BacSim, a simulator for individual-based modelling of bacterial colony growth

Flagellar interference with plasmid uptake in biofilms: a joint experimental and modeling study

Plasmid conjugation is a key facilitator of horizontal gene transfer (HGT), and plasmids encoding antibiotic resistance drive the increasing prevalence of antibiotic resistance. In natural, engineered, and clinical environments, bacteria often grow in protective biofilms. Therefore, a better understanding of plasmid transfer in biofilms is needed. Our aim was to investigate plasmid transfer in a biofilm-adapted wrinkly colony mutant of Xanthomonas retroflexus (XRw) with enhanced matrix production and reduced motility. We found that XRw biofilms had an increased uptake of the broad host-range IncP-1ϵ plasmid pKJK5 compared to the wild type (WT). Proteomics revealed fewer flagellar-associated proteins in XRw, suggesting that flagella were responsible for reducing plasmid uptake. This was confirmed by the higher plasmid uptake of non-flagellated fliM mutants of the X. retroflexus wrinkly mutant as well as the wild type. Moreover, testing several flagellar mutants of Pseudomonas putida suggested that the flagellar effect was more general. We identified seven mechanisms with the potential to explain the flagellar effect and simulated them in an individual-based model. Two mechanisms could thus be eliminated (increased distances between cells and increased lag times due to flagella). Another mechanism identified as viable in the modeling was eliminated by further experiments. The possibility of steric hindrance of pilus movement and binding by flagella, reducing the frequency of contact and thus plasmid uptake, proved viable, and the three other viable mechanisms had a reduced probability of plasmid transfer in common. Our findings highlight the important yet complex effects of flagella during bacterial conjugation in biofilms.IMPORTANCEBiofilms are the dominant form of microbial life and bacteria living in biofilms are markedly different from their planktonic counterparts, yet the impact of the biofilm lifestyle on horizontal gene transfer (HGT) is still poorly understood. Horizontal gene transfer by conjugative plasmids is a major driver in bacterial evolution and adaptation, as exemplified by the troubling spread of antibiotic resistance. To either limit or promote plasmid prevalence and dissemination, we need a better understanding of plasmid transfer between bacterial cells, especially in biofilms. Here, we identified a new factor impacting the transfer of plasmids, flagella, which are required for many types of bacterial motility. We show that their absence or altered activity can lead to enhanced plasmid uptake in two bacterial species, Xanthomonas retroflexus and Pseudomonas putida. Moreover, we demonstrate the utility of mathematical modeling to eliminate hypothetical mechanisms.

Partial privatization and cooperation in biofilms

The evolution of cooperation in microbes is a challenge to explain because microbes producing costly goods for the benefit of any strain types (cooperators) often withstand the threat of elimination by interacting with individuals that exploit these benefits without contributing (defectors). Here we developed an individual-based model to investigate whether partial privatization via the partial secretion of goods can favor cooperation in structured, surface-attaching microbial populations, biofilms. Whether partial secretion can favor cooperation in biofilms is unclear for two reasons. First, while partial privatization has been shown to foster cooperation in unstructured populations, little is known about the role of partial privatization in biofilms. Second, while limited diffusion of goods favors cooperation in biofilms because molecules are more likely to be shared with genetically-related individuals, partial secretion reduces goods that could have been directed towards genetically related individuals. Our results show that although partial secretion weakens the role that limited diffusion has on fostering cooperation, partial secretion favors cooperation in biofilms. Overall, our results provide predictions that future experiments could test to reveal contributions of relatedness and partial secretion to the social evolution of biofilms.

From microbiome composition to functional engineering, one step at a time

SUMMARYCommunities of microorganisms (microbiota) are present in all habitats on Earth and are relevant for agriculture, health, and climate. Deciphering the mechanisms that determine microbiota dynamics and functioning within the context of their respective environments or hosts (the microbiomes) is crucially important. However, the sheer taxonomic, metabolic, functional, and spatial complexity of most microbiomes poses substantial challenges to advancing our knowledge of these mechanisms. While nucleic acid sequencing technologies can chart microbiota composition with high precision, we mostly lack information about the functional roles and interactions of each strain present in a given microbiome. This limits our ability to predict microbiome function in natural habitats and, in the case of dysfunction or dysbiosis, to redirect microbiomes onto stable paths. Here, we will discuss a systematic approach (dubbed the N+1/N-1 concept) to enable step-by-step dissection of microbiome assembly and functioning, as well as intervention procedures to introduce or eliminate one particular microbial strain at a time. The N+1/N-1 concept is informed by natural invasion events and selects culturable, genetically accessible microbes with well-annotated genomes to chart their proliferation or decline within defined synthetic and/or complex natural microbiota. This approach enables harnessing classical microbiological and diversity approaches, as well as omics tools and mathematical modeling to decipher the mechanisms underlying N+1/N-1 microbiota outcomes. Application of this concept further provides stepping stones and benchmarks for microbiome structure and function analyses and more complex microbiome intervention strategies.

MIL-CELL: a tool for multi-scale simulation of yeast replication and prion transmission

The single-celled baker's yeast, Saccharomyces cerevisiae, can sustain a number of amyloid-based prions, the three most prominent examples being [URE3], [PSI+], and [PIN+]. In the laboratory, haploid S. cerevisiae cells of a single mating type can acquire an amyloid prion in one of two ways (i) spontaneous nucleation of the prion within the yeast cell, and (ii) receipt via mother-to-daughter transmission during the cell division cycle. Similarly, prions can be lost due to (i) dissolution of the prion amyloid by its breakage into non-amyloid monomeric units, or (ii) preferential donation/retention of prions between the mother and daughter during cell division. Here we present a computational tool (Monitoring Induction and Loss of prions in Cells; MIL-CELL) for modelling these four general processes using a multiscale approach describing both spatial and kinetic aspects of the yeast life cycle and the amyloid-prion behavior. We describe the workings of the model, assumptions upon which it is based and some interesting simulation results pertaining to the wave-like spread of the epigenetic prion elements through the yeast population. MIL-CELL is provided as a stand-alone GUI executable program for free download with the paper. MIL-CELL is equipped with a relational database allowing all simulated properties to be searched, collated and graphed. Its ability to incorporate variation in heritable properties means MIL-CELL is also capable of simulating loss of the isogenic nature of a cell population over time. The capability to monitor both chronological and reproductive age also makes MIL-CELL potentially useful in studies of cell aging.

A novel model for biofilm initiation in porous media flow

Bacteria often form biofilms in porous environments where an external flow is present, such as soil or filtration systems. To understand the initial stages of biofilm formation, one needs to study the interactions between cells, the fluid and the confining geometries. Here, we present an agent based numerical model for bacteria that takes into account the planktonic stage of motile cells as well as surface attachment and biofilm growth in a lattice Boltzmann fluid. In the planktonic stage we show the importance of the interplay between complex flow and cell motility when determining positions of surface attachment. In the growth stage we show the applicability of our model by investigating how external flow and biofilm stiffness determine qualitative colony morphologies as well as quantitative measurements of, e.g., permeability.

In Search of Proximate Triggers of Anthrax Outbreaks in Wildlife: A Hypothetical Individual-Based Model of Plasmid Transfer within Bacillus Communities

Bacillus anthracis, the causative agent of anthrax in humans, livestock, and wildlife, exists in a community with hundreds of other species of bacteria in the environment. Work on the genetics of these communities has shown that B. anthracis shares a high percentage of chromosomal genes with both B. thuringiensis and B. cereus, and that phenotypic differences among these bacteria can result from extra-chromosomal DNA in the form of plasmids. We developed a simple hypothetical individual-based model to simulate the likelihood of detecting plasmids with genes encoding anthrax toxins within bacterial communities composed of B. anthracis, B. thuringiensis, and B. cereus, and the surrounding matrix of extra-cellular polymeric substances. Simulation results suggest the horizontal transfer of plasmids with genes encoding anthrax toxins among Bacillus species persisting outside the host could function as a proximate factor triggering anthrax outbreaks.

Use of the speckle imaging sub-pixel correlation analysis in revealing a mechanism of microbial colony growth

The microbial colony growth is driven by the activity of the cells located on the edges of the colony. However, this process is not visible unless specific staining or cross-sectioning of the colony is done. Speckle imaging technology is a non-invasive method that allows visualization of the zones of increased microbial activity within the colony. In this study, the laser speckle imaging technique was used to record the growth of the microbial colonies. This method was tested on three different microorganisms: Vibrio natriegens, Escherichia coli, and Staphylococcus aureus. The results showed that the speckle analysis system is not only able to record the growth of the microbial colony but also to visualize the microbial growth activity in different parts of the colony. The developed speckle imaging technique visualizes the zone of "the highest microbial activity" migrating from the center to the periphery of the colony. The results confirm the accuracy of the previous models of colony growth and provide algorithms for analysis of microbial activity within the colony.

Agent-Based Modeling of Microbial Communities

Microbial communities are complex living systems that populate the planet with diverse functions and are increasingly harnessed for practical human needs. To deepen the fundamental understanding of their organization and functioning as well as to facilitate their engineering for applications, mathematical modeling has played an increasingly important role. Agent-based models represent a class of powerful quantitative frameworks for investigating microbial communities because of their individualistic nature in describing cells, mechanistic characterization of molecular and cellular processes, and intrinsic ability to produce emergent system properties. This review presents a comprehensive overview of recent advances in agent-based modeling of microbial communities. It surveys the state-of-the-art algorithms employed to simulate intracellular biomolecular events, single-cell behaviors, intercellular interactions, and interactions between cells and their environments that collectively serve as the driving forces of community behaviors. It also highlights three lines of applications of agent-based modeling, namely, the elucidation of microbial range expansion and colony ecology, the design of synthetic gene circuits and microbial populations for desired behaviors, and the characterization of biofilm formation and dispersal. The review concludes with a discussion of existing challenges, including the computational cost of the modeling, and potential mitigation strategies.

Ecological modelling approaches for predicting emergent properties in microbial communities

Recent studies have brought forward the critical role of emergent properties in shaping microbial communities and the ecosystems of which they are a part. Emergent properties-patterns or functions that cannot be deduced linearly from the properties of the constituent parts-underlie important ecological characteristics such as resilience, niche expansion and spatial self-organization. While it is clear that emergent properties are a consequence of interactions within the community, their non-linear nature makes mathematical modelling imperative for establishing the quantitative link between community structure and function. As the need for conservation and rational modulation of microbial ecosystems is increasingly apparent, so is the consideration of the benefits and limitations of the approaches to model emergent properties. Here we review ecosystem modelling approaches from the viewpoint of emergent properties. We consider the scope, advantages and limitations of Lotka-Volterra, consumer-resource, trait-based, individual-based and genome-scale metabolic models. Future efforts in this research area would benefit from capitalizing on the complementarity between these approaches towards enabling rational modulation of complex microbial ecosystems.

Models predict planned phosphorus load reduction will make Lake Erie more toxic

Harmful cyanobacteria are a global environmental problem, yet we lack actionable understanding of toxigenic versus nontoxigenic strain ecology and toxin production. We performed a large-scale meta-analysis including 103 papers and used it to develop a mechanistic, agent-based model of Microcystis growth and microcystin production. Simulations for Lake Erie suggest that the observed toxigenic-to-nontoxigenic strain succession during the 2014 Toledo drinking water crisis was controlled by different cellular oxidative stress mitigation strategies (protection by microcystin versus degradation by enzymes) and the different susceptibility of those mechanisms to nitrogen limitation. This model, as well as a simpler empirical one, predicts that the planned phosphorus load reduction will lower biomass but make nitrogen and light more available, which will increase toxin production, favor toxigenic cells, and increase toxin concentrations.

Nutrient starvation intensifies chlorine disinfection-stressed biofilm formation

Bacterial surface attachment and subsequent biofilm expansion represent an essential adaptation to environmental signals and stresses, which are of great concern for many natural and engineered ecosystems. Yet the underlying mechanisms and driving forces of biofilm formation in a chlorinated and nutrient-restricted system remain sketchy. In this study, we coupled an experimental investigation and modeling simulation to understand how chlorination and nutrient limitation conspire to form biofilm using Pseudomonas aeruginosa as a model bacterium. Experimental results showed that moderate chlorination at 1.0 mg/L led to biofilm development amplified to 2.6 times of those without chlorine, while additional nutrient limitation (of 1/50-diluted or 0.4 g/L LB broth culture) achieved 4.6 times increment as compared to those of undiluted scenarios (of 20 g/L LB broth culture) with absence of chlorination after 24 h exposure. Meanwhile, intermediate chlorination stimulated instant flagellar motility and subsequently extracellular polymeric substances (EPS) secretion, particularly under limited nutrient condition (of 1/50-diluted or 0.4 g/L LB broth culture) that retarded chlorine consumption and provoked bacterial nutrient-limitation response. From our simulations, chlorine and resource levels along with associated spatio-temporal variations collectively drove bacterial cell movement and EPS excretion. Our results demonstrated that restraining nutrient intensified chlorination-excited cell movement and EPS production that reinforced biological and cell-surface interactions, thereby encouraging bacterial surface attachment and subsequent biofilm development. The findings provide the insights into the linkage of disinfectant and nutrient-regulated bacterial functional responses with consequent micro-habitats and biofilm dynamics.

Rules of Engagement: A Guide to Developing Agent-Based Models

Agent-based models (ABM), also called individual-based models, first appeared several decades ago with the promise of nearly real-time simulations of active, autonomous individuals such as animals or objects. The goal of ABMs is to represent a population of individuals (agents) interacting with one another and their environment. Because of their flexible framework, ABMs have been widely applied to study systems in engineering, economics, ecology, and biology. This chapter is intended to guide the users in the development of an agent-based model by discussing conceptual issues, implementation, and pitfalls of ABMs from first principles. As a case study, we consider an ABM of the multi-scale dynamics of cellular interactions in a microbial community. We develop a lattice-free agent-based model of individual cells whose actions of growth, movement, and division are influenced by both their individual processes (cell cycle) and their contact with other cells (adhesion and contact inhibition).

Successful microbial colonization of space in a more dispersed manner

Many organisms live in habitats with limited nutrients or space, competition for these resources is ubiquitous. Although spatial factors related to the population's manner of colonizing space influences its success in spatial competition, what these factors are and to what extent they influence the outcome remains underexplored. Here, we applied a simulated competitive model to explore the spatial factors affecting outcomes of competition for space. By quantifying spatial factors, we show that colonizing space in a more dispersed manner contributes to microbial competitive success. We also find that the competitive edge deriving from a more dispersed manner in colonization can compensate for the disadvantage arising from either a lower growth rate or lower initial abundance. These findings shed light on the role of space colonization manners on maintaining biodiversity within ecosystems and provide novel insights critical for understanding how competition for space drives evolutionary innovation.

Predation strategies of the bacterium Bdellovibrio bacteriovorus result in overexploitation and bottlenecks

With increasing antimicrobial resistance, alternatives for treating infections or removing resistant bacteria are urgently needed, such as the bacterial predator Bdellovibrio bacteriovorus or bacteriophage. Therefore, we need to better understand microbial predator-prey dynamics. We developed mass-action mathematical models of predation for chemostats, which capture the low substrate concentration and slow growth typical for intended application areas of the predators such as wastewater treatment, aquaculture or the gut. Our model predicted that predator survival required a minimal prey cell size, explaining why Bdellovibrio is much smaller than its prey. A too good predator (attack rate too high, mortality too low) overexploited its prey leading to extinction (tragedy of the commons). Surprisingly, a predator taking longer to produce more offspring outcompeted a predator producing fewer offspring more rapidly (rate versus yield trade-off). Predation was only efficient in a narrow region around optimal parameters. Moreover, extreme oscillations under a wide range of conditions led to severe bottlenecks. These could be avoided when two prey species became available in alternating seasons. A bacteriophage outcompeted Bdellovibrio due to its higher burst size and faster life cycle. Together, results suggest that Bdellovibrio would struggle to survive on a single prey, explaining why it must be a generalist predator and suggesting it is better suited than phage to environments with multiple prey. Importance The discovery of antibiotics led to a dramatic drop in deaths due to infectious disease. Increasing levels of antimicrobial resistance, however, threaten to reverse this progress. There is thus a need for alternatives, such as therapies based on phage and predatory bacteria that kill bacteria regardless of whether they are pathogens or resistant to antibiotics. To best exploit them, we need to better understand what determines their effectiveness. By using a mathematical model to study bacterial predation in realistic slow growth conditions, we found that the generalist predator Bdellovibrio is most effective within a narrow range of conditions for each prey. For example, a minimum prey cell size is required, and the predator should not be too good as this would result in over-exploitation risking extinction. Together these findings give insights into the ecology of microbial predation and help explain why Bdellovibrio needs to be a generalist predator.

Application of Machine Learning Techniques to an Agent-Based Model of Pantoea

Agent-based modeling (ABM) is a powerful simulation technique which describes a complex dynamic system based on its interacting constituent entities. While the flexibility of ABM enables broad application, the complexity of real-world models demands intensive computing resources and computational time; however, a metamodel may be constructed to gain insight at less computational expense. Here, we developed a model in NetLogo to describe the growth of a microbial population consisting of Pantoea. We applied 13 parameters that defined the model and actively changed seven of the parameters to modulate the evolution of the population curve in response to these changes. We efficiently performed more than 3,000 simulations using a Python wrapper, NL4Py. Upon evaluation of the correlation between the active parameters and outputs by random forest regression, we found that the parameters which define the depth of medium and glucose concentration affect the population curves significantly. Subsequently, we constructed a metamodel, a dense neural network, to predict the simulation outputs from the active parameters and found that it achieves high prediction accuracy, reaching an R² coefficient of determination value up to 0.92. Our approach of using a combination of ABM with random forest regression and neural network reduces the number of required ABM simulations. The simplified and refined metamodels may provide insights into the complex dynamic system before their transition to more sophisticated models that run on high-performance computing systems. The ultimate goal is to build a bridge between simulation and experiment, allowing model validation by comparing the simulated data to experimental data in microbiology.

The Inclusion of the Food Microstructural Influence in Predictive Microbiology: State-of-the-Art

Predictive microbiology has steadily evolved into one of the most important tools to assess and control the microbiological safety of food products. Predictive models were traditionally developed based on experiments in liquid laboratory media, meaning that food microstructural effects were not represented in these models. Since food microstructure is known to exert a significant effect on microbial growth and inactivation dynamics, the applicability of predictive models is limited if food microstructure is not taken into account. Over the last 10-20 years, researchers, therefore, developed a variety of models that do include certain food microstructural influences. This review provides an overview of the most notable microstructure-including models which were developed over the years, both for microbial growth and inactivation.

Lattice Boltzmann Method in Modeling Biofilm Formation, Growth and Detachment

Biofilms are a complex and heterogeneous aggregation of multiple populations of microorganisms linked together by their excretion of extracellular polymer substances (EPS). Biofilms can cause many serious problems, such as chronic infections, food contamination and equipment corrosion, although they can be useful for constructive purposes, such as in wastewater treatment, heavy metal removal from hazardous waste sites, biofuel production, power generation through microbial fuel cells and microbially enhanced oil recovery; however, biofilm formation and growth are complex due to interactions among physicochemical and biological processes under operational and environmental conditions. Advanced numerical modeling techniques using the lattice Boltzmann method (LBM) are enabling the prediction of biofilm formation and growth and microbial community structures. This study is the first attempt to perform a general review on major contributions to LBM-based biofilm models, ranging from pioneering efforts to more recent progress. We present our understanding of the modeling of biofilm formation, growth and detachment using LBM-based models and present the fundamental aspects of various LBM-based biofilm models. We describe how the LBM couples with cellular automata (CA) and individual-based model (IbM) approaches and discuss their applications in assessing the spatiotemporal distribution of biofilms and their associated parameters and evaluating bioconversion efficiency. Finally, we discuss the main features and drawbacks of LBM-based biofilm models from ecological and biotechnological perspectives and identify current knowledge gaps and future research priorities.

Modelling microbial communities: Harnessing consortia for biotechnological applications

Microbes propagate and thrive in complex communities, and there are many benefits to studying and engineering microbial communities instead of single strains. Microbial communities are being increasingly leveraged in biotechnological applications, as they present significant advantages such as the division of labour and improved substrate utilisation. Nevertheless, they also present some interesting challenges to surmount for the design of efficient biotechnological processes. In this review, we discuss key principles of microbial interactions, followed by a deep dive into genome-scale metabolic models, focussing on a vast repertoire of constraint-based modelling methods that enable us to characterise and understand the metabolic capabilities of microbial communities. Complementary approaches to model microbial communities, such as those based on graph theory, are also briefly discussed. Taken together, these methods provide rich insights into the interactions between microbes and how they influence microbial community productivity. We finally overview approaches that allow us to generate and test numerous synthetic community compositions, followed by tools and methodologies that can predict effective genetic interventions to further improve the productivity of communities. With impending advancements in high-throughput omics of microbial communities, the stage is set for the rapid expansion of microbial community engineering, with a significant impact on biotechnological processes.

The influence of the crowding assumptions in biofilm simulations

Microorganisms are frequently organized into crowded structures that affect the nutrients diffusion. This reduction in metabolite diffusion could modify the microbial dynamics, meaning that computational methods for studying microbial systems need accurate ways to model the crowding conditions. We previously developed a computational framework, termed CROMICS, that incorporates the effect of the (time-dependent) crowding conditions on the spatio-temporal modeling of microbial communities, and we used it to demonstrate the crowding influence on the community dynamics. To further identify scenarios where crowding should be considered in microbial modeling, we herein applied and extended CROMICS to simulate several environmental conditions that could potentially boost or dampen the crowding influence in biofilms. We explore whether the nutrient supply (rich- or low-nutrient media), the cell-packing configuration (square or hexagonal spherical cell arrangement), or the cell growing conditions (planktonic state or biofilm) modify the crowding influence on the growth of Escherichia coli. Our results indicate that the growth rate, the abundance and appearance time of different cell phenotypes as well as the amount of by-products secreted to the medium are sensitive to some extent to the local crowding conditions in all scenarios tested, except in rich-nutrient media. Crowding conditions enhance the formation of nutrient gradient in biofilms, but its effect is only appreciated when cell metabolism is controlled by the nutrient limitation. Thus, as soon as biomass (and/or any other extracellular macromolecule) accumulates in a region, and cells occupy more than 14% of the volume fraction, the crowding effect must not be underestimated, as the microbial dynamics start to deviate from the ideal/expected behaviour that assumes volumeless cells or when a homogeneous (reduced) diffusion is applied in the simulation. The modeling and simulation of the interplay between the species diversity (cell shape and metabolism) and the environmental conditions (nutrient quality, crowding conditions) can help to design effective strategies for the optimization and control of microbial systems.

Selfishness driving reductive evolution shapes interdependent patterns in spatially structured microbial communities

Microbes release a wide variety of metabolites to the environment that benefit the whole population, called public goods. Public goods sharing drives adaptive function loss, and allows the rise of metabolic cross-feeding. However, how public goods sharing governs the succession of communities over evolutionary time scales remains unclear. To resolve this issue, we constructed an individual-based model, where an autonomous population that possessed functions to produce three essential public goods, was allowed to randomly lose functions. Simulations revealed that function loss genotypes could evolve from the autonomous ancestor, driven by the selfish public production trade-off at the individual level. These genotypes could then automatically develop to three possible types of interdependent patterns: complete functional division, one-way dependency, and asymmetric functional complementation, which were influenced by function cost and function redundancy. In addition, we found random evolutionary events, i.e., the priority and the relative spatial positioning of genotype emergence, are also important in governing community assembly. Moreover, communities occupied by interdependent patterns exhibited better resistance to environmental perturbation, suggesting such patterns are selectively favored. Our work integrates ecological interactions with evolution dynamics, providing a new perspective to explain how reductive evolution shapes microbial interdependencies and governs the succession of communities.

The ecology of plasmid-coded antibiotic resistance: a basic framework for experimental research and modeling

Many antibiotic resistance genes are associated with plasmids. The ecological success of these mobile genetic elements within microbial communities depends on varying mechanisms to secure their own propagation, not only on environmental selection. Among the most important are the cost of plasmids and their ability to be transferred to new hosts through mechanisms such as conjugation. These are regulated by dynamic control systems of the conjugation machinery and genetic adaptations that plasmid-host pairs can acquire in coevolution. However, in complex communities, these processes and mechanisms are subject to a variety of interactions with other bacterial species and other plasmid types. This article summarizes basic plasmid properties and ecological principles particularly important for understanding the persistence of plasmid-coded antibiotic resistance in aquatic environments. Through selected examples, it further introduces to the features of different types of simulation models such as systems of ordinary differential equations and individual-based models, which are considered to be important tools to understand these complex systems. This ecological perspective aims to improve the way we study and understand the dynamics, diversity and persistence of plasmids and associated antibiotic resistance genes.

Not Just Numbers: Mathematical Modelling and Its Contribution to Anaerobic Digestion Processes

Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.

From Microbial Communities to Distributed Computing Systems

A distributed biological system can be defined as a system whose components are located in different subpopulations, which communicate and coordinate their actions through interpopulation messages and interactions. We see that distributed systems are pervasive in nature, performing computation across all scales, from microbial communities to a flock of birds. We often observe that information processing within communities exhibits a complexity far greater than any single organism. Synthetic biology is an area of research which aims to design and build synthetic biological machines from biological parts to perform a defined function, in a manner similar to the engineering disciplines. However, the field has reached a bottleneck in the complexity of the genetic networks that we can implement using monocultures, facing constraints from metabolic burden and genetic interference. This makes building distributed biological systems an attractive prospect for synthetic biology that would alleviate these constraints and allow us to expand the applications of our systems into areas including complex biosensing and diagnostic tools, bioprocess control and the monitoring of industrial processes. In this review we will discuss the fundamental limitations we face when engineering functionality with a monoculture, and the key areas where distributed systems can provide an advantage. We cite evidence from natural systems that support arguments in favor of distributed systems to overcome the limitations of monocultures. Following this we conduct a comprehensive overview of the synthetic communities that have been built to date, and the components that have been used. The potential computational capabilities of communities are discussed, along with some of the applications that these will be useful for. We discuss some of the challenges with building co-cultures, including the problem of competitive exclusion and maintenance of desired community composition. Finally, we assess computational frameworks currently available to aide in the design of microbial communities and identify areas where we lack the necessary tools.

Flagellar motility mediates early-stage biofilm formation in oligotrophic aquatic environment

Flagellar motility enables resource acquisition and noxious substance evasion, underpinning imperative ecological processes in aquatic environments. Yet the underlying mechanism that links flagellar motility with surface attachment and thereby biofilm formation, especially in conditions of limited resource availability, remains elusive. Here, we present experimental and modeling evidence to unveil bacterial motility and biofilm formation under nutrient-limited stresses with Pseudomonas aeruginosa (WT) and its nonflagellated isogenic mutant (ΔfliC) as model bacteria. Results revealed that boosted flagellar motility of WT strain promoted biofilm initialization to a peak value of 0.99 × 10⁷ cells/cm² at 1/50 dilution after 20 min incubation. We hypothesized that bacteria can invoke instant motility acceleration for survival confronting nutrient-limited stress, accompanied by optimized chemotactic foraging through sensing ambient chemical gradients. Accordingly, accelerated cell motility in oligotrophic environment created increased cell-cell and cell-surface interactions and thereof facilitated biofilm initialization. It was confirmed by the consistence of modeling predictions and experimental results of cell velocity and surface attachment. With the development of biofilm, promotion effect of flagellar motility responding to nutrient deprivation-stress faded out. Instead, loss of motility profiting increased growth rates and extracellular protein excretion, associated with an enhancement of biofilm development for the mutant in oligotrophic aquatic environment. For both strains, nutrient limitation evidently reduced planktonic cell propagation as expected. Our results offer new insights into the mechanical understanding of biofilm formation shaped by environmental stresses and associating biological responses.

NUFEB: A massively parallel simulator for individual-based modelling of microbial communities

We present NUFEB (Newcastle University Frontiers in Engineering Biology), a flexible, efficient, and open source software for simulating the 3D dynamics of microbial communities. The tool is based on the Individual-based Modelling (IbM) approach, where microbes are represented as discrete units and their behaviour changes over time due to a variety of processes. This approach allows us to study population behaviours that emerge from the interaction between individuals and their environment. NUFEB is built on top of the classical molecular dynamics simulator LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), which we extended with IbM features. A wide range of biological, physical and chemical processes are implemented to explicitly model microbial systems, with particular emphasis on biofilms. NUFEB is fully parallelised and allows for the simulation of large numbers of microbes (10⁷ individuals and beyond). The parallelisation is based on a domain decomposition scheme that divides the domain into multiple sub-domains which are distributed to different processors. NUFEB also offers a collection of post-processing routines for the visualisation and analysis of simulation output. In this article, we give an overview of NUFEB’s functionalities and implementation details. We provide examples that illustrate the type of microbial systems NUFEB can be used to model and simulate.

Individual-based Models (IbM) are one of the most promising frameworks to study microbial communities, as they can explicitly describe the behaviour of each cell. The development of a general-purpose IbM solver should focus on efficiency and flexibility due to the unique characteristics of microbial systems. However, available tools for these purposes present significant limitations. Most of them only facilitate serial computing for single simulation, or only focus on biological processes, but do not model mechanical and chemical processes in detail. In this work, we introduce the IbM solver NUFEB that addresses some of these shortcomings. The tool facilitates the modelling of much needed biological, chemical, physical and individual microbes in detail, and offers the flexibility of model extension and customisation. NUFEB is also fully parallelised and allows for the simulation of large complex microbial system. In this paper, we first give an overview of NUFEB’s functionalities and implementation details. Then, we use NUFEB to model and simulate a biofilm system with fluid dynamics, and a large and complex biofilm system with multiple microbial functional groups and multiple nutrients.

Cooperation and spatial self-organization determine rate and efficiency of particulate organic matter degradation in marine bacteria

Microorganisms can cooperate by secreting public goods that benefit local neighbors; however, the conditions that favor cooperative growth in the environment, and the way in which this growth alters microbes’ contribution to ecosystem functions, remain unexplored. Here, we show that cooperation mediates the degradation of polysaccharide particles recalcitrant to hydrolysis in aquatic environments. Combining experiments and models, we define the physiological and environmental parameters that mediate the transition from cooperation to competition. Cooperation emerges through the self-organization of cells into ∼10- to 20-µm clusters that enable uptake of diffusible hydrolysis products. When cooperation is required, the degradation of recalcitrant biopolymers can only take place when degraders exceed a critical cell concentration, underscoring the importance of microbial interactions for ecosystem function.

The recycling of particulate organic matter (POM) by microbes is a key part of the global carbon cycle. This process is mediated by the extracellular hydrolysis of polysaccharides, which can trigger social behaviors in bacteria resulting from the production of public goods. Despite the potential importance of public good-mediated interactions, their relevance in the environment remains unclear. In this study, we developed a computational and experimental model system to address this challenge and studied how the POM depolymerization rate and its uptake efficiency (2 main ecosystem function parameters) depended on social interactions and spatial self-organization on particle surfaces. We found an emergent trade-off between rate and efficiency resulting from the competition between oligosaccharide diffusion and cellular uptake, with low rate and high efficiency being achieved through cell-to-cell cooperation between degraders. Bacteria cooperated by aggregating in cell clusters of ∼10 to 20 µm, in which cells were able to share public goods. This phenomenon, which was independent of any explicit group-level regulation, led to the emergence of critical cell concentrations below which degradation did not occur, despite all resources being available in excess. In contrast, when particles were labile and turnover rates were high, aggregation promoted competition and decreased the efficiency of carbon use. Our study shows how social interactions and cell aggregation determine the rate and efficiency of particulate carbon turnover in environmentally relevant scenarios.

Burst statistics in an early biofilm quorum sensing model: the role of spatial colony-growth heterogeneity

Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called “autoinducers”) and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a “cluster” of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get “induced” into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.

Individual Based Model Links Thermodynamics, Chemical Speciation and Environmental Conditions to Microbial Growth

Individual based Models (IbM) must transition from research tools to engineering tools. To make the transition we must aspire to develop large, three dimensional and physically and biologically credible models. Biological credibility can be promoted by grounding, as far as possible, the biology in thermodynamics. Thermodynamic principles are known to have predictive power in microbial ecology. However, this in turn requires a model that incorporates pH and chemical speciation. Physical credibility implies plausible mechanics and a connection with the wider environment. Here, we propose a step toward that ideal by presenting an individual based model connecting thermodynamics, pH and chemical speciation and environmental conditions to microbial growth for 5·105 individuals. We have showcased the model in two scenarios: a two functional group nitrification model and a three functional group anaerobic community. In the former, pH and connection to the environment had an important effect on the outcomes simulated. Whilst in the latter pH was less important but the spatial arrangements and community productivity (that is, methane production) were highly dependent on thermodynamic and reactor coupling. We conclude that if IbM are to attain their potential as tools to evaluate the emergent properties of engineered biological systems it will be necessary to combine the chemical, physical, mechanical and biological along the lines we have proposed. We have still fallen short of our ideals because we cannot (yet) calculate specific uptake rates and must develop the capacity for longer runs in larger models. However, we believe such advances are attainable. Ideally in a common, fast and modular platform. For future innovations in IbM will only be of use if they can be coupled with all the previous advances.

Modeling metabolic networks of individual bacterial agents in heterogeneous and dynamic soil habitats (IndiMeSH)

Natural soil is characterized as a complex habitat with patchy hydrated islands and spatially variable nutrients that is in a constant state of change due to wetting-drying dynamics. Soil microbial activity is often concentrated in sparsely distributed hotspots that contribute disproportionally to macroscopic biogeochemical nutrient cycling and greenhouse gas emissions. The mechanistic representation of such dynamic hotspots requires new modeling approaches capable of representing the interplay between dynamic local conditions and the versatile microbial metabolic adaptations. We have developed IndiMeSH (Individual-based Metabolic network model for Soil Habitats) as a spatially explicit model for the physical and chemical microenvironments of soil, combined with an individual-based representation of bacterial motility and growth using adaptive metabolic networks. The model uses angular pore networks and a physically based description of the aqueous phase as a backbone for nutrient diffusion and bacterial dispersal combined with dynamic flux balance analysis to calculate growth rates depending on local nutrient conditions. To maximize computational efficiency, reduced scale metabolic networks are used for the simulation scenarios and evaluated strategically to the genome scale model. IndiMeSH was compared to a well-established population-based spatiotemporal metabolic network model (COMETS) and to experimental data of bacterial spatial organization in pore networks mimicking soil aggregates. IndiMeSH was then used to strategically study dynamic response of a bacterial community to abrupt environmental perturbations and the influence of habitat geometry and hydration conditions. Results illustrate that IndiMeSH is capable of representing trophic interactions among bacterial species, predicting the spatial organization and segregation of bacterial populations due to oxygen and carbon gradients, and provides insights into dynamic community responses as a consequence of environmental changes. The modular design of IndiMeSH and its implementation are adaptable, allowing it to represent a wide variety of experimental and in silico microbial systems.

Soil bacterial communities are key players in global biogeochemical cycles and drive other soil regulatory and provisional ecosystem functions. Despite the relatively high bacterial abundance found in fertile soil, bacteria occupy only a small fraction of the soil surfaces and often form hotspots with disproportionate contributions to observed biogenic fluxes. As soil opacity and complexity limit detailed observations of such hotspots in situ, we have developed a modeling platform, IndiMeSH (Individual-based Metabolic network model for Soil Habitats), to enable systematic study of dense multispecies bacterial communities within a structured habitat resembling (but not limited) to soil. The model is capable of representing multispecies trophic interactions and spatial self-organization in response to nutrient gradients, as confirmed in comparison with published results. IndiMeSH offers new opportunities for quantifying bacterial hotspot formation and dynamics and observe their resilience and response to perturbations in hydration and nutrient conditions.

Spatiotemporal establishment of dense bacterial colonies growing on hard agar

The physical interactions of growing bacterial cells with each other and with their surroundings significantly affect the structure and dynamics of biofilms. Here a 3D agent-based model is formulated to describe the establishment of simple bacterial colonies expanding by the physical force of their growth. With a single set of parameters, the model captures key dynamical features of colony growth by non-motile, non EPS-producing E. coli cells on hard agar. The model, supported by experiment on colony growth in different types and concentrations of nutrients, suggests that radial colony expansion is not limited by nutrients as commonly believed, but by mechanical forces. Nutrient penetration instead governs vertical colony growth, through thin layers of vertically oriented cells lifting up their ancestors from the bottom. Overall, the model provides a versatile platform to investigate the influences of metabolic and environmental factors on the growth and morphology of bacterial colonies.

Understanding the mechanical link between oriented cell division and cerebellar morphogenesis

The cerebellum is a tightly folded structure located at the back of the head. Unlike the folds of the cerebrum, the folds of the cerebellum are aligned such that the external surface appears to be covered in parallel grooves. Experiments have shown that anchoring center initiation drives cerebellar foliation. However, the mechanism guiding the location of these anchoring centers, and subsequently cerebellar morphology, remains poorly understood. In particular, there is no definitive mechanistic explanation for the preferential emergence of parallel folds instead of an irregular folding pattern like in the cerebral cortex. Here we use mechanical modeling on the cellular and tissue scales to show that the oriented granule cell division observed in the experimental setting leads to the characteristic parallel folding pattern of the cerebellum. Specifically, we propose an agent-based model of cell clones, a strategy for propagating information from our in silico cell clones to the tissue scale, and an analytical solution backed by numerical results to understand how differential growth between the cerebellar layers drives geometric instability in three dimensional space on the tissue scale. This proposed mechanical model provides further insight into the process of anchoring center initiation and establishes a framework for future multiscale mechanical analysis of developing organs.

Soil aggregates as biogeochemical reactors and implications for soil-atmosphere exchange of greenhouse gases-A concept

Soil-atmosphere exchange significantly influences the global atmospheric abundances of carbon dioxide (CO₂ ), methane (CH₄ ), and nitrous oxide (N₂ O). These greenhouse gases (GHGs) have been extensively studied at the soil profile level and extrapolated to coarser scales (regional and global). However, finer scale studies of soil aggregation have not received much attention, even though elucidating the GHG activities at the full spectrum of scales rather than just coarse levels is essential for reducing the large uncertainties in the current atmospheric budgets of these gases. Through synthesizing relevant studies, we propose that aggregates, as relatively separate micro-environments embedded in a complex soil matrix, can be viewed as biogeochemical reactors of GHGs. Aggregate reactivity is determined by both aggregate size (which determines the reactor size) and the bulk soil environment including both biotic and abiotic factors (which further influence the reaction conditions). With a systematic, dynamic view of the soil system, implications of aggregate reactors for soil-atmosphere GHG exchange are determined by both an individual reactor's reactivity and dynamics in aggregate size distributions. Emerging evidence supports the contention that aggregate reactors significantly influence soil-atmosphere GHG exchange and may have global implications for carbon and nitrogen cycling. In the context of increasingly frequent and severe disturbances, we advocate more analyses of GHG activities at the aggregate scale. To complement data on aggregate reactors, we suggest developing bottom-up aggregate-based models (ABMs) that apply a trait-based approach and incorporate soil system heterogeneity.

Ecology of Contaminant Biotransformation in the Mycosphere: Role of Transport Processes

Fungi and bacteria often share common microhabitats. Their co-occurrence and coevolution give rise to manifold ecological interactions in the mycosphere, here defined as the microhabitats surrounding and affected by hyphae and mycelia. The extensive structure of mycelia provides ideal "logistic networks" for transport of bacteria and matter in structurally and chemically heterogeneous soil ecosystems. We describe the characteristics of the mycosphere as a unique and highly dynamic bacterial habitat and a hot spot for contaminant biotransformation. In particular, we emphasize the role of the mycosphere for (i) bacterial dispersal and colonization of subsurface interfaces and new habitats, (ii) matter transport processes and contaminant bioaccessibility, and (iii) the functional stability of microbial ecosystems when exposed to environmental fluctuations such as stress or disturbances. Adopting concepts from ecological theory, the chapter disentangles bacterial-fungal impacts on contaminant biotransformation in a systemic approach that interlinks empirical data from microbial ecosystems with simulation data from computational models. This approach provides generic information on key factors, processes, and ecological principles that drive microbial contaminant biotransformation in soil. We highlight that the transport processes create favorable habitat conditions for efficient bacterial contaminant degradation in the mycosphere. In-depth observation, understanding, and prediction of the role of mycosphere transport processes will support the use of bacterial-fungal interactions in nature-based solutions for contaminant biotransformation in natural and man-made ecosystems, respectively.

Spatiotemporal disturbance characteristics determine functional stability and collapse risk of simulated microbial ecosystems

Terrestrial microbial ecosystems are exposed to many types of disturbances varying in their spatial and temporal characteristics. The ability to cope with these disturbances is crucial for maintaining microbial ecosystem functions, especially if disturbances recur regularly. Thus, understanding microbial ecosystem dynamics under recurrent disturbances and identifying drivers of functional stability and thresholds for functional collapse is important. Using a spatially explicit ecological model of bacterial growth, dispersal, and substrate consumption, we simulated spatially heterogeneous recurrent disturbances and investigated the dynamic response of pollutant biodegradation – exemplarily for an important ecosystem function. We found that thresholds for functional collapse are controlled by the combination of disturbance frequency and spatial configuration (spatiotemporal disturbance regime). For rare disturbances, the occurrence of functional collapse is promoted by low spatial disturbance fragmentation. For frequent disturbances, functional collapse is almost inevitable. Moreover, the relevance of bacterial growth and dispersal for functional stability also depends on the spatiotemporal disturbance regime. Under disturbance regimes with moderate severity, microbial properties can strongly affect functional stability and shift the threshold for functional collapse. Similarly, networks facilitating bacterial dispersal can delay functional collapse. Consequently, measures to enhance or sustain bacterial growth/dispersal are promising strategies to prevent functional collapses under moderate disturbance regimes.

A tutorial on uncertainty propagation techniques for predictive microbiology models: A critical analysis of state-of-the-art techniques

Building mathematical models in predictive microbiology is a data driven science. As such, the experimental data (and its uncertainty) has an influence on the final predictions and even on the calculation of the model prediction uncertainty. Therefore, the current research studies the influence of both the parameter estimation and uncertainty propagation method on the calculation of the model prediction uncertainty. The study is intended as well as a tutorial to uncertainty propagation techniques for researchers in (predictive) microbiology. To this end, an in silico case study was applied in which the effect of temperature on the microbial growth rate was modelled and used to make simulations for a temperature profile that is characterised by variability. The comparison of the parameter estimation methods demonstrated that the one-step method yields more accurate and precise calculations of the model prediction uncertainty than the two-step method. Four uncertainty propagation methods were assessed. The current work assesses the applicability of these techniques by considering the effect of experimental uncertainty and model input uncertainty. The linear approximation was demonstrated not always to provide reliable results. The Monte Carlo method was computationally very intensive, compared to its competitors. Polynomial chaos expansion was computationally efficient and accurate but is relatively complex to implement. Finally, the sigma point method was preferred as it is (i) computationally efficient, (ii) robust with respect to experimental uncertainty and (iii) easily implemented.

A Bayesian approach to modelling the impact of hydrodynamic shear stress on biofilm deformation

We investigate the feasibility of using a surrogate-based method to emulate the deformation and detachment behaviour of a biofilm in response to hydrodynamic shear stress. The influence of shear force, growth rate and viscoelastic parameters on the patterns of growth, structure and resulting shape of microbial biofilms was examined. We develop a statistical modelling approach to this problem, using combination of Bayesian Poisson regression and dynamic linear models for the emulation. We observe that the hydrodynamic shear force affects biofilm deformation in line with some literature. Sensitivity results also showed that the expected number of shear events, shear flow, yield coefficient for heterotrophic bacteria and extracellular polymeric substance (EPS) stiffness per unit EPS mass are the four principal mechanisms governing the bacteria detachment in this study. The sensitivity of the model parameters is temporally dynamic, emphasising the significance of conducting the sensitivity analysis across multiple time points. The surrogate models are shown to perform well, and produced ≈ 480 fold increase in computational efficiency. We conclude that a surrogate-based approach is effective, and resulting biofilm structure is determined primarily by a balance between bacteria growth, viscoelastic parameters and applied shear stress.

How do environment-dependent switching rates between susceptible and persister cells affect the dynamics of biofilms faced with antibiotics?

Persisters form sub-populations of stress-tolerant cells that play a major role in the capacity of biofilms to survive and recover from disturbances such as antibiotic treatments. The mechanisms of persistence are diverse and influenced by environmental conditions, and persister populations are more heterogeneous than formerly suspected. We used computational modeling to assess the impact of three switching strategies between susceptible and persister cells on the capacity of bacterial biofilms to grow, survive and recover from antibiotic treatments. The strategies tested were: (1) constant switches, (2) substrate-dependent switches and (3) antibiotic-dependent switches. We implemented these strategies in an individual-based biofilm model and simulated antibiotic shocks on virtual biofilms. Because of limited available data on switching rates in the literature, nine parameter sets were assessed for each strategy. Substrate and antibiotic-dependent switches allowed high switching rates without affecting the growth of the biofilms. Compared to substrate-dependent switches, constant and antibiotic-dependent switches were associated with higher proportions of persisters in the top of the biofilms, close to the substrate source, which probably confers a competitive advantage within multi-species biofilms. The constant and substrate-dependent strategies need a compromise between limiting the wake-up and death of persisters during treatments and leaving the persister state fast enough to recover quickly after antibiotic-removal. Overall, the simulations gave new insights into the relationships between the dynamics of persister populations in biofilms and their dynamics of growth, survival and recovery when faced with disturbances.

Spatial organization of bacterial populations in response to oxygen and carbon counter-gradients in pore networks

Microbial activity in soil is spatially heterogeneous often forming spatial hotspots that contribute disproportionally to biogeochemical processes. Evidence suggests that bacterial spatial organization contributes to the persistence of anoxic hotspots even in unsaturated soils. Such processes are difficult to observe in situ at the microscale, hence mechanisms and time scales relevant for bacterial spatial organization remain largely qualitative. Here we develop an experimental platform based on glass-etched micrometric pore networks that mimics resource gradients postulated in soil aggregates to observe spatial organization of fluorescently tagged aerobic and facultative anaerobic bacteria. Two initially intermixed bacterial species, Pseudomonas putida and Pseudomonas veronii, segregate into preferential regions promoted by opposing gradients of carbon and oxygen (such persistent coexistence is not possible in well-mixed cultures). The study provides quantitative visualization and modeling of bacterial spatial organization within aggregate-like hotspots, a key step towards developing a mechanistic representation of bacterial community organization in soil pores.

A Microfluidics and Agent-Based Modeling Framework for Investigating Spatial Organization in Bacterial Colonies: The Case of Pseudomonas Aeruginosa and H1-Type VI Secretion Interactions

The factors leading to changes in the organization of microbial assemblages at fine spatial scales are not well characterized or understood. However, they are expected to guide the succession of community development and function toward specific outcomes that could impact human health and the environment. In this study, we put forward a combined experimental and agent-based modeling framework and use it to interpret unique spatial organization patterns of H1-Type VI secretion system (T6SS) mutants of P. aeruginosa under spatial confinement. We find that key parameters, such as T6SS-mediated cell contact and lysis, spatial localization, relative species abundance, cell density and local concentrations of growth substrates and metabolites are influenced by spatial confinement. The model, written in the accessible programming language NetLogo, can be adapted to a variety of biological systems of interest and used to simulate experiments across a broad parameter space. It was implemented and run in a high-throughput mode by deploying it across multiple CPUs, with each simulation representing an individual well within a high-throughput microwell array experimental platform. The microfluidics and agent-based modeling framework we present in this paper provides an effective means by which to connect experimental studies in microbiology to model development. The work demonstrates progress in coupling experimental results to simulation while also highlighting potential sources of discrepancies between real-world experiments and idealized models.

Simulation of Escherichia coli Dynamics in Biofilms and Submerged Colonies with an Individual-Based Model Including Metabolic Network Information

Clustered microbial communities are omnipresent in the food industry, e.g., as colonies of microbial pathogens in/on food media or as biofilms on food processing surfaces. These clustered communities are often characterized by metabolic differentiation among their constituting cells as a result of heterogeneous environmental conditions in the cellular surroundings. This paper focuses on the role of metabolic differentiation due to oxygen gradients in the development of Escherichia coli cell communities, whereby low local oxygen concentrations lead to cellular secretion of weak acid products. For this reason, a metabolic model has been developed for the facultative anaerobe E. coli covering the range of aerobic, microaerobic, and anaerobic environmental conditions. This metabolic model is expressed as a multiparametric programming problem, in which the influence of low extracellular pH values and the presence of undissociated acid cell products in the environment has been taken into account. Furthermore, the developed metabolic model is incorporated in MICRODIMS, an in-house developed individual-based modeling framework to simulate microbial colony and biofilm dynamics. Two case studies have been elaborated using the MICRODIMS simulator: (i) biofilm growth on a substratum surface and (ii) submerged colony growth in a semi-solid mixed food product. In the first case study, the acidification of the biofilm environment and the emergence of typical biofilm morphologies have been observed, such as the mushroom-shaped structure of mature biofilms and the formation of cellular chains at the exterior surface of the biofilm. The simulations show that these morphological phenomena are respectively dependent on the initial affinity of pioneer cells for the substratum surface and the cell detachment process at the outer surface of the biofilm. In the second case study, a no-growth zone emerges in the colony center due to a local decline of the environmental pH. As a result, cellular growth in the submerged colony is limited to the colony periphery, implying a linear increase of the colony radius over time. MICRODIMS has been successfully used to reproduce complex dynamics of clustered microbial communities.

Extracellular Polymeric Substance Production and Aggregated Bacteria Colonization Influence the Competition of Microbes in Biofilms

The production of extracellular polymeric substance (EPS) is important for the survival of biofilms. However, EPS production is costly for bacteria and the bacterial strains that produce EPS (EPS+) grow in the same environment as non-producers (EPS-) leading to competition between these strains for nutrients and space. The outcome of this competition is likely to be dependent on factors such as initial attachment, EPS production rate, ambient nutrient levels and quorum sensing. We use an Individual-based Model (IbM) to study the competition between EPS+ and EPS- strains by varying the nature of initial colonizers which can either be in the form of single cells or multicellular aggregates. The microbes with EPS+ characteristics obtain a competitive advantage if they initially colonize the surface as smaller aggregates and are widely spread-out between the cells of EPS-, when both are deposited on the substratum. Furthermore, the results show that quorum sensing-regulated EPS production may significantly reduce the fitness of EPS producers when they initially deposit as aggregates. The results provide insights into how the distribution of bacterial aggregates during initial colonization could be a deciding factor in the competition among different strains in biofilms.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for “bottom up” prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

Growth of bacteria in 3-d colonies

The dynamics of growth of bacterial populations has been extensively studied for planktonic cells in well-agitated liquid culture, in which all cells have equal access to nutrients. In the real world, bacteria are more likely to live in physically structured habitats as colonies, within which individual cells vary in their access to nutrients. The dynamics of bacterial growth in such conditions is poorly understood, and, unlike that for liquid culture, there is not a standard broadly used mathematical model for bacterial populations growing in colonies in three dimensions (3-d). By extending the classic Monod model of resource-limited population growth to allow for spatial heterogeneity in the bacterial access to nutrients, we develop a 3-d model of colonies, in which bacteria consume diffusing nutrients in their vicinity. By following the changes in density of E. coli in liquid and embedded in glucose-limited soft agar, we evaluate the fit of this model to experimental data. The model accounts for the experimentally observed presence of a sub-exponential, diffusion-limited growth regime in colonies, which is absent in liquid cultures. The model predicts and our experiments confirm that, as a consequence of inter-colony competition for the diffusing nutrients and of cell death, there is a non-monotonic relationship between total number of colonies within the habitat and the total number of individual cells in all of these colonies. This combined theoretical-experimental study reveals that, within 3-d colonies, E. coli cells are loosely packed, and colonies produce about 2.5 times as many cells as the liquid culture from the same amount of nutrients. We verify that this is because cells in liquid culture are larger than in colonies. Our model provides a baseline description of bacterial growth in 3-d, deviations from which can be used to identify phenotypic heterogeneities and inter-cellular interactions that further contribute to the structure of bacterial communities.

The vast majority of theoretical and experimental studies assume that bacteria exist as planktonic cells in well-mixed liquid cultures, all with equal access to nutrients, wastes, toxins, antibiotics, bacterial viruses, and each other. However, in the real world, bacteria are more often found in physically structured, spatially heterogeneous habitats as colonies and micro-colonies. While one can experimentally explore the population and evolutionary dynamics of bacteria in such physically structured habitats, there is dearth of mathematical models to generate hypotheses for and to interpret results of these experiments. As a step towards the construction of a theory of the population dynamics of bacteria in physically structured habitats, we develop and experientially explore the simplest such model of the dynamics of bacterial growth in 3-d structured colonies.