A Mathematical Model of Quorum Sensing Induced Biofilm Detachment

Examination of the Structure and Formation Streptococcus mutans Biofilm Induced by Glucose, Lactose, Soy Protein, and Iron

OBJECTIVE

 Streptococcus mutans, the main causative agent of caries, have the ability to form biofilms on the surface of teeth. The availability of nutrients such as glucose, lactose, soy protein, and iron can influence S. mutans in biofilm formation. All four sources of nutrients have been shown to increase the formation of S. mutans biofilms. The purpose of this study was to determine the structure and thickness of S. mutans biofilms induced by glucose, lactose, soy protein, and iron.

MATERIALS AND METHODS

 This experimental laboratory study aimed to examine the formation of biofilm structures (chemical elements) and determine the thickness of S. mutans biofilms induced by glucose, lactose, soy protein, and iron. The structures (chemical elements) were examined using scanning electron microscopy-energy-dispersive X-ray (SEM-EDX) analysis. Confocal laser scanning microscopy (CLSM) was used to determine the thickness of S. mutans biofilms with an Olympus FV1000 microscope, and the findings were analyzed using Olympus Fluoview Ver. 4.2a software.

RESULTS

 It was established that the results of SEM-EDX examination of the structure of S. mutans biofilms induced by glucose had oxygen (O) as the dominant chemical element (30.24 w%); lactose reported oxygen (O) as the dominant element (29.65 w%); soy protein had carbon (C) as the dominant element (34.31 w%); and iron showed oxygen (O) as the dominant element (32.51 w%). The thickness (measured by the CLSM examination) of biofilms induced by glucose, lactose, soy protein, and iron were 17,666, 12,666, 18,000, and 15,666 nm, respectively.

CONCLUSION

 The structure of S. mutans biofilms induced by glucose, lactose, and iron contain the following elements in amounts from the highest to lowest: O, C, N, P, and S; the biofilm produced by S. mutans induced by soy protein in amounts from the highest to lowest comprised the elements: C, O, N, S, and P. The S. mutans biofilms induced by soy protein had the maximum thickness, followed by those induced by glucose, iron, and lactose.

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.

A pore-scale reactive transport modeling study for quorum sensing-driven biofilm dispersal in heterogeneous porous media

Microorganisms regulate the expression of energetically expensive phenotypes via a collective decision-making mechanism known as quorum sensing (QS). This study investigates the intricate dynamics of biofilm growth and QS-controlled biofilm dispersal in heterogeneous porous media, employing a pore-scale reactive transport modeling approach. Model simulations carried out under various fluid flow conditions and biofilm growth scenarios reveal that QS processes are influenced not only by the biomass density of biofilm colonies but also by a complex interplay between pore architecture, flow velocity, and the rates of biofilm growth and dispersal. This study demonstrates that pore architecture controls the initiation of QS processes and advection gives rise to oscillatory growth of biofilms. Such oscillation is suppressed if biofilm dynamics are in favor of sustaining a sufficiently high signal concentration, such as fast growth or slow dispersal rates. By establishing a mathematical framework, this study contributes to the fundamental understanding of QS-controlled biofilm dynamics in complex environments.

Mathematical models of cystic fibrosis as a systemic disease

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

Signaling in microbial communities with open boundaries

Microbial communities such as swarms or biofilms often form at the interfaces of solid substrates and open fluid flows. At the same time, in laboratory environments these communities are commonly studied using microfluidic devices with media flows and open boundaries. Extracellular signaling within these communities is therefore subject to different constraints than signaling within classic, closed-boundary systems such as developing embryos or tissues, yet is understudied by comparison. Here, we use mathematical modeling to show how advective-diffusive boundary flows and population geometry impact cell-cell signaling in monolayer microbial communities. We reveal conditions where the intercellular signaling lengthscale depends solely on the population geometry and not on diffusion or degradation, as commonly expected. We further demonstrate that diffusive coupling with the boundary flow can produce signal gradients within an isogenic population, even when there is no flow within the population. We use our theory to provide new insights into the signaling mechanisms of published experimental results, and we make several experimentally verifiable predictions. Our research highlights the importance of carefully evaluating boundary dynamics and environmental geometry when modeling microbial cell-cell signaling and informs the study of cell behaviors in both natural and synthetic systems.

Pseudomonas aeruginosa's greenish-blue pigment pyocyanin: its production and biological activities

A subject of great interest is the bioprospecting of microorganisms and their bioactive byproducts, such as pigments. Microbial pigments have various benefits, including being safe to use due to their natural makeup, having therapeutic effects, and being produced all year round, regardless of the weather or location. Pseudomonas aeruginosa produces phenazine pigments that are crucial for interactions between Pseudomonas species and other living things. Pyocyanin pigment, which is synthesized by 90-95% of P. aeruginosa, has potent antibacterial, antioxidant, and anticancer properties. Herein, we will concentrate on the production and extraction of pyocyanin pigment and its biological use in different areas of biotechnology, engineering, and biology.

Stochastic effects in bacterial communication mediated by extracellular vesicles

Quorum sensing (QS) allows bacterial cells to sense changes in local cell density and, hence, to regulate multicellular processes, including biofilm formation, regulation of virulence, and horizontal gene transfer. While, traditionally, QS was thought to involve the exchange of extracellular signal molecules free in solution, recent experiments have shown that for some bacterial systems a substantial fraction of signal molecules are packaged and delivered in extracellular vesicles. How the packaging of signal molecules in extracellular vesicles influences the ability of cells to communicate and coordinate multicellular behaviors remains largely unknown. We present here a stochastic reaction-diffusion model of QS that accounts for the exchange of both freely diffusing and vesicle-associated signal molecules. We find that the delivery of signal molecules via extracellular vesicles amplifies local fluctuations in the signal concentration, which can strongly affect the dynamics and spatial range of bacterial communication. For systems with multiple bacterial colonies, extracellular vesicles provide an alternate pathway for signal transport between colonies, and may be crucial for long-distance signal exchange in environments with strong degradation of free signal molecules.

Signaling in microbial communities with open boundaries

Microbial communities such as swarms or biofilms often form at the interfaces of solid substrates and open fluid flows. At the same time, in laboratory environments these communities are commonly studied using microfluidic devices with media flows and open boundaries. Extracellular signaling within these communities is therefore subject to different constraints than signaling within classic, closed-boundary systems such as developing embryos or tissues, yet is understudied by comparison. Here, we use mathematical modeling to show how advective-diffusive boundary flows and population geometry impact cell-cell signaling in monolayer microbial communities. We reveal conditions where the intercellular signaling lengthscale depends solely on the population geometry and not on diffusion or degradation, as commonly expected. We further demonstrate that diffusive coupling with the boundary flow can produce signal gradients within an isogenic population, even when there is no flow within the population. We use our theory to provide new insights into the signaling mechanisms of published experimental results, and we make several experimentally verifiable predictions. Our research highlights the importance of carefully evaluating boundary dynamics and environmental geometry when modeling microbial cell-cell signaling and informs the study of cell behaviors in both natural and synthetic systems.

Scaling relations for auxin waves

We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions that is parameterized by the height of the auxin-pulse. We uncover scaling relations for the speed and width of these waves and verify these rigorous results with numerical computations. In addition, we provide explicit expressions for the leading-order wave profiles, which allows the influence of the biological parameters in the problem to be readily identified. Our proofs are based on a generalization of the scaling principle developed by Friesecke and Pego to construct pulse solutions to the classic Fermi-Pasta-Ulam-Tsingou model, which describes a one-dimensional chain of coupled nonlinear springs.

Metagenomic analysis of pioneer biofilm-forming marine bacteria with emphasis on Vibrio gigantis adhesion dynamics

Marine biofilms occur frequently and spontaneously in seawater, on almost any submerged solid surface. At the early stages of colonization, it consists of bacteria and evolves into a more complex community. Using 16S rRNA amplicon sequencing and comparative metagenomics, the composition and predicted functional potential of one- to three-day old bacterial communities in surface biofilms were investigated and compared to that of seawater. This confirmed the autochthonous marine bacterium Vibrio gigantis as an early and very abundant biofilm colonizer, also functionally linked to the genes associated with cell motility, surface attachment, and communication via signaling molecules (quorum sensing), all crucial for biofilm formation. The dynamics of adhesion on a solid surface of V. gigantis alone was also monitored in controlled laboratory conditions, using a newly designed and easily implementable protocol. Resulting in a calculated percentage of bacteria-covered surface, a convincing tendency of spontaneous adhering was confirmed. From the multiple results, its quantified and reproducible adhesion dynamics will be used as a basis for future experiments involving surface modifications and coatings, with the goal of preventing adhesion.

Engineering modeling frameworks for microbial food safety at various scales

The landscape of mathematical model-based understanding of microbial food safety is wide and deep, covering interdisciplinary fields of food science, microbiology, physics, and engineering. With rapidly growing interest in such model-based approaches that increasingly include more fundamental mechanisms of microbial processes, there is a need to build a general framework that steers this evolutionary process by synthesizing literature spread over many disciplines. The framework proposed here shows four interconnected, complementary levels of microbial food processes covering sub-cellular scale, microbial population scale, food scale, and human population scale (risk). A continuum of completely mechanistic to completely empirical models, widely-used and emerging, are integrated into the framework; well-known predictive microbiology modeling being a part of this spectrum. The framework emphasizes fundamentals-based approaches that should get enriched over time, such as the basic building blocks of microbial population scale processes (attachment, migration, growth, death/inactivation and communication) and of food processes (e.g., heat and moisture transfer). A spectrum of models are included, for example, microbial population modeling covers traditional predictive microbiology models to individual-based models and cellular automata. The models are shown in sufficient quantitative detail to make obvious their coupling, or their integration over various levels. Guidelines to combine sub-processes over various spatial and time scales into a complete interdisciplinary and multiphysics model (i.e., a system) are provided, covering microbial growth/inactivation/transport and physical processes such as fluid flow and heat transfer. As food safety becomes increasingly predictive at various scales, this synthesis should provide its roadmap. This big picture and framework should be futuristic in driving novel research and educational approaches.

Mutagenic strategies against luxS gene affect the early stage of biofilm formation of Campylobacter jejuni

Currently, it is clear that the luxS gene has an impact on the process of biofilm formation in Campylobacter jejuni. However, even within the species, naturally occurring strains of Campylobacter lacking the luxS gene exist, which can form biofilms. In order to better understand the genetic determinants and the role of quorum sensing through the LuxS/AI-2 pathway in biofilm formation, a set of mutant/complemented strains of C. jejuni 81-176 were prepared. Additionally, the impact of the mutagenic strategy used against the luxS gene was investigated. Biofilm formation was affected by both the presence and absence of the luxS gene, and by the mutagenic strategy used. Analysis by CLSM showed that all mutant strains formed significantly less biofilm mass when compared to the wild-type. Interestingly, the deletion mutant (∆luxS) showed a larger decrease in biofilm mass than the substitution (∙luxS) and insertional inactivated ([Formula: see text]luxS) mutants, even though all the mutant strains lost the ability to produce autoinducer-2 molecules. Moreover, the biofilm of the ∆luxS mutant lacked the characteristic microcolonies observed in all other strains. The complementation of all mutant strains resulted in restored ability to produce AI-2, to form a complex biofilm, and to develop microcolonies at the level of the wild-type.

Regulation of Cunninghamella spp. biofilm growth by tryptophol and tyrosol

Fungi belonging to the genus Cunninghamella are often used as microbial models of mammalian metabolism owing to their ability to transform a range of xenobiotic compounds. Furthermore, under specific growth conditions species such as Cunninghamellaelegans and Cunninghamellaechinulata grow as biofilms enabling a convenient semi-continuous production of valuable drug metabolites. However, the molecular mechanism of biofilm regulation is not understood, thus controlling biofilm thickness limits the productive applications of it. In this paper we describe the identification of two molecules, tyrosol and tryptophol, that were identified in C. blakesleeana cultures, but not in C. elegans and C. echinulata. The molecules are known quorum sensing molecules (QSMs) in yeast and their potential role in Cunninghamella biofilm regulation was explored. Both were present in higher concentrations in C. blakesleeana planktonic cultures compared with biofilms; they inhibited the growth of the fungus on agar plates and selectively inhibited biofilm growth in liquid cultures. The molecules had a comparatively minor impact on the biofilm growth of C. elegans and C. echinulata and on the growth of these fungi on agar plates. Finally, when exogenous tyrosol or tryptophol was added to previously grown C. blakesleeana biofilm, detachment was visible and new additional planktonic culture was measured, confirming that these molecules specifically regulate biofilm growth in this fungus.

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Tyrosol and tryptophol were identified in culture supernatants of Cunninghamella blakesleeana.

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Concentrations of the compounds were substantially higher in planktonic cultures compared with biofilms.

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Bioassays revealed that tyrosol and tryptophol inhibited growth of C. blakesleeana on agar plates.

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Biofilm growth was inhibited by exogenous addition of the compounds whereas planktonic growth was unaffected.

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The compounds caused detachment of previously grown biofilms.

Effects of Material Type on Biofilm Response to an Oxidising Biocide in a Laboratory-Scale Cooling Tower System : Effect of material type in response to biocide

Biofilms in industrial cooling tower systems are an important problem. The importance of the surface material in the response to an oxidising biocide (chloramine T trihydrate) was substantiated in our study. Polyvinyl chloride (PVC) cooling tower fill material, stainless steel cooling tower construction material and glass surfaces were compared by evaluating the bacterial loads on materials before and after biocidal treatment. The greatest logarithmic decrease in bacterial load was recorded as >3 log for glass after the first two months and for PVC after the second month. Actively respiring bacterial counts and adenosine triphosphate (ATP) measurements showed that there was no significant difference in the sensitivity of biofilm-associated cells to the biocide on the different surfaces. In addition, the effect of the biocidal treatment decreased with increasing biofilm age, regardless of the material.

Modeling of Symbiotic Bacterial Biofilm Growth with an Example of the Streptococcus-Veillonella sp. System

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus-Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.

Colour Me Blue: The History and the Biotechnological Potential of Pyocyanin

Pyocyanin was the first natural phenazine described. The molecule is synthesized by about 95% of the strains of Pseudomonas aeruginosa. From discovery up to now, pyocyanin has been characterised by a very rich and avant-garde history, which includes its use in antimicrobial therapy, even before the discovery of penicillin opened the era of antibiotic therapy, as well as its use in electric current generation. Exhibiting an exuberant blue colour and being easy to obtain, this pigment is the subject of the present review, aiming to narrate its history as well as to unveil its mechanisms and suggest new horizons for applications in different areas of engineering, biology and biotechnology.

Persistence as an Optimal Hedging Strategy

Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new, to our knowledge, theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation and design. Overall, we provide a new, to our knowledge, way of conceptualizing and modeling cellular decision making in volatile environments by explicitly unifying theory from mathematical biology and finance.

A computational study of combination HIFU-chemotherapy as a potential means of overcoming cancer drug resistance

The application of local hyperthermia, particularly in conjunction with other treatment strategies (like chemotherapy and radiotherapy) has been known to be a useful means of enhancing tumor treatment outcomes. However, to our knowledge, there has been no mathematical model designed to capture the impact of the combination of hyperthermia and chemotherapies on tumor growth and control. In this study, we propose a nonlinear Partial Differential Equation (PDE) model which describes the tumor response to chemotherapy, and use the model to study the effects of hyperthermia on the response of prototypical tumor to the generic chemotherapeutic agent. Ultrasound energy is delivered to the tumor through High Intensity Focused Ultrasound (HIFU), as a noninvasive technique to elevate the tumor temperature in a controlled manner. The proposed tumor growth model is coupled with the nonlinear density dependent Westervelt and Penne's bio-heat equations, used to calculate the net delivered energy and temperature of the tumor and its surrounding normal tissue. The tumor is assumed to be composed of two species: drug-sensitive and drug-resistant. The central assumption underlying our model is that the drug-resistant species is converted to a drug-sensitive type when the tumor temperature is elevated above a certain threshold temperature. The "in silico" results obtained, confirm that hyperthermia can result in less aggressive tumor development and emphasize the importance of designing an optimized thermal dose strategy. Furthermore, our results suggest that increasing the length of the on/off cycle of the transducer is an efficient approach to treatment scheduling in the sense of optimizing tumor eradication.

Controlling biofilms using synthetic biology approaches

Bacterial biofilms are formed by the complex but ordered regulation of intra- or inter-cellular communication, environmentally responsive gene expression, and secretion of extracellular polymeric substances. Given the robust nature of biofilms due to the non-growing nature of biofilm bacteria and the physical barrier provided by the extracellular matrix, eradicating biofilms is a very difficult task to accomplish with conventional antibiotic or disinfectant treatments. Synthetic biology holds substantial promise for controlling biofilms by improving and expanding existing biological tools, introducing novel functions to the system, and re-conceptualizing gene regulation. This review summarizes synthetic biology approaches used to eradicate biofilms via protein engineering of biofilm-related enzymes, utilization of synthetic genetic circuits, and the development of functional living agents. Synthetic biology also enables beneficial applications of biofilms through the production of biomaterials and patterning biofilms with specific temporal and spatial structures. Advances in synthetic biology will add novel biofilm functionalities for future therapeutic, biomanufacturing, and environmental applications.

Simulation Based Exploration of Bacterial Cross Talk Between Spatially Separated Colonies in a Multispecies Biofilm Community

We present a simple mesoscopic model for bacterial cross-talk between growing biofilm colonies. The simulation setup mimics a novel microfludic biofilm growth reactor which allows a 2D description. The model is a stiff quasilinear system of diffusion-reaction equations with simultaneously a super-diffusion singularity and a degeneracy (as in the porous medium equation) that leads to the formation of sharp interfaces with finite speed of propagation and gradient blow up. We use a finite volume method with arithmetic flux averaging, and a time adaptive stiff time integrator. We find that signal and nutrient transport between colonies can greatly control and limit biofilm response to induction signals, leading to spatially heterogeneous biofilm behavior.

Human antibody repertoire frequently includes antibodies to a bacterial biofilm associated protein

We have previously described a native human monoclonal antibody, TRL1068, that disrupts bacterial biofilms by extracting from the biofilm matrix key scaffolding proteins in the DNABII family, which are present in both gram positive and gram negative bacterial species. The antibiotic resistant sessile bacteria released from the biofilm then revert to the antibiotic sensitive planktonic state. Qualitative resensitization to antibiotics has been demonstrated in three rodent models of acute infections. We report here the surprising discovery that antibodies against the target family were found in all twenty healthy humans surveyed, albeit at a low level requiring a sensitive single B-cell assay for detection. We have cloned 21 such antibodies. Aside from TRL1068, only one (TRL1330) has all the biochemical properties believed necessary for pharmacological efficacy (broad spectrum epitope specificity and high affinity). We suggest that the other anti-DNABII antibodies, while not necessarily curative, reflect an immune response at some point in the donor's history to these components of biofilms. Such an immune response could reflect exposure to bacterial reservoirs that have been previously described in chronic non-healing wounds, periodontal disease, chronic obstructive pulmonary disease, colorectal cancer, rheumatoid arthritis, and atherosclerotic artery explants. The detection of anti-DNABII antibodies in all twenty surveyed donors with no active infection suggests that bacterial biofilm reservoirs may be present periodically in most healthy individuals. Biofilms routinely shed bacteria, creating a continuous low level inflammatory stimulus. Since chronic subclinical inflammation is thought to contribute to most aging-related diseases, suppression of bacterial biofilm has potential value in delaying age-related pathology.

Challenges of biofilm control and utilization: lessons from mathematical modelling

This article reviews modern applications of mathematical descriptions of biofilm formation. The focus is on theoretically obtained results which have implications for areas including the medical sector, food industry and wastewater treatment. Examples are given as to how models have contributed to the overall knowledge on biofilms and how they are used to predict biofilm behaviour. We conclude that the use of mathematical models of biofilms has demonstrated over the years the ability to significantly contribute to the vast field of biofilm research. Among other things, they have been used to test various hypotheses on the nature of interspecies interactions, viability of biofilm treatment methods or forces behind observed biofilm pattern formations. Mathematical models can also play a key role in future biofilm research. Many models nowadays are analysed through computer simulations and continue to improve along with computational capabilities. We predict that models will keep on providing answers to important challenges involving biofilm formation. However, further strengthening of the ties between various disciplines is necessary to fully use the tools of collective knowledge in tackling the biofilm phenomenon.

Exploring the transcriptome of luxI- and ΔainS mutants and the impact of N-3-oxo-hexanoyl-L- and N-3-hydroxy-decanoyl-L-homoserine lactones on biofilm formation in Aliivibrio salmonicida

Background

Bacterial communication through quorum sensing (QS) systems has been reported to be important in coordinating several traits such as biofilm formation. In Aliivibrio salmonicida two QS systems the LuxI/R and AinS/R, have been shown to be responsible for the production of eight acyl-homoserine lactones (AHLs) in a cell density dependent manner. We have previously demonstrated that inactivation of LitR, the master regulator of the QS system resulted in biofilm formation, similar to the biofilm formed by the AHL deficient mutant ΔainSluxI⁻. In this study, we aimed to investigate the global gene expression patterns of luxI and ainS autoinducer synthases mutants using transcriptomic profiling. In addition, we examined the influence of the different AHLs on biofilm formation.

Results

The transcriptome profiling of ΔainS and luxI⁻ mutants allowed us to identify genes and gene clusters regulated by QS in A. salmonicida. Relative to the wild type, the ΔainS and luxI⁻ mutants revealed 29 and 500 differentially expressed genes (DEGs), respectively. The functional analysis demonstrated that the most pronounced DEGs were involved in bacterial motility and chemotaxis, exopolysaccharide production, and surface structures related to adhesion. Inactivation of luxI, but not ainS genes resulted in wrinkled colony morphology. While inactivation of both genes (ΔainSluxI⁻) resulted in strains able to form wrinkled colonies and mushroom structured biofilm. Moreover, when the ΔainSluxI⁻ mutant was supplemented with N-3-oxo-hexanoyl-L-homoserine lactone (3OC6-HSL) or N-3-hydroxy-decanoyl-L-homoserine lactone (3OHC10-HSL), the biofilm did not develop. We also show that LuxI is needed for motility and for repression of EPS production, where repression of EPS is likely operated through the RpoQ-sigma factor.

Conclusion

These findings imply that the LuxI and AinS autoinducer synthases play a critical role in the regulation of biofilm formation, EPS production, and motility.

Abrupt and gradual onset of synchronized oscillations due to dynamical quorum sensing in the single-cathode multi-anode nickel electrodissolution system

The nonlinear dynamics of an oscillatory Ni electrodissolution-hydrogen ion reduction system are explored in a multi-electrode anode-single cathode system. A mathematical analysis of the charge balance equations reveals that the coupling scheme is similar to dynamical quorum sensing, where the number of anode wires affects a parameter related to the population density. In a parameter region where the large population exhibits stationary behavior, with sufficiently strong coupling (with small individual resistances attached to the anode wires), synchronized oscillations emerge abruptly with decreasing the number of anodes. Therefore, an "inverse" dynamical quorum sensing takes place. With weak coupling the transition is gradual. The experiments are supported by numerical simulation of a kinetic model of the process. The results thus show that the description of nontrivial cathode-anode interactions in the form of dynamical quorum sensing provides an efficient way of analyzing the dynamical response of complex, interacting electrochemical reactions.

Molecules Autoinducer 2 and cjA and Their Impact on Gene Expression in

Quorum sensing is a widespread form of cell-to-cell communication, which is based on the production of signaling molecules known as autoinducers (AIs). The first group contains highly species-specific N-acyl homoserine lactones (N-AHLs), generally known as AI-1, which are produced by AHL synthase. The second group, possessing the characteristic structure of a furanone ring, are known as AI-2. The enzyme responsible for their production is S-ribosylhomocysteine lyase (LuxS). In <i>Campylobacter jejuni</i>, AI-2 and LuxS play a role in many important processes, including biofilm formation, stress response, motility, expression of virulence factors, and colonization. However, neither the receptor protein nor the exact structure of the AI-2 molecule have been identified to date. Similarly, little is known about the possible existence of AHL-synthase producing AI-1 and its impact on gene expression. Recently, an analogue of homoserine lactone, called cjA, was isolated from a cell-free supernatant of <i>C. jejuni</i> strain<i></i> 81–176 and from the food isolate c11. The molecule cjA particularly impacted the expression of virulence factors and biofilm formation. This review summarizes the role of AI-2 and cjA in the context of biofilm formation, motility, stress responses, and expression of virulence factors.

Periprosthetic bacterial biofilm and quorum sensing

Periprosthetic joint infection (PJI) is a common complication after total joint arthroplasty leading to severe morbidity and mortality. With an aging population and increasing prevalence of total joint replacement procedures, the burden of PJI will be felt not only by individual patients, but in increased healthcare costs. Current treatment of PJI is inadequate resulting in incredibly high failure rates. This is believed to be largely mediated by the presence of bacterial biofilms. These polymicrobial bacterial colonies form within secreted extracellular matrices, adhering to the implant surface and local tissue. The biofilm architecture is believed to play a complex and critical role in a variety of bacterial processes including nutrient supplementation, metabolism, waste management, and antibiotic and immune resistance. The establishment of these biofilms relies heavily on the quorum sensing communication systems utilized by bacteria. Early stage research into disrupting bacterial communication by targeting quorum sensing show promise for future clinical applications. However, prevention of the biofilm formation via early forced induction of the biofilm forming process remains yet unexplored. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:2331-2339, 2018.

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.

Mesoscopic Energy Minimization Drives Pseudomonas aeruginosa Biofilm Morphologies and Consequent Stratification of Antibiotic Activity Based on Cell Metabolism

Segregation of bacteria based on their metabolic activities in biofilms plays an important role in the development of antibiotic resistance. Mushroom-shaped biofilm structures, which are reported for many bacteria, exhibit topographically varying levels of multiple drug resistance from the cap of the mushroom to its stalk. Understanding the dynamics behind the formation of such structures can aid in design of drug delivery systems, antibiotics, or physical systems for removal of biofilms. We explored the development of metabolically heterogeneous Pseudomonas aeruginosa biofilms using numerical models and laboratory knockout experiments on wild-type and chemotaxis-deficient mutants. We show that chemotactic processes dominate the transformation of slender and hemispherical structures into mushroom structures with a signature cap. Cellular Potts model simulation and experimental data provide evidence that accelerated movement of bacteria along the periphery of the biofilm, due to nutrient cues, results in the formation of mushroom structures and bacterial segregation. Multidrug resistance of bacteria is one of the most threatening dangers to public health. Understanding the mechanisms of the development of mushroom-shaped biofilms helps to identify the multidrug-resistant regions. We decoded the dynamics of the structural evolution of bacterial biofilms and the physics behind the formation of biofilm structures as well as the biological triggers that produce them. Combining in vitro gene knockout experiments with in silico models showed that chemotactic motility is one of the main driving forces for the formation of stalks and caps. Our results provide physicists and biologists with a new perspective on biofilm removal and eradication strategies.

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.

Mathematical modelling of CRISPR-Cas system effects on biofilm formation

Clustered regularly interspaced short palindromic repeats (CRISPR), linked with CRISPR associated (Cas) genes, can confer adaptive immunity to bacteria, against bacteriophage infections. Thus from a therapeutic standpoint, CRISPR immunity increases biofilm resistance to phage therapy. Recently, however, CRISPR-Cas genes have been implicated in reducing biofilm formation in lysogenized cells. Thus CRISPR immunity can have complex effects on phage-host-lysogen interactions, particularly in a biofilm. In this contribution, we develop and analyse a series of dynamical systems to elucidate and disentangle these interactions. Two competition models are used to study the effects of lysogens (first model) and CRISPR-immune bacteria (second model) in the biofilm. In the third model, the effect of delivering lysogens to a CRISPR-immune biofilm is investigated. Using standard analyses of equilibria, stability and bifurcations, our models predict that lysogens may be able to displace CRISPR-immune bacteria in a biofilm, and thus suggest strategies to eliminate phage-resistant biofilms.

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.

Detection of Diverse N-Acyl-Homoserine Lactones in Vibrio alginolyticus and Regulation of Biofilm Formation by N-(3-Oxodecanoyl) Homoserine Lactone In vitro

Quorum sensing (QS) is a cell-to-cell communication system based on the exchange of small intercellular signal molecules, such as N-Acyl homoserine lactones (AHLs), which act as cell-density mediators of QS gene expression, and are highly variable both in types and amounts in most Gram-negative Proteobacteria. Understanding the regulation of AHLs may contribute to the elucidation of cell density-dependent phenomena, such as biofilm formation. Vibrio alginolyticus is among the most frequently observed marine opportunistic Vibrio pathogens. However, AHL production of this species and its effects on biofilm formation remain to be understood. Here, our study reported the diverse AHL profiles of 47 marine-isolated V. alginolyticus strains and the effects of exogenous 3-oxo-C₁₀-HSL on biofilm formation under different temperature conditions (16°C and 28°C). A total of 11 detected AHLs were produced by the isolates, of which 3-OH-C₄-HSL, 3-oxo-C₁₀-HSL and 3-oxo-C₁₄-HSL comprised the largest proportions. We also observed that moderate levels of exogenous 3-oxo-C₁₀-HSL (10 and 20 μM) could induce or enhance biofilm formation and alter its structure, while high levels (40 and 100 μM) did not significantly improve and even inhibited biofilm formation in V. alginolyticus. Further, regulation by exogenous 3-oxo-C₁₀-HSL was both concentration- and temperature-dependent in V. alginolyticus.

Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects

We analyze a mathematical model of quorum sensing induced biofilm dispersal. It is formulated as a system of non-linear, density-dependent, diffusion-reaction equations. The governing equation for the sessile biomass comprises two non-linear diffusion effects, a degeneracy as in the porous medium equation and fast diffusion. This equation is coupled with three semi-linear diffusion-reaction equations for the concentrations of growth limiting nutrients, autoinducers, and dispersed cells. We prove the existence and uniqueness of bounded non-negative solutions of this system and study the behavior of the model in numerical simulations, where we focus on hollowing effects in established biofilms.

Three-Dimensional Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

We develop a multiphasic hydrodynamic theory for biofilms taking into account interactions among various bacterial phenotypes, extracellular polymeric substance (EPS), quorum sensing (QS) molecules, solvent, and antibiotics. In the model, bacteria are classified into down-regulated QS, up-regulated QS, and non-QS cells based on their QS ability. The model is first benchmarked against an experiment yielding an excellent fit to experimental measurements on the concentration of QS molecules and the cell density during biofilm development. It is then applied to study development of heterogeneous structures in biofilms due to interactions of QS regulation, hydrodynamics, and antimicrobial treatment. Our 3D numerical simulations have confirmed that (i). QS is beneficial for biofilm development in a long run by building a robust EPS population to protect the biofilm; (ii). biofilms located upstream can induce QS downstream when the colonies are close enough spatially; (iii). QS induction may not be fully operational and can even be compromised in strong laminar flows; (v). the hydrodynamic stress alters the biofilm morphology. Through further numerical investigations, our model suggests that (i). QS-regulated EPS production contributes to the structural formation of heterogeneous biofilms; (ii) QS down-regulated cells tend to grow at the surface of the biofilm while QS up-regulated ones tend to grow in the bulk; (iii) when nutrient supply is sufficient, QS induction might be more effective upstream than downstream; (iv) QS may be of little benefit in a short timescale in term of fighting against invading strain/species; (v) the material properties of biomass (bacteria and EPS) have strong impact on the dilution of QS molecules under strong shear flow. In addition, with this modeling framework, hydrodynamic details and rheological quantities associated with biofilm formation under QS regulation can be resolved.

Influence of Nutrient Availability and Quorum Sensing on the Formation of Metabolically Inactive Microcolonies Within Structurally Heterogeneous Bacterial Biofilms: An Individual-Based 3D Cellular Automata Model

The resistance of bacterial biofilms to antibiotic treatment has been attributed to the emergence of structurally heterogeneous microenvironments containing metabolically inactive cell populations. In this study, we use a three-dimensional individual-based cellular automata model to investigate the influence of nutrient availability and quorum sensing on microbial heterogeneity in growing biofilms. Mature biofilms exhibited at least three structurally distinct strata: a high-volume, homogeneous region sandwiched between two compact sections of high heterogeneity. Cell death occurred preferentially in layers in close proximity to the substratum, resulting in increased heterogeneity in this section of the biofilm; the thickness and heterogeneity of this lowermost layer increased with time, ultimately leading to sloughing. The model predicted the formation of metabolically dormant cellular microniches embedded within faster-growing cell clusters. Biofilms utilizing quorum sensing were more heterogeneous compared to their non-quorum sensing counterparts, and resisted sloughing, featuring a cell-devoid layer of EPS atop the substratum upon which the remainder of the biofilm developed. Overall, our study provides a computational framework to analyze metabolic diversity and heterogeneity of biofilm-associated microorganisms and may pave the way toward gaining further insights into the biophysical mechanisms of antibiotic resistance.

Spatial dispersal of bacterial colonies induces a dynamical transition from local to global quorum sensing

Bacteria communicate using external chemical signals called autoinducers (AI) in a process known as quorum sensing (QS). QS efficiency is reduced by both limitations of AI diffusion and potential interference from neighboring strains. There is thus a need for predictive theories of how spatial community structure shapes information processing in complex microbial ecosystems. As a step in this direction, we apply a reaction-diffusion model to study autoinducer signaling dynamics in a single-species community as a function of the spatial distribution of colonies in the system. We predict a dynamical transition between a local quorum sensing (LQS) regime, with the AI signaling dynamics primarily controlled by the local population densities of individual colonies, and a global quorum sensing (GQS) regime, with the dynamics being dependent on collective intercolony diffusive interactions. The crossover between LQS to GQS is intimately connected to a trade-off between the signaling network's latency, or speed of activation, and its throughput, or the total spatial range over which all the components of the system communicate.

A Mixed-Culture Biofilm Model with Cross-Diffusion

We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system.