Simulation-Based Exploration of Quorum Sensing Triggered Resistance of Biofilms to Antibiotics.

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.

Evidence of autoinducer-dependent and -independent heterogeneous gene expression in Sinorhizobium fredii NGR234.

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.

Modelling and analysis of a gene-regulatory feed-forward loop with basal expression of the second regulator.

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.

Analysis of N-acylhomoserine lactone dynamics in continuous cultures of Pseudomonas putida IsoF by use of ELISA and UHPLC/qTOF-MS-derived measurements and mathematical models.

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.

Individual-based model for quorum sensing with background flow.

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.

Dynamics of AHL mediated quorum sensing under flow and non-flow conditions.

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.

Dynamics of glucose and insulin concentration connected to the ß-cell cycle: model development and analysis.

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 ß-cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the ß-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 ß-cell cycle. The interplay of glucose, insulin, and ß-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 ß-cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the ß-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 ß-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.

Spatial heterogeneity of autoinducer regulation systems.

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.

A mathematical model of quorum sensing regulated EPS production in biofilm communities.

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.

Evolutionary Stabilization of Cooperative Toxin Production through a Bacterium-Plasmid-Phage Interplay.

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.

Interplay of two quorum sensing regulation systems of Vibrio fischeri.

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).

Sensitivity of the quorum sensing system is achieved by low pass filtering.

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.

Transcription, intercellular variability and correlated random walk.

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.

Differential Equations Models to Study Quorum Sensing.

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.

Corrigendum: Why Quorum Sensing Controls Private Goods.

[This corrects the article on p. 885 in vol. 8, PMID: 28579979.].

Why Quorum Sensing Controls Private Goods.

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.

Selection of Functional Quorum Sensing Systems by Lysogenic Bacteriophages in Pseudomonas aeruginosa.

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.

Nonylphenol induced changes in trophic web structure of plankton analysed by multivariate statistical approaches.

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.

Core principles of bacterial autoinducer systems.

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.