maintaining the process chain (3) substrate uptake is controlled and (4) evolution optimized the control of substrate uptake. These assumptions result in relatively simple mathematical models. In case of two substrates, our main finding is the following: Depending on the overall topology of the metabolic pathway, three different behavioral patterns can be identified. (1) both substrates are consumed at a time, (2) one substrate is preferred and represses the uptake of the other (catabolite repression), or (3) a cell feeds exclusively on one or the other substrate, possibly leading to a population that splits in two sub-populations, each of them specialized on one substrate only. Batch-culture and retentostat data of toluene, benzoate, and acetate uptake by Geobacter metallireducens are used to demonstrate that the model structure is suited for a quantitative description of uptake dynamics., (Copyright © 2014 Elsevier Inc. All rights reserved.)

Quorum sensing is a wide-spread mode of cell-cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for N cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration u of the signalling substance, coupled with N ODEs for the masses ai of the substance within each cell. The cells are balls of radius R in R3, and under some scaling assumptions we formally derive an effective system of N ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations.

We investigate the evolution of bet-hedging in a population that experiences a stochastically switching environment by means of adaptive dynamics. The aim is to extend known results to the situation at hand, and to deepen the understanding of the range of validity of these results. We find three different types of evolutionarily stable strategies (ESSs) depending on the frequency at which the environment changes: for a rapid change, a monomorphic phenotype adapted to the mean environment; for an intermediate range, a bimorphic bet-hedging phenotype; for slowly changing environments, a monomorphic phenotype adapted to the current environment. While the last result is only obtained by means of heuristic arguments and simulations, the first two results are based on the analysis of Lyapunov exponents for stochastically switching systems., (© 2013 Elsevier Ltd. All rights reserved.)

The non-essential cation caesium (Cs(+)) is assimilated by all organisms. Thus, anthropogenically released radiocaesium is of concern to agriculture. Cs(+) accumulates owing to its chemical similarity to the potassium ion (K(+)). The apparent lack of a Cs(+)-specific uptake mechanism has obstructed attempts to manipulate Cs(+) accumulation without causing pleiotropic effects. Here we show that the SNARE protein Sec22p/SEC22 specifically impacts Cs(+) accumulation in yeast and in plants. Loss of Saccharomyces cerevisiae Sec22p does not affect K(+) homeostasis, yet halves Cs(+) concentration compared with the wild type. Mathematical modelling of the uptake time course predicts a compromised vacuolar Cs(+) deposition in sec22Δ. Biochemical fractionation confirms this and indicates a new feature of Sec22p in enhancing non-selective cation deposition. A developmentally controlled loss-of-function mutant of the orthologous Arabidopsis thaliana SEC22 phenocopies the reduced Cs(+) uptake without affecting plant growth. This finding provides a new strategy to reduce radiocaesium entry into the food chain.

Background: Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the β-cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the β-cell cycle for the development of diabetes mellitus., Methods: This paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the β-cell cycle. The interplay of glucose, insulin, and β-cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability., Results: Our model shows the connection of glucose and insulin concentrations to the β-cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the β-cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose-insulin regulatory system showed in biological experiments., Conclusions: This work focus on modeling the physiological situation of the glucose-insulin regulatory system with a detailed consideration of the β-cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

Pseudomonas syringae is a gram-negative bacterium which lives on leaf surfaces. Its growth has been described using epifluorescence microscopy and image analysis; it was found to be growing in aggregates of a wide range of sizes. We develop a stochastic model to describe aggregate distribution and determine the mechanisms generating experimental observations. We found that a logistic birth-death model with migration (time-homogeneous Markov process) provides the best description of the observed data. We discuss how to analyze the joint distribution of the numbers of aggregates of different sizes at a given time and explore how to account for new aggregates being created, that is, the joint distribution of the family size statistics conditional on the total number of aggregates. We compute the first two moments. Through simulations we examine how the model's parameters affect the aggregate size distribution and successfully explain the quantitative experimental data available. Aggregation formation is thought to be the first step towards pathogenic behavior of this bacterium; understanding aggregate size distribution would prove useful to understand the switch from epiphytic to pathogenic behavior., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Quorum sensing (QS) describes the capability of microbes to communicate with each other by the aid of small molecules. Here we investigate the dynamics of QS-regulated gene expression induced by acylhomoserine lactones (AHLs) in Pseudomonas putida IsoF containing a green fluorescent protein-based AHL reporter. The fluorescence time course of individual colonies is monitored following the external addition of a defined AHL concentration to cells which had previously reached the QS-inactive state in AHL-free medium. Using a microfluidic setup the experiment is performed both under flow and non-flow conditions. We find that without supplying external AHL gene expression is induced without flow while flow suppresses the induction. Both without and with flow, at a low AHL concentration the fluorescence onset is significantly delayed while fluorescence starts to increase directly upon the addition of AHL at a high concentration. The differences between no flow and flow can be accounted for using a two-compartment model. This indicates AHL accumulation in a volume which is not affected by the flow. The experiments furthermore show significant cell-to-cell and colony-to-colony variability which is discussed in the context of a compartmentalized QS mechanism.

Autoinducer signals enable coordinated behaviour of bacterial populations, a phenomenon originally described as quorum sensing. Autoinducer systems are often controlled by environmental substances as nutrients or secondary metabolites (signals) from neighbouring organisms. In cell aggregates and biofilms gradients of signals and environmental substances emerge. Mathematical modelling is used to analyse the functioning of the system. We find that the autoinducer regulation network generates spatially heterogeneous behaviour, up to a kind of multicellularity-like division of work, especially under nutrient-controlled conditions. A hybrid push/pull concept is proposed to explain the ecological function. The analysis allows to explain hitherto seemingly contradicting experimental findings.

Background: Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to coordinate gene expression and behaviour in groups, based on population densities., Model: We mathematically model quorum sensing and EPS production in a growing biofilm under various environmental conditions, to study how a developing biofilm impacts quorum sensing, and conversely, how a biofilm is affected by quorum sensing-regulated EPS production. We investigate circumstances when using quorum-sensing regulated EPS production is a beneficial strategy for biofilm cells., Results: We find that biofilms that use quorum sensing to induce increased EPS production do not obtain the high cell populations of low-EPS producers, but can rapidly increase their volume to parallel high-EPS producers. Quorum sensing-induced EPS production allows a biofilm to switch behaviours, from a colonization mode (with an optimized growth rate), to a protection mode., Conclusions: A biofilm will benefit from using quorum sensing-induced EPS production if bacteria cells have the objective of acquiring a thick, protective layer of EPS, or if they wish to clog their environment with biomass as a means of securing nutrient supply and outcompeting other colonies in the channel, of their own or a different species.

The biocontrol strain Pseudomonas putida IsoF, which was isolated from a tomato rhizosphere, is a known N-acyl-homoserine lactone (AHL) producer with only one LuxI/LuxR-like quorum-sensing (QS) system. The production and degradation of AHLs were analysed in different growth phases of the bacterium. Using the analytical tools of ultra performance liquid chromatography and high resolution MS, it was possible to determine not only the various AHLs synthesized over time but also their degradation products. 3-oxo-decanoyl-homoserine lactone was found to be the dominant AHL, which reached its maximum in the early logarithmic growth phase. Although the pH of the medium was neutral, the AHLs were degraded thereafter rapidly to the corresponding homoserines and other metabolites. The proposed lactonase gene of P. putida IsoF could not be identified, because it is apparently quite different from hitherto described lactonases. The analytical data were used to calculate the rates and thresholds of AHL production by mathematical modelling, allowing quantitative predictions and a further understanding of the QS-based regulations in this bacterium. This study, combining microbiological, chemical and mathematical approaches, suggests that AHL degradation is an integral part of the whole autoinducer circuit of P. putida IsoF.

Background: The permeabilization of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the calcium-induced mitochondrial permeability transition. Upon Ca2+-uptake into mitochondria an increase in inner membrane permeability occurs by a yet unclear mechanism. This leads to a net water influx in the mitochondrial matrix, mitochondrial swelling, and finally the rupture of the outer membrane. Although already described more than thirty years ago, many unsolved questions surround this important biological phenomenon. Importantly, theoretical modeling of the mitochondrial permeability transition has only started recently and the existing mathematical models fail to characterize the swelling process throughout the whole time range., Results: We propose here a new mathematical approach to the mitochondrial permeability transition introducing a specific delay equation and resulting in an optimized representation of mitochondrial swelling. Our new model is in accordance with the experimentally determined course of volume increase throughout the whole swelling process, including its initial lag phase as well as its termination. From this new model biological consequences can be deduced, such as the confirmation of a positive feedback of mitochondrial swelling which linearly depends on the Ca2+-concentration, or a negative exponential dependence of the average swelling time on the Ca2+-concentration. Finally, our model can show an initial shrinking phase of mitochondria, which is often observed experimentally before the actual swelling starts., Conclusions: We present a model of the mitochondrial swelling kinetics. This model may be adapted and extended to diverse other inducing/inhibiting conditions or to mitochondria from other biological sources and thus may benefit a better understanding of the mitochondrial permeability transition.

We develop a simple model for the random distribution of a gene product. It is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a simple positive feedback loop is considered. The simplicity of the model allows for an explicit solution also in this setting. These findings in turn allow, e.g., for easy parameter scans. We find that bistable behavior translates into bimodal distributions. These theoretical findings are in line with experimental results.

Autoinducer sensing, also known as quorum sensing, is the communication of bacteria by autoinducer (small signaling molecules). Cells respond on extremely low concentrations of autoinducer: only one or two molecules per cell are sufficient. At this signal level a high degree of noise is inherent. We ask for the mechanism that is able to overcome the stochasticity of the signal. By means of a model and parameter fitting we show that the sensing module acts as a low pass filter, representing the biochemical equivalent of a moving average. It is shown that the system works most sensitive in the range of 0-50 nM autoinducer. Moreover, the time scale of the reaction depends on the signal strength in a crucial manner. Nonlinear feedback is able to further enhance the sensitivity. The biological implications of the low pass filter property are discussed.

Many bacteria developed a possibility to recognise aspects of their environment or to communicate with each other by chemical signals. An important strategy is the so-called quorum sensing (QS), a regulatory mechanism for the gene expression, where the bacteria measure their own cell density by means of this signalling pathway. One of the best-studied species using QS is the marine luminescent bacterium Vibrio fischeri which is considered here as a model organism. The two main regulatory pathways (lux and ain) are combined to a regulation system, the dynamics is modelled by an ODE system. This system is analysed thoroughly, considering stationary states, dynamical behaviour and the possible biological meaning of it. The influence of different parameter values on the behaviour is examined, the same basic system is able to reflect the peculiarities of different bacteria strains (respectively, their mutants).

We investigated effects of 17alpha-ethinylestradiol (EE) in vertebrate free 230 L still water microcosms. Zooplankton composition and physico-chemical variables were observed during 4 weeks of pre-application, 6 weeks of dosing via controlled release, and a 12 weeks post-treatment period. In the treated microcosms, time-weighted averages of EE concentration ranged between 7 and 220 ng/L during the dosing period, with concentration maxima up to 724 ng/L. EE exposure resulted in a decrease of species numbers and diversity (Shannon-Wiener, Simpson). Abundances of cladocerans, copepods, and, less unambiguously, rotifers declined. Strongest affected groups were the offspring of cladocerans and copepods and, on species level, the cladoceran species Daphnia longispina and Chydorus sphaericus as well as the rotifer species Keratella quadrata and Polyarthra sp. EE apparently affected the phosphate cycle as indicated by increased phosphate concentrations in the water. During post-treatment period, the treated microcosms recovered, but especially the highest treated microcosms did not fully re-approximate to the controls. Whereas EE affected cladocerans and copepods directly, shifts of rotifers may (partly) be caused indirectly, e.g. by competition with crustaceae. Although not providing an absolute proof, the traits of direct and indirect effects on different taxonomic groups and larval stages as well as the time course of the effects indicate that effects primarily resulted from endocrine activity of EE.

Effects of 17alpha-ethinylestradiol (EE) on phytoplankton were investigated in a lentic freshwater microcosm study. Treatment with EE caused a shift in the species composition as shown by a principle response curve. Whereas densities of Cyanophyceae, Dinophyceae, and Chrysophyceae increased, those of Conjugatophyceae and Cryptophyceae decreased. Furthermore, relative density of Chlorophyceae declined after EE treatment. The changes showed taxa-specific time dependencies. Some species, especially the cyanobacterium Cyanobium parvum, bloomed after the treatment. EE treatment promoted total abundance and biomass of phytoplankton. Although the number of species per microcosm increased, the diversity indices (Shannon-Wiener, Simpson) tended to lower values. The ecosystem only partly recovered during the investigated post-treatment period of 6 weeks. Probably at least the main effects were caused indirectly, i.e. via decrease of grazing zooplankton (crustaceans). The relation of EE to variation of phytoplankton composition was closer than those of other abiotic factors, indicating the relevance of its impact. EE also probably affected nutrients of the phytoplankton.

Quorum sensing faces evolutionary problems from non-producing or over-producing cheaters. Such problems are circumvented in diffusion sensing, an alternative explanation for quorum sensing. However, both explanations face the problems of signalling in complex environments such as the rhizosphere where, for example, the spatial distribution of cells can be more important for sensing than cell density, which we show by mathematical modelling. We argue that these conflicting concepts can be unified by a new hypothesis, efficiency sensing, and that some of the problems associated with signalling in complex environments, as well as the problem of maintaining honesty in signalling, can be avoided when the signalling cells grow in microcolonies.

Several bacterial taxa change their behavior if the population density exceeds a certain threshold. This phenomenon is the consequence of a communication system between the bacteria and is called quorum sensing (QS). Up to now, this phenomenon is mostly modeled at population level. However, new experimental techniques allow for single cell analysis. We introduce a modeling approach for the description of this QS system, including a discussion of the regulatory network and its bistable behavior. Based on this single-cell model we develop and analyze a spatially structured model for a cell population. Special attention is given to the scaling behavior w.r.t. the cell size (leading to an approximation theorem for stationary solutions) and its consequences for the interpretation of cell communication (QS versus diffusion sensing). Concluding, we apply the modeling approach to spatially structured experimental data.

Microcosm studies unveil relevant information in ecotoxicology. However, statistical evaluation of data gained from the different parts of the ecosystem often remain on unsatisfying, discretely level, e.g. separately for different species communities. A combination of different multivariate statistical methods enables an ecological interpretation of the found changes in zoo- and phytoplankton abundances in connection with the physico-chemical variables. To investigate the effects of nonylphenol (NP) on plankton communities, NP was continuously applicated in microcosms by controlled release. Plankton taxa were identified and quantified, various physico-chemical variables were measured. Maximum NP concentration ranged between 29 and 129 microg/L. The most important abiotic variable explaining both zoo- and phytoplankton abundances was NP concentration. NP primarily inhibited Crustaceae, especially juveniles. Cladocera and Copepoda abundances decreased. Rotatoria tend to increase, probably due to a decline of competition and predator pressure. Shifts in phytoplankton structure occurred with a time lag. Aggregating phytoplankton on class level did not show NP effects, whereas aggregating them according to feeding protection strategies did. Thus NP influences phytoplankton at least prevailingly indirectly via zooplankton. Zooplankton shifts led to species composition with different feeding preferences and strategies. Thereby the feeding pressure on phytoplankton changed. NP reorganized the plankton interrelation. Whereas without NP phytoplankton composition was dominated by Rotatoria, in the NP treated microcosms the Crustaceae unveiled highest explanatory power. The found effects were reversible in all but the highest treated microcosm. There are indications that the found effects were caused by endocrine activity of the chemical. Iteratively combining multivariate statistical methods with ecological and toxicological knowledge proved to provide a deeper insight into the mode of ecosystem disturbance by toxic substances.

The effects of 17 alpha-ethinylestradiol (EE), an endocrine disruptor, on zoo- and phytoplankton were studied in outdoor 230-L still-water microcosms. Cell density and biomass, diversity, and community composition were analyzed. Five microcosms were treated by controlled release for six weeks, three by direct application of EE. To investigate recovery, sampling was continued for four weeks after treatment. Most characteristics of the zooplankton were not unambiguously affected by EE. Only the relative density of copepods, especially of their larvae, decreased significantly after EE application. For phytoplankton, no unambiguous concentration- or toxodose-correlated effects on any biotic characteristics could be found. However, most properties of the phytoplankton deviated from those of controls, i.e. tended to be smaller (number of species per microcosm, biomass, cell density) or covered a wider range (diversity, evenness). PCA indicated a shift of species structure in the treated microcosms. This was supported by the species scores calculated by the principal response curve method, although the principal response curve itself showed no clear EE-correlated shifts. High variability within the biocenosis between microcosms and over time, probably because of disturbance of the ecosystem before starting of the test, might have superimposed EE-dependent effects.

The effects of nonylphenol (NP) on phytoplankton and periphyton were studied in 230 L outdoor microcosms. Phytoplankton cell density and biomass, phytoplankton and periphyton diversity, and assemblage composition were analyzed during a four-week preapplication period, followed by six weeks of NP treatment via controlled release and a six weeks postapplication period. Changes in species richness and diversity were not correlated with NP concentrations. However, changes in phytoplankton cell densities during the first week of the postapplication period were related to previous exposure. In the controls and the lowest-dosed microcosm. Conjugatophyceae constituted most of the biomass during the dosing and the postapplication period. In contrast, Dinophyceae dominated the biomass during the dosing and the postapplication period at higher NP concentrations. Principal response curves revealed changes in phytoplankton assemblage composition during the dosing and the postapplication period. Dinophyceae and most Cyanophyceae were more abundant at intermediate and higher NP concentrations, whereas Conjugatophyceae were less abundant compared to controls. Assemblages only partly recovered during the postapplication period. Periphyton taxon richness, diversity, and assemblage change was not related to NP concentrations. At the lowest and intermediate concentration, assemblages were significantly different from the controls and the higher concentrations, which were similar during the treatment period.