Mathematical Modelling of Bacterial Quorum Sensing: A Review

Single-cell level LasR-mediated quorum sensing response of Pseudomonas aeruginosa to pulses of signal molecules

Quorum sensing (QS) is a communication form between bacteria via small signal molecules that enables global gene regulation as a function of cell density. We applied a microfluidic mother machine to study the kinetics of the QS response of Pseudomonas aeruginosa bacteria to additions and withdrawals of signal molecules. We traced the fast buildup and the subsequent considerably slower decay of a population-level and single-cell-level QS response. We applied a mathematical model to explain the results quantitatively. We found significant heterogeneity in QS on the single-cell level, which may result from variations in quorum-controlled gene expression and protein degradation. Heterogeneity correlates with cell lineage history, too. We used single-cell data to define and quantitatively characterize the population-level quorum state. We found that the population-level QS response is well-defined. The buildup of the quorum is fast upon signal molecule addition. At the same time, its decay is much slower following signal withdrawal, and the quorum may be maintained for several hours in the absence of the signal. Furthermore, the quorum sensing response of the population was largely repeatable in subsequent pulses of signal molecules.

Unveiling bacterial communication with a MATLAB GUI implementing the diffusion-based quorum sensing model

Bacteria employ quorum sensing as a remarkable mechanism for coordinating behaviors and communicating within their communities. In this study, we introduce a MATLAB Graphical User Interface (GUI) that offers a versatile platform for exploring the dynamics of quorum sensing. Our computational framework allows for the assessment of quorum sensing, the investigation of parameter dependencies, and the prediction of minimum biofilm thickness required for its initiation. A pivotal observation from our simulations underscores the pivotal role of the diffusion coefficient in quorum sensing, surpassing the influence of bacterial cell dimensions. Varying the diffusion coefficient reveals significant fluctuations in autoinducer concentration, highlighting its centrality in shaping bacterial communication. Additionally, our GUI facilitates the prediction of the minimum biofilm thickness necessary to trigger quorum sensing, a parameter contingent on the diffusion coefficient. This feature provides valuable insights into spatial constraints governing quorum sensing initiation. The interplay between production rates and cell concentrations emerges as another critical facet of our study. We observe that higher production rates or cell concentrations expedite quorum sensing, underscoring the intricate relationship between cell communication and population dynamics in bacterial communities. While our simulations align with mathematical models reported in the literature, we acknowledge the complexity of living organisms, emphasizing the value of our GUI for standardizing results and facilitating early assessments of quorum sensing. This computational approach offers a window into the environmental conditions conducive to quorum sensing initiation, encompassing parameters such as the diffusion coefficient, cell concentration, and biofilm thickness. In conclusion, our MATLAB GUI serves as a versatile tool for understanding the diverse aspects of quorum sensing especially for non-biologists. The insights gained from this computational framework advance our understanding of bacterial communication, providing researchers with the means to explore diverse ecological contexts where quorum sensing plays a pivotal role.

Modeling the reactive oxygen species (ROS) wave in Chlamydomonas reinhardtii colonies

Reactive oxygen species (ROS) play a crucial role as signaling molecules in both plant and animal cells, enabling rapid responses to various stimuli. Among the many cellular mechanisms used to generate and transduce ROS signals, ROS-induced-ROS release (RIRR) is emerging as an important pathway involved in the responses of various multicellular and unicellular organisms to environmental stresses. In RIRR, one cellular compartment, organelle, or cell generates or releases ROS, triggering an increased ROS production and release by another compartment, organelle, or cell, thereby giving rise to a fast propagating ROS wave. This RIRR-based signal relay has been demonstrated to facilitate mitochondria-to-mitochondria communication in animal cells and long-distance systemic signaling in plants in response to biotic and abiotic stresses. More recently, it has been discovered that different unicellular microorganism communities also exhibit a RIRR cell-to-cell signaling process triggered by a localized stress treatment. However, the precise mechanism underlying the propagation of the ROS signal among cells within these unicellular communities remained elusive. In this study, we employed a reaction-diffusion model incorporating the RIRR mechanism to analyze the propagation of ROS-mediated signals. By effectively balancing production and scavenging processes, our model successfully reproduces the experimental ROS signal velocities observed in unicellular green algae (Chlamydomonas reinhardtii) colonies grown on agar plates, furthering our understanding of intercellular ROS communication.

Meta-analyzing the mechanism of pyrogenic biochar strengthens nitrogen removal performance in sulfur-driven autotrophic denitrification system: Evidence from metatranscriptomics

Sulfur-driven autotrophic denitrification (SAD) exhibits significant benefits in treating low carbon/nitrogen wastewater. This study presents an eco-friendly, cost-effective, and highly efficient method for enhancing nitrogen removal performance. The addition of biochar prepared at 300 °C (BC300) notably increased nitrogen removal efficiency by 31.60 %. BC300 concurrently enhanced electron production, the activities of the electron transfer system, and electron acceptors. With BC300, the ratio of NADH/NAD+ rose 2.00±0.11 times compared to without biochar, and the expression of NAD(P)H dehydrogenase genes was markedly up-regulated. In the electron transfer system, BC300 improved the electroactivity of extracellular polymeric substances and the activities of NADH dehydrogenase and complex III in intracellular electron transfer. Subsequently, electrons were directed into denitrification enzymes, where the nar, nir, nor, and nos related genes were highly expressed with BC300 addition. Significantly, BC300 activated the Clp and quorum sensing systems, positively influencing numerous gene expressions and microbial communication. Furthermore, the O%, H%, molar O/C, and aromaticity index in biochar were identified as crucial bioavailable parameters for enhancing nitrogen removal in the SAD process. This study not only confirms the application potential of biochar in SAD, but also advances our comprehension of its underlying mechanisms.

Cooperation in bioluminescence: understanding the role of autoinducers by a stochastic random resistor model

Quorum sensing is a communication mechanism adopted by different bacterial strains for the regulation of gene transcription. It takes place through the exchange of molecules called autoinducers. Bioluminescence is an emergent threshold phenomenon shown by some bacteria strains. Its precise relationship to quorum sensing is a debated topic, particularly regarding the role of the different autoinducers used by bacteria. In this paper, assuming a direct relationship between bioluminescence and quorum sensing, we investigate the role of multiple autoinducers in the bioluminescence response of Vibrio harveyi, considered as a model bioluminescent strain, due to its quorum sensing circuitry involving an array of three different autoinducers. Experiments on mutants of this bacterium, obtained by suppression of one or more autoinducers, reveal their relative non-trivial relevance and cooperative interaction patterns. The proposed analysis is implemented on a regular lattice, whose nodes represent microbial entities equipped with charges, which represent the ability to up/down regulate the gene expression. Quorum sensing results from a Coulomb-type field, produced by the charges. In analogy with random resistor network models, the lattice is permeated by an effective current which accounts for the amount and distribution of the charges. We propose that the presence of different autoinducers correspond to a different up/down regulation of gene expression, i.e., to a different way to account for the charges. Then, by introducing a modulation of the charge dependence into the current flowing within the network, we show that it is able to describe the bioluminescence exhibited by V. harveyi mutants. Furthermore, modulation of the charge dependence allows the interactions between the different autoinducers to be taken into account, providing a prediction regarding the data obtainable under specific growth conditions.

A review of mechanism analysis methods in multi-species biofilm of foodborne pathogens

Biofilms are an aggregation of microorganisms that have high resistance to antimicrobial agents. In the food industry, it has been widely studied that foodborne pathogens on both food surfaces and food-contact surfaces can form biofilms thereby threatening the safety of the food. In the natural environment, multi-species biofilms formed by more than two different microorganisms are abundant. In addition, the resistance of multi-species biofilms to antimicrobial agents is higher than that of mono-species biofilms. Therefore, studies to elucidate the mechanisms of multi-species biofilms formed by foodborne pathogens are still required in the food industry. In this review paper, we summarized the novel analytical methods studied to evaluate the mechanisms of multi-species biofilms formed by foodborne pathogens by dividing them into four categories: spatial distribution, bacterial interaction, extracellular polymeric substance production and quorum sensing analytical methods.

Parameters, architecture and emergent properties of the Pseudomonas aeruginosa LasI/LasR quorum-sensing circuit

Quorum sensing is a widespread process in bacteria that controls collective behaviours in response to cell density. Populations of cells coordinate gene expression through the perception of self-produced chemical signals. Although this process is well-characterized genetically and biochemically, quantitative information about network properties, including induction dynamics and steady-state behaviour, is scarce. Here we integrate experiments with mathematical modelling to quantitatively analyse the LasI/LasR quorum sensing pathway in the opportunistic pathogen Pseudomonas aeruginosa. We determine key kinetic parameters of the pathway and, using the parametrized model, show that quorum sensing behaves as a bistable hysteretic switch, with stable on and off states. We investigate the significance of feedback architecture and find that positive feedback on signal production is critical for induction dynamics and bistability, whereas positive feedback on receptor expression and negative feedback on signal production play a minor role. Taken together, our data-based modelling approach reveals fundamental and emergent properties of a bacterial quorum sensing circuit, and provides evidence that native quorum sensing can indeed function as the gene expression switch it is commonly perceived to be.

The aggregate distribution of Pseudomonas aeruginosa on biochar facilitates quorum sensing and biofilm formation

Biochar when applied into soil, together with soil clay minerals, may provide habitats for soil microbes and shift soil microbial community structure. Although several mechanisms have been proposed to explain the effects of biochar on microbial community, the impact of biochar on quorum sensing (QS) and QS-regulated behavior is poorly understood. In this study, we compared the effects of biochar and three common soil minerals (i.e., montmorillonite, kaolinite, and goethite) on QS and biofilm formation. Pseudomonas aeruginosa PAO1 with complete QS systems was selected as a model organism. Our results showed that biochar and goethite effectively promoted microbial QS and biofilm formation, while montmorillonite and kaolinite posed no significant effect. Live/Dead staining, SEM and density-dependent QS activity indicated that biochar was beneficial to cell viability maintenance and cell aggregations, which improved the efficiency of intercellular communications through QS. QS mutant strain experiments confirmed that biochar enhanced PAO1 biofilm formation by promoting QS. Goethite promoted biofilm formation with a different mechanism that cell debris induced by iron ions and positive charge on goethite surface provided raw materials for bacterial biofilm formation. Our findings provide evidence that the presence of biochar can enhance QS and biofilm formation through a feedforward loop of the QS system. This contributes to better understand biochar-mediated microbial cell to cell communications through QS.

Collective decision-making in Pseudomonas aeruginosa involves transient segregation of quorum-sensing activities across cells

A hallmark of bacterial sociality is that groups can coordinate cooperative actions through a cell-to-cell communication process called quorum sensing (QS). QS regulates key bacterial phenotypes such as virulence in infections and digestion of extracellular compounds in the environment. Although QS responses are typically studied as group-level phenotypes, it is unclear whether individuals coordinate their actions at the single-cell level or whether group phenotypes simply reflect the sum of their noisy members. Here, we studied the behavior of Pseudomonas aeruginosa individuals by tracking their temporal commitments to the two intertwined Las and Rhl-QS systems, from low to high population density. Using chromosomally integrated fluorescent gene reporters, we found that QS gene expression (signal, receptor, and cooperative exoproduct) was noisy with heterogeneity peaking during the build-up phase of QS. Moreover, we observed the formation of discrete subgroups of cells that transiently segregate into two gene expression states: low Las-receptor expressers that instantly activate exoproduct production and high Las-receptor expressers with delayed exoproduct production. Later, gene expression activities converged with all cells fully committing to QS. We developed general mathematical models to show that gene expression segregation can mechanistically be spurred by molecular resource limitations during the initiation phase of regulatory cascades such as QS. Moreover, our models indicate that gene expression segregation across cells can operate as a built-in brake enabling a temporary bet-hedging strategy in unpredictable environments. Altogether, our work reveals that studying the behavior of bacterial individuals is key to understanding emergent collective actions at the group level.

'Phase transitions' in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

Dynamics of the Protein Search for Targets on DNA in Quorum Sensing Cells

Quorum sensing (QS) is a bacterial cell-cell communication process that regulates gene expression. The search and binding of the AHL-bound LuxR-type proteins to specific sites on DNA in quorum sensing cells in Gram-negative bacteria is a complex process and has been theoretically investigated based on a discrete-state stochastic approach. It is shown that several factors such as the rate of formation of the AHL-bound LuxR protein within the cells and its dissociation to freely diffusing autoinducer molecule (AHL), the diffusion of the latter in and out of the cells, positive feedback loops, and the cell population density play an important role in the protein target search and can control the gene regulation processes. Physical-chemical arguments to explain these observations are presented. Our calculations of the dynamic properties are also supplemented by Monte Carlo computer simulations. Our theoretical model provides physical insights into the complex mechanisms of protein target search in quorum sensing cells.

Quorum-sensing induced transitions between bistable steady-states for a cell-bulk ODE-PDE model with lux intracellular kinetics

Intercellular signaling and communication are used by bacteria to regulate a variety of behaviors. In a type of cell-cell communication known as quorum sensing (QS), which is mediated by a diffusible signaling molecule called an autoinducer, bacteria can undergo sudden changes in their behavior at a colony-wide level when the density of cells exceeds a critical threshold. In mathematical models of QS behavior, these changes can include the switch-like emergence of intracellular oscillations through a Hopf bifurcation, or sudden transitions between bistable steady-states as a result of a saddle-node bifurcation of equilibria. As an example of this latter type of QS transition, we formulate and analyze a cell-bulk ODE-PDE model in a 2-D spatial domain that incorporates the prototypical LuxI/LuxR QS system for a collection of stationary bacterial cells, as modeled by small circular disks of a common radius with a cell membrane that is permeable only to the autoinducer. By using the method of matched asymptotic expansions, it is shown that the steady-state solutions for the cell-bulk model exhibit a saddle-node bifurcation structure. The linear stability of these branches of equilibria are determined from the analysis of a nonlinear matrix eigenvalue problem, called the globally coupled eigenvalue problem. The key role on QS behavior of a bulk degradation of the autoinducer field, which arises from either a Robin boundary condition on the domain boundary or from a constant bulk decay, is highlighted. With bulk degradation, it is shown analytically that the effect of coupling identical bacterial cells to the bulk autoinducer diffusion field is to create an effective bifurcation parameter that depends on the population of the colony, the bulk diffusivity, the membrane permeabilities, and the cell radius. QS transitions occur when this effective parameter passes through a saddle-node bifurcation point of the Lux ODE kinetics for an isolated cell. In the limit of a large but finite bulk diffusivity, it is shown that the cell-bulk system is well-approximated by a simpler ODE-DAE system. This reduced system, which is used to study the effect of cell location on QS behavior, is easily implemented for a large number of cells. Predictions from the asymptotic theory for QS transitions between bistable states are favorably compared with full numerical solutions of the cell-bulk ODE-PDE system.

Growth of Salmonella Enteritidis in the presence of quorum sensing signaling compounds produced by Pseudomonas aeruginosa

Quorum sensing (QS) can exist in food-related bacteria and potentially affect bacterial growth through acyl-homoserine lactones (AHLs). To verify the role of QS compounds in the cell-free supernatant, this study examined the effect of supernatant extracted from Pseudomonas aeruginosa culture on the growth kinetics of Salmonella Enteritidis. The results showed that the lag time (λ) of S. Enteritidis was apparently reduced (p < 0.05) under the influence of P. aeruginosa culture supernatant compared with the S. Enteritidis culture supernatant. HPLC-MS/MS test demonstrated that AHLs secreted by P. aeruginosa were mainly C14-HSL with a content of 85.71 μg/mL and a small amount of 3-oxo-C12-HSL. In addition, the commercially synthetic C14-HSL had positive effects on the growth of S. Enteritidis, confirming once again that the growth of S. Enteritidis was affected by AHL metabolized by other bacteria and the complexity of bacterial communication.

Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard

The study of biofilm formation is undoubtedly important due to micro-organisms forming a protected mode from the host defense mechanism, which may result in alteration in the host gene transcription and growth rate. A mathematical model of the nonlinear advection–diffusion–reaction equation has been studied for biofilm formation. In this paper, we present two novel non-standard finite difference schemes to obtain an approximate solution to the mathematical model of biofilm formation. One explicit non-standard finite difference scheme is proposed for biomass density equation and one property-conserving scheme for a coupled substrate–biomass system of equations. The nonlinear term in the mathematical model has been handled efficiently. The proposed schemes maintain dynamical consistency (positivity, boundedness, merging of colonies, biofilm annihilation), which is revealed through experimental observation. In order to verify the accuracy and effectiveness of our proposed schemes, we compare our results with those obtained from standard finite difference schemes and earlier known results in the literature. The proposed schemes (NSFD1 and NSFD2) show good performance. The NSFD2 scheme reveals that the processes of biofilm formation and nutritive substrate growth are intricately linked.

Wavelike propagation of quorum activation through a spatially distributed bacterial population under natural regulation

Many bacteria communicate using diffusible pheromone signals known as autoinducers. When the autoinducer concentration reaches a threshold, which requires a minimum population density or 'quorum', the bacteria activate specific gene regulatory pathways. Simple diffusion of autoinducer can activate quorum-dependent pathways in cells that are located at substantial distances from the secreting source. However, modeling has predicted that autoinducer diffusion, coupled with positive feedback regulation in autoinducer synthesis, could also allow a quorum-regulated behavior to spread more rapidly through a population by moving as a self-sustaining front at constant speed. Here we show that such propagation can occur in a population of bacteria whose quorum pathway operates under its own natural regulation. We find that in unstirred populations ofVibrio fischeri, introduction of autoinducer at one location triggers a wavelike traveling front of natural bioluminescence. The front moves with a well-defined speed ∼2.5 mm h^-1, eventually outrunning the slower diffusional spreading of the initial stimulus. Consistent with predictions from modeling, the wave travels until late in growth, when population-wide activation occurs due to basal autoinducer production. Subsequent rounds of waves, including waves propagating in the reverse direction, can also be observed late in the growth ofV.fischeriunder natural regulation. Using an engineered,lac-dependent strain, we show that local stimuli other than autoinducers can also elicit a self-sustaining, propagating response. Our data show that the wavelike dynamics predicted by simple mathematical models of quorum signaling are readily detected in bacterial populations functioning under their own natural regulation, and that other, more complex traveling phenomena are also present. Because a traveling wave can substantially increase the efficiency of intercellular communication over macroscopic distances, our data indicate that very efficient modes of communication over distance are available to unmixed populations ofV.fischeriand other microbes.

AHLs-mediated quorum sensing threshold and its response towards initial adhesion of wastewater biofilms

Quorum sensing (QS) plays a crucial role during initial biofilm formation, however the QS threshold and the response of biofilm formation towards N-acyl-homoserine lactones (AHLs) remains largely unknown due to the limitation of nondestructive online methods for monitoring bacterial adherence and the complexity of QS system, which limits the application of QS signal reagents in biofilm reactors. In this study, bacterial QS threshold and its response of biofilm formation to AHLs in purely cultured Sphingomonas rubra biofilm as well as in three different wastewater biofilms #1-3 were investigated via real time cell analysis (RTCA). The main perspective was to study the biomass adherence in response to 12 different forms of AHLs at different concentrations. Results showed that bacterial adhesion was significantly improved by exogenous AHLs with the maximum increase of 2.26-, 2.36-, 2.52-, and 2.80- times biomass production in the four respective biofilms. Although the preferred form of AHL differed for various biofilms, the long-chain AHLs (12-14 carbons) resulted in an overall improvement of bacterial adhesion due to their stronger hydrophobicity and hydrolysis resistance. In addition, bacterial QS threshold of AHLs was observed to have a wide range of concentration from 10 ng/L to 10 μg/L. Meanwhile, QS response time to AHLs also showed a significant difference in different biofilms. Biofilm #2 inoculated with bulking sludge had lower QS threshold of 10 ng/L and faster response to most AHLs that is less than 6 h. Thus, considering the improvement of biofilm adhesion by AHLs, 10 ng/L of C12-HSL, 10 ng/L of C12-HSL, and 10 ng/L of C6-HSL were preferentially selected for wastewater biofilms #1-3 respectively. Unexpectedly, adding high-concentration of AHLs detected in sludges did not significantly improved the bacterial adhesion. Infact the addition of these AHLs at low concentrations or even undetected concentrations substantially improved bacterial adhesion, which could be explained by bacterial communities composition. According to the Pearson correlation analysis, 62% of the top 50 most abundant genera in bacterial communities were significantly negatively related to the response time of multiple AHLs, representing their fast QS response. The QS bacteria, Dechloromonas and Nitrospira have fast QS response for C4-HSL and C8-HSL while, Comamonadaceae has fast QS response for 3OC8-HSL, 3OC10-HSL, 3OC12-HSL, and 3OC14-HSL. In contrast, the rest 38% of the top most abundant genera, such as Ferruginibacter, Hyphomicrobium, and Terrimonas quickly responded to only one AHL, showing significant negative relationship with the response time of C6-HSL. Overall, this study provides an effective and convenient means to select appropriate AHL reagents to promote bacterial adhesion in biofilm systems. Moreover, it also suggests that exogenous AHLs may be useful in improving the settling property of bulking sludge.

Emergent robustness of bacterial quorum sensing in fluid flow

Bacteria use intercellular signaling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment; consequently, they are affected by factors such as removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans. To understand how QS genetic architectures in cells promote appropriate population-level phenotypes throughout the bacterial life cycle requires knowledge of how these architectures determine the QS response in realistic spatiotemporally varying flow conditions. Here we develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. We predict that when a subset of the population meets these conditions, cell-level positive feedback promotes a robust collective response by overcoming flow-induced autoinducer concentration gradients. By accounting for a dynamic flow in our theory, we predict that positive feedback in cells acts as a low-pass filter at the population level in oscillatory flow, allowing a population to respond only to changes in flow that occur over slow enough timescales. Our theory is readily extendable and provides a framework for assessing the functional roles of diverse QS network architectures in realistic flow conditions.

Indwelling Device-Associated Biofilms in Critically Ill Cancer Patients-Study Protocol

Health care-associated infections are a leading cause of inpatient complications. Rapid pathogen detection/identification is a major challenge in sepsis management that highly influences the successful outcome. The current standard of microorganism identification relies on bacterial growth in culture, which has several limitations. Gene sequencing research has developed culture-independent techniques for microorganism identification, with the aim to improve etiological diagnosis and, therefore, to change sepsis outcome. A prospective, observational, non-interventional, single-center study was designed that assesses biofilm-associated pathogens in a specific subpopulation of septic critically ill cancer patients. Indwelling device samples will be collected in septic patients at the moment of the removal of the arterial catheter, central venous catheter, endotracheal tube and urinary catheter. Concomitantly, clinical data regarding 4 sites (nasal, pharyngeal, rectal and skin) of pathogen colonization at the time of hospital/intensive care admission will be collected. The present study aims to offer new insights into biofilm-associated infections and to evaluate the infection caused by catheter-specific and patient-specific biofilm-associated pathogens in association with the extent of colonization. The analysis relies on the two following detection/identification techniques: standard microbiological method and next generation sequencing (NGS). Retrospectively, the study will estimate the clinical value of the NGS-based detection and its virtual potential in changing patient management and outcome, notably in the subjects with missing sepsis source or lack of response to anti-infective treatment.

Interspecies evolutionary dynamics mediated by public goods in bacterial quorum sensing

Bacterial quorum sensing is the communication that takes place between bacteria as they secrete certain molecules into the intercellular medium that later get absorbed by the secreting cells themselves and by others. Depending on cell density, this uptake has the potential to alter gene expression and thereby affect global properties of the community. We consider the case of multiple bacterial species coexisting, referring to each one of them as a genotype and adopting the usual denomination of the molecules they collectively secrete as public goods. A crucial problem in this setting is characterizing the coevolution of genotypes as some of them secrete public goods (and pay the associated metabolic costs) while others do not but may nevertheless benefit from the available public goods. We introduce a network model to describe genotype interaction and evolution when genotype fitness depends on the production and uptake of public goods. The model comprises a random graph to summarize the possible evolutionary pathways the genotypes may take as they interact genetically with one another, and a system of coupled differential equations to characterize the behavior of genotype abundance in time. We study some simple variations of the model analytically and more complex variations computationally. Our results point to a simple trade-off affecting the long-term survival of those genotypes that do produce public goods. This trade-off involves, on the producer side, the impact of producing and that of absorbing the public good. On the nonproducer side, it involves the impact of absorbing the public good as well, now compounded by the molecular compatibility between the producer and the nonproducer. Depending on how these factors turn out, producers may or may not survive.

Eco-Evolutionary Effects of Bacterial Cooperation on Phage Therapy: An Unknown Risk?

If there is something we have learned from the antibiotic era, it is that indiscriminate use of a therapeutic agent without a clear understanding of its long-term evolutionary impact can have enormous health repercussions. This knowledge is particularly relevant when the therapeutic agents are remarkably adaptable and diverse biological entities capable of a plethora of interactions, most of which remain largely unexplored. Although phage therapy (PT) undoubtedly holds the potential to save lives, its current efficacy in case studies recalls the golden era of antibiotics, when these compounds were highly effective and the possibility of them becoming ineffective seemed remote. Safe PT schemes depend on our understanding of how phages interact with, and evolve in, highly complex environments. Here, we summarize and review emerging evidence in a commonly overlooked theme in PT: bacteria-phage interactions. In particular, we discuss the influence of quorum sensing (QS) on phage susceptibility, the consequent role of phages in modulating bacterial cooperation, and the potential implications of this relationship in PT, including how we can use this knowledge to inform PT strategies. We highlight that the influence of QS on phage susceptibility seems to be widespread but can have contrasting outcomes depending on the bacterial host, underscoring the need to thoroughly characterize this link in various bacterial models. Furthermore, we encourage researchers to exploit competition experiments, experimental evolution, and mathematical modeling to explore this relationship further in relevant infection models. Finally, we emphasize that long-term PT success requires research on phage ecology and evolution to inform the design of optimal therapeutic schemes.

Long-term antibacterial activity of a composite coating on titanium for dental implant application

Dental implants are the most innovative and superior treatment modality for tooth replacement. However, titanium implants still suffer from insufficient antibacterial capability and peri-implant diseases remain one of the most common and intractable complications. To prevent peri-implant diseases, a composite coating containing a new antibacterial agent, (Z-)-4-bromo-5-(bromomethylene)-2(5H)-furanone (BBF) was fabricated on titanium. This study was designed to investigate the antibacterial activity of the composite coating against two common peri-implant pathogens (Porphyromonas gingivalis and Actinobacillus actinomycetemcomitans). The morphology of the composite coating showed that BBF-loaded poly(L-lactic acid) nanospheres were well-distributed in the pores of the microarc oxidation coating, and cross-linked with each other and the wall pores by gelatin. A release study indicated that the antibacterial coating could sustain the release of BBF for 60 d, with a slight initial burst release occurring during the first 4 h. The antibacterial rate of the composite coating for adhering bacteria was the highest (over 97%) after 1 d and over 90% throughout a 30-day incubation period. The total fluorescence intensity of the composite coating was the lowest, and the vast majority of the fluorescence was red (dead bacteria). Moreover, real-time polymerase chain reaction analysis confirmed that the relative gene expression of the adherent bacteria on the composite coating was down-regulated. It was therefore concluded that the composite coating fabricated on titanium, which showed excellent and relatively long-term antibacterial activity against Porphyromonas gingivalis and Actinobacillus actinomycetemcomitans, is a potential and promising strategy to be applied on dental implants for the prevention of peri-implant diseases.

Numerical investigation of microbial quorum sensing under various flow conditions

Microorganisms efficiently coordinate phenotype expressions through a decision-making process known as quorum sensing (QS). We investigated QS amongst distinct, spatially distributed microbial aggregates under various flow conditions using a process-driven numerical model. Model simulations assess the conditions suitable for QS induction and quantify the importance of advective transport of signaling molecules. In addition, advection dilutes signaling molecules so that faster flow conditions require higher microbial densities, faster signal production rates, or higher sensitivities to signaling molecules to induce QS. However, autoinduction of signal production can substantially increase the transport distance of signaling molecules in both upstream and downstream directions. We present empirical approximations to the solutions of the advection–diffusion–reaction equation that describe the concentration profiles of signaling molecules for a wide range of flow and reaction rates. These empirical relationships, which predict the distribution of dissolved solutes along pore channels, allow to quantitatively estimate the effective communication distances amongst multiple microbial aggregates without further numerical simulations.

Quorum sensing for population-level control of bacteria and potential therapeutic applications

Quorum sensing (QS), a microbial cell-to-cell communication process, dynamically regulates a variety of metabolism and physiological activities. In this review, we provide an update on QS applications based on autoinducer molecules including acyl-homoserine lactones (AHLs), auto-inducing peptides (AIPs), autoinducer 2 (AI-2) and indole in population-level control of bacteria, and highlight the potential in developing novel clinical therapies. We summarize the development in the combination of various genetic circuits such as genetic oscillators, toggle switches and logic gates with AHL-based QS devices in Gram-negative bacteria. An overview is then offered to the state-of-the-art of much less researched applications of AIP-based QS devices with Gram-positive bacteria, followed by a review of the applications of AI-2 and indole based QS for interspecies communication among microbial communities. Building on these general-purpose QS applications, we highlight the disruptions and manipulations of QS devices as potential clinical therapies for diseases caused by biofilm formation, antibiotic resistance and the phage invasion. The last part of reviewed literature is dedicated to mathematical modelling for QS applications. Finally, the key challenges and future perspectives of QS applications in monoclonal synthetic biology and synthetic ecology are discussed.

Self-regulation versus social influence for promoting cooperation on networks

Cooperation is a relevant and controversial phenomenon in human societies. Indeed, although it is widely recognized essential for tackling social dilemmas, finding suitable policies for promoting cooperation can be arduous and expensive. More often, it is driven by pre-established schemas based on norms and punishments. To overcome this paradigm, we highlight the interplay between the influence of social interactions on networks and spontaneous self-regulating mechanisms on individuals behavior. We show that the presence of these mechanisms in a prisoner's dilemma game, may oppose the willingness of individuals to defect, thus allowing them to behave cooperatively, while interacting with others and taking conflicting decisions over time. These results are obtained by extending the Evolutionary Game Equations over Networks to account for self-regulating mechanisms. Specifically, we prove that players may partially or fully cooperate whether self-regulating mechanisms are sufficiently stronger than social pressure. The proposed model can explain unconditional cooperation (strong self-regulation) and unconditional defection (weak self-regulation). For intermediate self-regulation values, more complex behaviors are observed, such as mutual defection, recruiting (cooperate if others cooperate), exploitation of cooperators (defect if others cooperate) and altruism (cooperate if others defect). These phenomena result from dynamical transitions among different game structures, according to changes of system parameters and cooperation of neighboring players. Interestingly, we show that the topology of the network of connections among players is crucial when self-regulation, and the associated costs, are reasonably low. In particular, a population organized on a random network with a Scale-Free distribution of connections is more cooperative than on a network with an Erdös-Rényi distribution, and, in turn, with a regular one. These results highlight that social diversity, encoded within heterogeneous networks, is more effective for promoting cooperation.

Bacterial quorum sensing in complex and dynamically changing environments

Quorum sensing is a process of bacterial cell-to-cell chemical communication that relies on the production, detection and response to extracellular signalling molecules called autoinducers. Quorum sensing allows groups of bacteria to synchronously alter behaviour in response to changes in the population density and species composition of the vicinal community. Quorum-sensing-mediated communication is now understood to be the norm in the bacterial world. Elegant research has defined quorum-sensing components and their interactions, for the most part, under ideal and highly controlled conditions. Indeed, these seminal studies laid the foundations for the field. In this Review, we highlight new findings concerning how bacteria deploy quorum sensing in realistic scenarios that mimic nature. We focus on how quorums are detected and how quorum sensing controls group behaviours in complex and dynamically changing environments such as multi-species bacterial communities, in the presence of flow, in 3D non-uniform biofilms and in hosts during infection.

In-situ monitoring AHL-mediated quorum-sensing regulation of the initial phase of wastewater biofilm formation

Initial attachment plays an important role in biofilm formation in wastewater treatment processes. However, the initial attachment process mediated by N-acyl-homoserine lactones (AHLs) is difficult to be fully understood due to the lack of non-invasive and on-line investigation techniques. In this study, the AHL-regulated wastewater biofilm attachment was quantified using ultrasonic time-domain reflectometry (UTDR) as an in-situ and non-invasive monitoring technique. Results demonstrated that the reversible adhesion time in municipal and industrial wastewaters was significantly decreased in the presence of exogenous AHLs. Biofilm thickness in municipal and industrial wastewaters increased significantly with the addition of exogenous AHLs. Also, the addition of acylase delayed the initial biofilm formation (lengthened reversible adhesion time and decreased biofilm thickness and density). Compared with biofilm behavior in the presence of low concentrations of AHLs (4.92 ± 0.17 μg/L), both reversible adhesion time and biofilm thickness were not significantly increased (p > 0.05) with an increase in AHL concentration (9.75 ± 0.41 μg/L). Furthermore, the addition of exogenous AHLs resulted in significant changes in the attached bacterial community structures, in which both QS and quorum-quenching (QQ) bacteria were stimulated. The current work presents an effective approach to in-situ monitoring of the regulation of AHL-mediated QS in the initial attachment of biofilms, especially in the reversible adhesion process, which may provide a potential strategy to facilitate biofilm establishment in wastewater treatment processes.

Systematic analysis of lysine acetylome reveals potential functions of lysine acetylation in Shewanella baltica, the specific spoilage organism of aquatic products

Protein lysine acetylation is a major post-translational modification and plays a critical regulatory role in almost every aspect in both eukaryotes and prokaryotes, yet there have been no data on Shewanella baltica, which is one of the specific spoilage organism (SSO) of aquatic products. Here, we performed the first global acetylproteome analysis of S. baltica. 2929 lysine acetylation sites were identified in 1103 proteins, accounting for 26.1% of the total proteins which participate in a wide variety of biological processes, especially in the constituent of ribosome, the biosynthesis of aminoacyl-tRNA, the amino acids and fatty acid metabolism. Besides, 14 conserved acetylation motifs were detected in S. baltica. Notably, various directly or indirectly spoilage-related proteins were prevalently acetylated, including enzymes involved in the unsaturated fatty acids biosynthesis closely related to the cold adaptability, cold shock proteins, pivotal enzymes involved in the putrescine biosynthesis, and a LuxR-type protein in quorum sensing system. The acetylome analysis in Shewanella can supplement the database and provide new insight into uncovering the spoilage mechanisms of S. baltica. The provided dataset illuminates the potential role of reversible acetylation in S. baltica, and serves as an important resource for exploring the physiological role of lysine acetylation in prokaryotes. SIGNIFICANCE: The psychrotrophic nature and the ability of S. baltica to make good use of "habitat" nutrients explain its importance in spoilage of seafood stored at low temperatures. However, the underlying mechanism of spoilage potential from the perspective of protein post-translational modification was rarely studied. This work identifies the first comprehensive survey of a lysine acetylome in S. baltica and uncovers the involvement of lysine acetylation in the diverse biological processes, especially in the closely spoilage-related pathways. This study provides a resource for functional analysis of acetylated proteins and creates opportunities for in-depth elucidation of the physiological role of protein acetylation in Shewanella spp.

Agent-Based Modeling Demonstrates How Local Chemotactic Behavior Can Shape Biofilm Architecture

Bacteria are often found living in aggregated multicellular communities known as biofilms. Biofilms are three-dimensional structures that confer distinct physical and biological properties to the collective of cells living within them. We used agent-based modeling to explore whether local cellular interactions were sufficient to give rise to global structural features of biofilms. Specifically, we asked whether chemorepulsion from a self-produced quorum-sensing molecule, autoinducer-2 (AI-2), was sufficient to recapitulate biofilm growth and cellular organization observed for biofilms of Helicobacter pylori, a common bacterial resident of human stomachs. To carry out this modeling, we modified an existing platform, Individual-based Dynamics of Microbial Communities Simulator (iDynoMiCS), to incorporate three-dimensional chemotaxis, planktonic cells that could join or leave the biofilm structure, and cellular production of AI-2. We simulated biofilm growth of previously characterized H. pylori strains with various AI-2 production and sensing capacities. Using biologically plausible parameters, we were able to recapitulate both the variation in biofilm mass and cellular distributions observed with these strains. Specifically, the strains that were competent to chemotax away from AI-2 produced smaller and more heterogeneously spaced biofilms, whereas the AI-2 chemotaxis-defective strains produced larger and more homogeneously spaced biofilms. The model also provided new insights into the cellular demographics contributing to the biofilm patterning of each strain. Our analysis supports the idea that cellular interactions at small spatial and temporal scales are sufficient to give rise to larger-scale emergent properties of biofilms.IMPORTANCE Most bacteria exist in aggregated, three-dimensional structures called biofilms. Although biofilms play important ecological roles in natural and engineered settings, they can also pose societal problems, for example, when they grow in plumbing systems or on medical implants. Understanding the processes that promote the growth and disassembly of biofilms could lead to better strategies to manage these structures. We had previously shown that Helicobacter pylori bacteria are repulsed by high concentrations of a self-produced molecule, AI-2, and that H. pylori mutants deficient in AI-2 sensing form larger and more homogeneously spaced biofilms. Here, we used computer simulations of biofilm formation to show that local H. pylori behavior of repulsion from high AI-2 could explain the overall architecture of H. pylori biofilms. Our findings demonstrate that it is possible to change global biofilm organization by manipulating local cell behaviors, which suggests that simple strategies targeting cells at local scales could be useful for controlling biofilms in industrial and medical settings.

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

BACKGROUND

Quorum sensing drives biofilm formation in bacteria in order to ensure that biofilm formation only occurs when colonies are of a sufficient size and density. This spatial behaviour is achieved by the broadcast communication of an autoinducer in a diffusion scenario. This is of interest, for example, when considering the role of gut microbiota in gut health. This behaviour occurs within the context of the four phases of bacterial growth, specifically in the exponential stage (phase 2) for autoinducer production and the stationary stage (phase 3) for biofilm formation.

RESULTS

We have used coloured hybrid Petri nets to step-wise develop a flexible computational model for E.coli biofilm formation driven by Autoinducer 2 (AI-2) which is easy to configure for different notions of space. The model describes the essential components of gene transcription, signal transduction, extra and intra cellular transport, as well as the two-phase nature of the system. We build on a previously published non-spatial stochastic Petri net model of AI-2 production, keeping the assumptions of a limited nutritional environment, and our spatial hybrid Petri net model of biofilm formation, first presented at the NETTAB 2017 workshop. First we consider the two models separately without space, and then combined, and finally we add space. We describe in detail our step-wise model development and validation. Our simulation results support the expected behaviour that biofilm formation is increased in areas of higher bacterial colony size and density. Our analysis techniques include behaviour checking based on linear time temporal logic.

CONCLUSIONS

The advantages of our modelling and analysis approach are the description of quorum sensing and associated biofilm formation over two phases of bacterial growth, taking into account bacterial spatial distribution using a flexible and easy to maintain computational model. All computational results are reproducible.

From Staphylococcus aureus gene regulation to its pattern formation

The focus of this paper is to develop a new partial differential equation model for the pattern formation of the human pathogen Staphylococcus aureus, starting from a newly developed model of selected gene regulation mechanisms. In our model, we do not only account for the bacteria densities and nutrient concentrations, but also for the quorum sensing and biofilm components, since they enable bacteria to coordinate their behavior and provide the environment in which the colony grows. To this end, we model the relevant gene regulation systems using ordinary differential equations and therefrom derive our evolution equations for quorum sensing and biofilm environment by time-scale arguments. Furthermore, we compare and validate our model and the corresponding simulation results with biological real data observations of Staphylococcus aureus mutant colony growth in the laboratory. We show that we are able to adequately display the qualitative biological features of pattern formation in selected mutants, using the parameter changes indicated by the gene regulation mechanisms.

Front-propagation in bacterial inter-colony communication

Many bacterial species exchange signaling molecules to coordinate population-wide responses. For this process, known as quorum sensing, the concentration of the respective molecules is crucial. Here, we consider the interaction between spatially distributed bacterial colonies so that the spreading of the signaling molecules in space becomes important. The exponential growth of the signal-producing populations and the corresponding increase in signaling molecule production result in an exponential concentration profile that spreads with uniform speed. The theoretical predictions are supported by experiments with different strains of the soil bacterium Sinorhizobium meliloti that display fluorescence when either producing or responding to the signaling molecules.

Information transmission in microbial and fungal communication: from classical to quantum

Microbes have their own communication systems. Secretion and reception of chemical signaling molecules and ion-channels mediated electrical signaling mechanism are yet observed two special ways of information transmission in microbial community. In this article, we address the aspects of various crucial machineries which set the backbone of microbial cell-to-cell communication process such as quorum sensing mechanism (bacterial and fungal), quorum sensing regulated biofilm formation, gene expression, virulence, swarming, quorum quenching, role of noise in quorum sensing, mathematical models (therapy model, evolutionary model, molecular mechanism model and many more), synthetic bacterial communication, bacterial ion-channels, bacterial nanowires and electrical communication. In particular, we highlight bacterial collective behavior with classical and quantum mechanical approaches (including quantum information). Moreover, we shed a new light to introduce the concept of quantum synthetic biology and possible cellular quantum Turing test.

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.

Ecological feedback in quorum-sensing microbial populations can induce heterogeneous production of autoinducers

Autoinducers are small signaling molecules that mediate intercellular communication in microbial populations and trigger coordinated gene expression via ‘quorum sensing’. Elucidating the mechanisms that control autoinducer production is, thus, pertinent to understanding collective microbial behavior, such as virulence and bioluminescence. Recent experiments have shown a heterogeneous promoter activity of autoinducer synthase genes, suggesting that some of the isogenic cells in a population might produce autoinducers, whereas others might not. However, the mechanism underlying this phenotypic heterogeneity in quorum-sensing microbial populations has remained elusive. In our theoretical model, cells synthesize and secrete autoinducers into the environment, up-regulate their production in this self-shaped environment, and non-producers replicate faster than producers. We show that the coupling between ecological and population dynamics through quorum sensing can induce phenotypic heterogeneity in microbial populations, suggesting an alternative mechanism to stochastic gene expression in bistable gene regulatory circuits.

DOI:http://dx.doi.org/10.7554/eLife.25773.001

Bacteria and other microbes can communicate with each other using chemical languages. They release small signaling molecules called autoinducers into their surroundings and sense the levels of the autoinducers in the environment. The response to these autoinducers – known as quorum sensing – can regulate how whole communities of microbes grow and behave; for example, autoinducers can alter the ability of microbes to infect humans or enable the microbes to collectively switch on light production.

Recent experiments suggest that, in a population of genetically identical microbes, some individuals may produce autoinducers while others do not. The coexistence of these different “phenotypes” in one population may enable different individuals to perform different roles, or act as a “bet-hedging” strategy that helps the population to survive if it is later exposed to a stressful situation.

It is not clear how microbes regulate autoinducer production so that only some individuals produce these molecules. Bauer, Knebel et al. developed a theoretical model to address this question. In the model, the microbes shape their environment by producing autoinducers and can respond to this self-shaped environment by changing their level of autoinducer production. Bauer, Knebel et al. found that this establishes a feedback loop that can result in autoinducers being produced by some individuals but not others.

The next step following on from this work is to carry out experiments to test the assumptions and predictions made by the theoretical model. These findings may help to understand how the coexistence of different phenotypes affects collective behaviors, and vice versa, in populations of microbes that use quorum-sensing.

DOI:http://dx.doi.org/10.7554/eLife.25773.002

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Computational Exploration of Putative LuxR Solos in Archaea and Their Functional Implications in Quorum Sensing

LuxR solos are unexplored in Archaea, despite their vital role in the bacterial regulatory network. They assist bacteria in perceiving acyl homoserine lactones (AHLs) and/or non-AHLs signaling molecules for establishing intraspecies, interspecies, and interkingdom communication. In this study, we explored the potential LuxR solos of Archaea from InterPro v62.0 meta-database employing taxonomic, probable function, distribution, and evolutionary aspects to decipher their role in quorum sensing (QS). Our bioinformatics analyses showed that putative LuxR solos of Archaea shared few conserved domains with bacterial LuxR despite having less similarity within proteins. Functional characterization revealed their ability to bind various AHLs and/or non-AHLs signaling molecules that involve in QS cascades alike bacteria. Further, the phylogenetic study indicates that Archaeal LuxR solos (with less substitution per site) evolved divergently from bacteria and share distant homology along with instances of horizontal gene transfer. Moreover, Archaea possessing putative LuxR solos, exhibit the correlation between taxonomy and ecological niche despite being the inhabitant of diverse habitats like halophilic, thermophilic, barophilic, methanogenic, and chemolithotrophic. Therefore, this study would shed light in deciphering the role of the putative LuxR solos of Archaea to adapt varied habitats via multilevel communication with other organisms using QS.

Stochastic Liouville equation for particles driven by dichotomous environmental noise

We analyze the stochastic dynamics of a large population of noninteracting particles driven by a global environmental input in the form of a dichotomous Markov noise process (DMNP). The population density of particle states evolves according to a stochastic Liouville equation with respect to different realizations of the DMNP. We then exploit the connection with previous work on diffusion in randomly switching environments, in order to derive moment equations for the distribution of solutions to the stochastic Liouville equation. We illustrate the theory by considering two simple examples of dichotomous flows, a velocity jump process and a two-state gene regulatory network. In both cases we show how the global environmental input induces statistical correlations between different realizations of the population density.