Ecological systems biology: The dynamics of interacting populations

Towards the human nasal microbiome: Simulating D. pigrum and S. aureus

The human nose harbors various microbes that decisively influence the wellbeing and health of their host. Among the most threatening pathogens in this habitat is Staphylococcus aureus. Multiple epidemiological studies identify Dolosigranulum pigrum as a likely beneficial bacterium based on its positive association with health, including negative associations with S. aureus. Carefully curated GEMs are available for both bacterial species that reliably simulate their growth behavior in isolation. To unravel the mutual effects among bacteria, building community models for simulating co-culture growth is necessary. However, modeling microbial communities remains challenging. This article illustrates how applying the NCMW fosters our understanding of two microbes' joint growth conditions in the nasal habitat and their intricate interplay from a metabolic modeling perspective. The resulting community model combines the latest available curated GEMs of D. pigrum and S. aureus. This uses case illustrates how to incorporate genuine GEM of participating microorganisms and creates a basic community model mimicking the human nasal environment. Our analysis supports the role of negative microbe-microbe interactions involving D. pigrum examined experimentally in the lab. By this, we identify and characterize metabolic exchange factors involved in a specific interaction between D. pigrum and S. aureus as an in silico candidate factor for a deep insight into the associated species. This method may serve as a blueprint for developing more complex microbial interaction models. Its direct application suggests new ways to prevent disease-causing infections by inhibiting the growth of pathogens such as S. aureus through microbe-microbe interactions.

Enhancing bioreactor arrays for automated measurements and reactive control with ReacSight

Small-scale, low-cost bioreactors provide exquisite control of environmental parameters of microbial cultures over long durations. Their use is gaining popularity in quantitative systems and synthetic biology. However, existing setups are limited in their measurement capabilities. Here, we present ReacSight, a strategy to enhance bioreactor arrays for automated measurements and reactive experiment control. ReacSight leverages low-cost pipetting robots for sample collection, handling and loading, and provides a flexible instrument control architecture. We showcase ReacSight capabilities on three applications in yeast. First, we demonstrate real-time optogenetic control of gene expression. Second, we explore the impact of nutrient scarcity on fitness and cellular stress using competition assays. Third, we perform dynamic control of the composition of a two-strain consortium. We combine custom or chi.bio reactors with automated cytometry. To further illustrate ReacSight's genericity, we use it to enhance plate-readers with pipetting capabilities and perform repeated antibiotic treatments on a bacterial clinical isolate.

Snowstorm Enhanced the Deterministic Processes of the Microbial Community in Cryoconite at Laohugou Glacier, Tibetan Plateau

Cryoconites harbor diverse microbial communities and are the metabolic hotspot in the glacial ecosystem. Glacial ecosystems are subjected to frequent climate disturbances such as precipitation (snowing), but little is known about whether microbial communities in cryoconite can maintain stability under such disturbance. Here, we investigated the bacterial community in supraglacial cryoconite before and after a snowfall event on the Laohugou Glacier (Tibetan Plateau), based on Illumina MiSeq sequencing of the 16S rRNA gene. Our results showed that the diversity of the microbial community significantly decreased, and the structure of the microbial community changed significantly after the disturbance of snowfall. This was partly due to the relative abundance increased of cold-tolerant bacterial taxa, which turned from rare into abundant sub-communities. After snowfall disturbance, the contribution of the deterministic process increased from 38 to 67%, which is likely due to the enhancement of environmental filtering caused by nitrogen limitation. These findings enhanced our understanding of the distribution patterns and assembly mechanisms of cryoconite bacterial communities on mountain glaciers.

Pathogens and predators impacting commercial production of microalgae and cyanobacteria

Production of phytoplankton (microalgae and cyanobacteria) in commercial raceway ponds and other systems is adversely impacted by phytoplankton pathogens, including bacteria, fungi and viruses. In addition, cultures are susceptible to productivity loss, or crash, through grazing by contaminating zooplankton such as protozoa, rotifers and copepods. Productivity loss and product contamination are also caused by otherwise innocuous invading phytoplankton that consume resources in competition with the species being cultured. This review is focused on phytoplankton competitors, pathogens and grazers of significance in commercial culture of microalgae and cyanobacteria. Detection and identification of these biological contaminants are discussed. Operational protocols for minimizing contamination, and methods of managing it, are discussed.

Snowdrift game induces pattern formation in systems of self-propelled particles

Evolutionary games between species are known to lead to intriguing spatiotemporal patterns in systems of diffusing agents. However, the role of interspecies interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active matter and evolutionary game theory and study a system of two species whose individuals are (self-)propelled and interact through a snowdrift game. We derive hydrodynamic equations for the density and velocity fields of both species from which we identify parameter regimes in which one or both species form macroscopic orientational order as well as regimes of propagating wave patterns. Interestingly, we find simultaneous wave patterns in both species that result from the interplay between alignment and snowdrift interactions-a feedback mechanism that we call game-induced pattern formation. We test these results in agent-based simulations and confirm the different regimes of order and spatiotemporal patterns as well as game-induced pattern formation.

A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS)

Genome-scale stoichiometric modeling of metabolism has become a standard systems biology tool for modeling cellular physiology and growth. Extensions of this approach are emerging as a valuable avenue for predicting, understanding and designing microbial communities. Computation of microbial ecosystems in time and space (COMETS) extends dynamic flux balance analysis to generate simulations of multiple microbial species in molecularly complex and spatially structured environments. Here we describe how to best use and apply the most recent version of COMETS, which incorporates a more accurate biophysical model of microbial biomass expansion upon growth, evolutionary dynamics and extracellular enzyme activity modules. In addition to a command-line option, COMETS includes user-friendly Python and MATLAB interfaces compatible with the well-established COBRA models and methods, as well as comprehensive documentation and tutorials. This protocol provides a detailed guideline for installing, testing and applying COMETS to different scenarios, generating simulations that take from a few minutes to several days to run, with broad applicability to microbial communities across biomes and scales.

Diverse communities behave like typical random ecosystems

In 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory. Yet, it remains unclear if and when we can treat real communities as random ecosystems. Here, we draw on recent progress in random matrix theory and statistical physics to extend May's approach to generalized consumer-resource models. We show that in diverse ecosystems adding even modest amounts of noise to consumer preferences results in a transition to "typicality," where macroscopic ecological properties of communities are indistinguishable from those of random ecosystems, even when resource preferences have prominent designed structures. We test these ideas using numerical simulations on a wide variety of ecological models. Our work offers an explanation for the success of random consumer resource models in reproducing experimentally observed ecological patterns in microbial communities and highlights the difficulty of scaling up bottom-up approaches in synthetic ecology to diverse communities.

Food web engineering: ecology and evolution to improve biological pest control

If we are to sustainably provide food to a rapidly growing human population, biological pest control (BPC) should integrate food web theory and evolution. This will account for the impacts of climate warming on the complex community settings of agroecosystems. We review recent studies looking for top-down augmentative pest control being hampered/promoted by biotic (community contexts) and/or abiotic (climate) drivers. Most studies found either positive or neutral effects on BPC. However, most ignored potential evolutionary responses occurring in the environments under study. We propose engineering food webs by engaging in a continuous feedback between ecological and evolutionary data, and individual-based modelling of agroecosystems. This should speed up the procurement of strains of efficient natural enemies better adapted to warming.

Optogenetic Tools for Control of Public Goods in Saccharomyces cerevisiae

Microorganisms live in dense and diverse communities, with interactions between cells guiding community development and phenotype. The ability to perturb specific intercellular interactions in space and time provides a powerful route to determining the critical interactions and design rules for microbial communities. Approaches using optogenetic tools to modulate these interactions offer promise, as light can be exquisitely controlled in space and time. We report new plasmids for rapid integration of an optogenetic system into Saccharomyces cerevisiae to engineer light control of expression of a gene of interest. In a proof-of-principle study, we demonstrate the ability to control a model cooperative interaction, namely, the expression of the enzyme invertase (SUC2) which allows S. cerevisiae to hydrolyze sucrose and utilize it as a carbon source. We demonstrate that the strength of this cooperative interaction can be tuned in space and time by modulating light intensity and through spatial control of illumination. Spatial control of light allows cooperators and cheaters to be spatially segregated, and we show that the interplay between cooperative and inhibitory interactions in space can lead to pattern formation. Our strategy can be applied to achieve spatiotemporal control of expression of a gene of interest in S. cerevisiae to perturb both intercellular and interspecies interactions.

IMPORTANCE Recent advances in microbial ecology have highlighted the importance of intercellular interactions in controlling the development, composition, and resilience of microbial communities. In order to better understand the role of these interactions in governing community development, it is critical to be able to alter them in a controlled manner. Optogenetically controlled interactions offer advantages over static perturbations or chemically controlled interactions, as light can be manipulated in space and time and does not require the addition of nutrients or antibiotics. Here, we report a system for rapidly achieving light control of a gene of interest in the important model organism Saccharomyces cerevisiae and demonstrate that by controlling expression of the enzyme invertase, we can control cooperative interactions. This approach will be useful for understanding intercellular and interspecies interactions in natural and synthetic microbial consortia containing S. cerevisiae and serves as a proof of principle for implementing this approach in other consortia.

The Good and the Bad: Ecological Interaction Measurements Between the Urinary Microbiota and Uropathogens

The human body harbors numerous populations of microorganisms in various ecological niches. Some of these microbial niches, such as the human gut and the respiratory system, are well studied. One system that has been understudied is the urinary tract, primarily because it has been considered sterile in the absence of infection. Thanks to modern sequencing and enhanced culture techniques, it is now known that a urinary microbiota exists. The implication is that these species live as communities in the urinary tract, forming microbial ecosystems. However, the interactions between species in such an ecosystem remains unknown. Various studies in different parts of the human body have highlighted the ability of the pre-existing microbiota to alter the course of infection by impacting the pathogenicity of bacteria either directly or indirectly. For the urinary tract, the effect of the resident microbiota on uropathogens and the phenotypic microbial interactions is largely unknown. No studies have yet measured the response of uropathogens to the resident urinary bacteria. In this study, we investigate the interactions between uropathogens, isolated from elderly individuals suffering from UTIs, and bacteria isolated from the urinary tract of asymptomatic individuals using growth measurements in conditioned media. We observed that bacteria isolated from individuals with UTI-like symptoms and bacteria isolated from asymptomatic individuals can affect each other's growth; for example, bacteria isolated from symptomatic individuals affect the growth of bacteria isolated from asymptomatic individuals more negatively than vice versa. Additionally, we show that Gram-positive bacteria alter the growth characteristics differently compared to Gram-negative bacteria. Our results are an early step in elucidating the role of microbial interactions in urinary microbial ecosystems that harbor both uropathogens and pre-existing microbiota.

Multi-Replicated Enrichment Communities as a Model System in Microbial Ecology

Recent advances in robotics and affordable genomic sequencing technologies have made it possible to establish and quantitatively track the assembly of enrichment communities in high-throughput. By conducting community assembly experiments in up to thousands of synthetic habitats, where the extrinsic sources of variation among replicates can be controlled, we can now study the reproducibility and predictability of microbial community assembly at different levels of organization, and its relationship with nutrient composition and other ecological drivers. Through a dialog with mathematical models, high-throughput enrichment communities are bringing us closer to the goal of developing a quantitative predictive theory of microbial community assembly. In this short review, we present an overview of recent research on this growing field, highlighting the connection between theory and experiments and suggesting directions for future work.

Automated design of synthetic microbial communities

Microbial species rarely exist in isolation. In naturally occurring microbial systems there is strong evidence for a positive relationship between species diversity and productivity of communities. The pervasiveness of these communities in nature highlights possible advantages for genetically engineered strains to exist in cocultures as well. Building synthetic microbial communities allows us to create distributed systems that mitigate issues often found in engineering a monoculture, especially as functional complexity increases. Here, we demonstrate a methodology for designing robust synthetic communities that include competition for nutrients, and use quorum sensing to control amensal bacteriocin interactions in a chemostat environment. We computationally explore all two- and three- strain systems, using Bayesian methods to perform model selection, and identify the most robust candidates for producing stable steady state communities. Our findings highlight important interaction motifs that provide stability, and identify requirements for selecting genetic parts and further tuning the community composition.

Why is cyclic dominance so rare?

Natural populations can contain multiple types of coexisting individuals. How does natural selection maintain such diversity within and across populations? A popular theoretical basis for the maintenance of diversity is cyclic dominance, illustrated by the rock-paper-scissor game. However, it appears difficult to find cyclic dominance in nature. Why is this the case? Focusing on continuously produced novel mutations, we theoretically addressed the rareness of cyclic dominance. We developed a model of an evolving population and studied the formation of cyclic dominance. Our results showed that the chance for cyclic dominance to emerge is lower when the newly introduced type is similar to existing types compared to the introduction of an unrelated type. This suggests that cyclic dominance is more likely to evolve through the assembly of unrelated types whereas it rarely evolves within a community of similar types.

The contest of microbial pigeon neighbors: Interspecies competition between Serratia marcescens and the human pathogen Cryptococcus neoformans

In nature, microorganisms often exhibit competitive behavior for nutrients and limited space, allowing them to alter the virulence determinants of pathogens. The human pathogenic yeast Cryptococcus neoformans can be found organized in biofilms, a complex community composed of an extracellular matrix which confers protection against predation. The aim of this study was to evaluate and characterize antagonistic interactions between two cohabiting microorganisms: C. neoformans and the bacteria Serratia marcescens. The interaction of S. marcescens with C. neoformans expressed a negative effect on biofilm formation, polysaccharide capsule, production of urease, and melanization of the yeast. These findings evidence that competition in mixed communities can result in dominance by one species, with direct impact on the physiological modulation of virulence determinants. Such an approach is key for understating the response of communities to the presence of competitors and, ultimately, rationally designing communities to prevent and treat certain diseases.

Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect

In microbial ecosystems, species not only compete for common resources but may also display mutualistic interactions as a result from metabolic cross-feeding. Such mutualism can lead to bistability. Depending on the initial population sizes, species will either survive or go extinct. Various phenomenological models have been suggested to describe bistability in mutualistic systems. However, these models do not account for interaction mediators such as nutrients. In contrast, nutrient-explicit models do not provide an intuitive understanding of what causes bistability. Here, we reduce a theoretical nutrient-explicit model of two mutualistic cross-feeders in a chemostat, uncovering an explicit relation to a growth model with an Allee effect. We show that the dilution rate in the chemostat leads to bistability by turning a weak Allee effect into a strong Allee effect. This happens as long as there is more production than consumption of cross-fed nutrients. Thanks to the explicit relationship of the reduced model with the underlying experimental parameters, these results allow to predict the biological conditions that sustain or prevent the survival of mutualistic species.

Understanding the evolution of interspecies interactions in microbial communities

Microbial communities are complex multi-species assemblages that are characterized by a multitude of interspecies interactions, which can range from mutualism to competition. The overall sign and strength of interspecies interactions have important consequences for emergent community-level properties such as productivity and stability. It is not well understood how interspecies interactions change over evolutionary timescales. Here, we review the empirical evidence that evolution is an important driver of microbial community properties and dynamics on timescales that have traditionally been regarded as purely ecological. Next, we briefly discuss different modelling approaches to study evolution of communities, emphasizing the similarities and differences between evolutionary and ecological perspectives. We then propose a simple conceptual model for the evolution of interspecies interactions in communities. Specifically, we propose that to understand the evolution of interspecies interactions, it is important to distinguish between direct and indirect fitness effects of a mutation. We predict that in well-mixed environments, traits will be selected exclusively for their direct fitness effects, while in spatially structured environments, traits may also be selected for their indirect fitness effects. Selection of indirectly beneficial traits should result in an increase in interaction strength over time, while selection of directly beneficial traits should not have such a systematic effect. We tested our intuitions using a simple quantitative model and found support for our hypotheses. The next step will be to test these hypotheses experimentally and provide input for a more refined version of the model in turn, thus closing the scientific cycle of models and experiments. This article is part of the theme issue 'Conceptual challenges in microbial community ecology'.

Strength of species interactions determines biodiversity and stability in microbial communities

Organisms-especially microbes-tend to live together in ecosystems. While some of these ecosystems are very biodiverse, others are not, and while some are very stable over time, others undergo strong temporal fluctuations. Despite a long history of research and a plethora of data, it is not fully understood what determines the biodiversity and stability of ecosystems. Theory and experiments suggest a connection between species interaction, biodiversity and the stability of ecosystems, where an increase in ecosystem stability with biodiversity could be observed in several cases. However, what causes these connections remains unclear. Here, we show in microbial ecosystems in the laboratory that the concentrations of available nutrients can set the strength of interactions between bacteria. High nutrient concentrations allowed the bacteria to strongly alter the chemical environment, causing on average more negative interactions between species. These stronger interactions excluded more species from the community, resulting in a loss of biodiversity. At the same time, the stronger interactions also decreased the stability of the microbial communities, providing a mechanistic link between species interaction, biodiversity and stability in microbial ecosystems.

Do Organic Substrates Drive Microbial Community Interactions in Arctic Snow?

The effect of nutrients on microbial interactions, including competition and collaboration, has mainly been studied in laboratories, but their potential application to complex ecosystems is unknown. Here, we examined the effect of changes in organic acids among other parameters on snow microbial communities in situ over 2 months. We compared snow bacterial communities from a low organic acid content period to that from a higher organic acid period. We hypothesized that an increase in organic acids would shift the dominant microbial interaction from collaboration to competition. To evaluate microbial interactions, we built taxonomic co-variance networks from OTUs obtained from 16S rRNA gene sequencing. In addition, we tracked marker genes of microbial cooperation (plasmid backbone genes) and competition (antibiotic resistance genes) across both sampling periods in metagenomes and metatranscriptomes. Our results showed a decrease in the average connectivity of the network during late spring compared to the early spring that we interpreted as a decrease of cooperation. This observation was strengthened by the significantly more abundant plasmid backbone genes in the metagenomes from the early spring. The modularity of the network from the late spring was also found to be higher than the one from the early spring, which is another possible indicator of increased competition. Antibiotic resistance genes were significantly more abundant in the late spring metagenomes. In addition, antibiotic resistance genes were also positively correlated to the organic acid concentration of the snow across both seasons. Snow organic acid content might be responsible for this change in bacterial interactions in the Arctic snow community.

Cooperation in Microbial Populations: Theory and Experimental Model Systems

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities.

Assessing interactions, predicting function, and increasing degradation potential of a PAH-degrading bacterial consortium by effect of an inoculant strain

A natural phenanthrene-degrading consortium CON was inoculated with an exogenous strain Sphingobium sp. (ex Sp. paucimobilis) 20006FA yielding the consortium called I-CON, in order to study ecological interactions into the bacterial community. DGGE and proteomic profiles and analyses by HTS (High-Throughput Sequencing) technologies demonstrated inoculant establishment and changes on CON composition. Inoculation increased degradation efficiency in I-CON and prevented intermediate HNA accumulation. This could be explained not only by the inoculation, but also by enrichment in Achromobacter genus at expense of a decrease in Klebsiella genus. After inoculation, cooperation between Sphingobium and Achromobacter genera were improved, thereby, some competition could have been generated, and as a consequence, species in minor proportion (cheaters), as Inquilinus sp. and Luteibacter sp., were not detected. Sequences of Sphingobium (corresponding to the inoculated strain) did not vary. PICRUSt predicted a network with bacterial phylotypes connected with enzymes, showing functional redundancy in the phenanthrene pathway, with exception of the first enzymes biphenyl-2,3-diol 1,2-dioxygenase and protocatechuate 4,5-dioxygenase that were only encoded in Sphingobium sp. This is the first report where a natural consortium that has been characterized by HTS technologies is inoculated with an exogenous strain in order to study competitiveness and interactions.

Toxicity drives facilitation between 4 bacterial species

Competition between microbes is extremely common, with many investing in mechanisms to harm other strains and species. Yet positive interactions between species have also been documented. What makes species help or harm each other is currently unclear. Here, we studied the interactions between 4 bacterial species capable of degrading metal working fluids (MWF), an industrial coolant and lubricant, which contains growth substrates as well as toxic biocides. We were surprised to find only positive or neutral interactions between the 4 species. Using mathematical modeling and further experiments, we show that positive interactions in this community were likely due to the toxicity of MWF, whereby each species' detoxification benefited the others by facilitating their survival, such that they could grow and degrade MWF better when together. The addition of nutrients, the reduction of toxicity, or the addition of more species instead resulted in competitive behavior. Our work provides support to the stress gradient hypothesis by showing how harsh, toxic environments can strongly favor facilitation between microbial species and mask underlying competitive interactions.

Disruption of microbial communication yields a two-dimensional percolation transition

Bacteria communicate with each other to coordinate macroscale behaviors including pathogenesis, biofilm formation, and antibiotic production. Empirical evidence suggests that bacteria are capable of communicating at length scales far exceeding the size of individual cells. Several mechanisms of signal interference have been observed in nature, and how interference influences macroscale activity within microbial populations is unclear. Here we examined the exchange of quorum sensing signals to coordinate microbial activity over long distances in the presence of a variable amount of interference through a neighboring signal-degrading strain. As the level of interference increased, communication over large distances was disrupted and at a critical amount of interference, large-scale communication was suppressed. We explored this transition in experiments and reaction-diffusion models, and confirmed that this transition is a two-dimensional percolation transition. These results demonstrate the utility of applying physical models to emergence in complex biological networks to probe robustness and universal quantitative features.

Scalable nonlinear programming framework for parameter estimation in dynamic biological system models

We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stiff differential equations as well as many experimental data sets and parameters. The proposed framework uses cutting-edge modeling and solution tools which are computationally efficient, robust, and easy-to-use. Specifically, our framework uses a time discretization approach that: i) avoids repetitive simulations of the dynamic model, ii) enables fully algebraic model implementations and computation of derivatives, and iii) enables the use of computationally efficient nonlinear interior point solvers that exploit sparse and structured linear algebra techniques. We demonstrate these capabilities by solving estimation problems for synthetic human gut microbiome community models. We show that an instance with 156 parameters, 144 differential equations, and 1,704 experimental data points can be solved in less than 3 minutes using our proposed framework (while an off-the-shelf simulation-based solution framework requires over 7 hours). We also create large instances to show that the proposed framework is scalable and can solve problems with up to 2,352 parameters, 2,304 differential equations, and 20,352 data points in less than 15 minutes. The proposed framework is flexible and easy-to-use, can be broadly applied to dynamic models of biological systems, and enables the implementation of sophisticated estimation techniques to quantify parameter uncertainty, to diagnose observability/uniqueness issues, to perform model selection, and to handle outliers.

Constructing and validating dynamic models of biological systems spanning biomolecular networks to ecological systems is a challenging problem. Here we present a scalable computational framework to rapidly infer parameters in complex dynamic models of biological systems from large-scale experimental data. The framework was applied to infer parameters of a synthetic microbial community model from large-scale time series data. We also demonstrate that this framework can be used to analyze parameter uncertainty, to diagnose whether the experimental data are sufficient to uniquely determine the parameters, to determine the model that best describes the data, and to infer parameters in the face of data outliers.

Modeling cell population dynamics

 Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.

Migration alters oscillatory dynamics and promotes survival in connected bacterial populations

Migration influences population dynamics on networks, thereby playing a vital role in scenarios ranging from species extinction to epidemic propagation. While low migration rates prevent local populations from becoming extinct, high migration rates enhance the risk of global extinction by synchronizing the dynamics of connected populations. Here, we investigate this trade-off using two mutualistic strains of E. coli that exhibit population oscillations when co-cultured. In experiments, as well as in simulations using a mechanistic model, we observe that high migration rates lead to synchronization whereas intermediate migration rates perturb the oscillations and change their period. Further, our simulations predict, and experiments show, that connected populations subjected to more challenging antibiotic concentrations have the highest probability of survival at intermediate migration rates. Finally, we identify altered population dynamics, rather than recolonization, as the primary cause of extended survival.

Collective motion conceals fitness differences in crowded cellular populations

Many cellular populations are tightly-packed, such as microbial colonies and biofilms, or tissues and tumors in multicellular organisms. Movement of one cell in those crowded assemblages requires motion of others, so that cell displacements are correlated over many cell diameters. Whenever movement is important for survival or growth, these correlated rearrangements could couple the evolutionary fate of different lineages. Yet, little is known about the interplay between mechanical forces and evolution in dense cellular populations. Here, by tracking slower-growing clones at the expanding edge of yeast colonies, we show that the collective motion of cells prevents costly mutations from being weeded out rapidly. Joint pushing by neighboring cells generates correlated movements that suppress the differential displacements required for selection to act. This mechanical screening of fitness differences allows slower-growing mutants to leave more descendants than expected under non-mechanical models, thereby increasing their chance for evolutionary rescue. Our work suggests that, in crowded populations, cells cooperate with surrounding neighbors through inevitable mechanical interactions. This effect has to be considered when predicting evolutionary outcomes, such as the emergence of drug resistance or cancer evolution.

Polymicrobial infections: Do bacteria behave differently depending on their neighbours?

Despite the number of examples that correlate interspecies interactions in polymicrobial infections with variations in pathogenicity and antibiotic susceptibility of individual organisms, antibiotic therapies are selected to target the most relevant pathogen, with no consideration of the consequences that the presence of other bacterial species may have in the pathogenicity and response to antimicrobial agents.

In this issue of Virulence, Garcia-Perez et al. [10] applied replica plating of used wound dressings to assess the topography of distinct S. aureus types in chronic wounds of patients with the genetic blistering disease epidermolysis bullosa, which is characterized by the development of chronic wounds upon simple mechanical trauma. This approach led to the identification of two strains of S. aureus coexisting with Bacillus thuringiensis and Klebsiella oxytoca. S. aureus is highly prevalent in chronic wound infections, whereas B. thuringiensis and K. oxytoca are regarded as opportunistic pathogens. These bacterial species did not inhibit each other's growth under laboratory conditions, suggesting that they do not compete through the production of inhibitory compounds. Using a top-down proteomic approach to explore the inherent relationships between these co-existing bacteria, the exoproteomes of the staphylococcal isolates in monoculture and co-culture with B. thuringiensis or K. oxytoca were characterized by Mass Spectrometry.

Complex microbial systems across different levels of description

Complex biological systems offer a variety of interesting phenomena at the different physical scales. With increasing abstraction, details of the microscopic scales can often be extrapolated to average or typical macroscopic properties. However, emergent properties and cross-scale interactions can impede naïve abstractions and necessitate comprehensive investigations of these complex systems. In this review paper, we focus on microbial communities, and first, summarize a general hierarchy of relevant scales and description levels to understand these complex systems: (1) genetic networks, (2) single cells, (3) populations, and (4) emergent multi-cellular properties. Second, we employ two illustrating examples, microbial competition and biofilm formation, to elucidate how cross-scale interactions and emergent properties enrich the observed multi-cellular behavior in these systems. Finally, we conclude with pointing out the necessity of multi-scale investigations to understand complex biological systems and discuss recent investigations.

Review and perspective on mathematical modeling of microbial ecosystems

Understanding microbial ecosystems means unlocking the path toward a deeper knowledge of the fundamental mechanisms of life. Engineered microbial communities are also extremely relevant to tackling some of today's grand societal challenges. Advanced meta-omics experimental techniques provide crucial insights into microbial communities, but have been so far mostly used for descriptive, exploratory approaches to answer the initial 'who is there?'

QUESTION

An ecosystem is a complex network of dynamic spatio-temporal interactions among organisms as well as between organisms and the environment. Mathematical models with their abstraction capability are essential to capture the underlying phenomena and connect the different scales at which these systems act. Differential equation models and constraint-based stoichiometric models are deterministic approaches that can successfully provide a macroscopic description of the outcome from microscopic behaviors. In this mini-review, we present classical and recent applications of these modeling methods and illustrate the potential of their integration. Indeed, approaches that can capture multiple scales are needed in order to understand emergent patterns in ecosystems and their dynamics regulated by different spatio-temporal phenomena. We finally discuss promising examples of methods proposing the integration of differential equations with constraint-based stoichiometric models and argue that more work is needed in this direction.

Microbial expansion-collision dynamics promote cooperation and coexistence on surfaces

Microbes colonizing a surface often experience colony growth dynamics characterized by an initial phase of spatial clonal expansion followed by collision between neighboring colonies to form potentially genetically heterogeneous boundaries. For species with life cycles consisting of repeated surface colonization and dispersal, these spatially explicit "expansion-collision dynamics" generate periodic transitions between two distinct selective regimes, "expansion competition" and "boundary competition," each one favoring a different growth strategy. We hypothesized that this dynamic could promote stable coexistence of expansion- and boundary-competition specialists by generating time-varying, negative frequency-dependent selection that insulates both types from extinction. We tested this experimentally in budding yeast by competing an exoenzyme secreting "cooperator" strain (expansion-competition specialists) against nonsecreting "defectors" (boundary-competition specialists). As predicted, we observed cooperator-defector coexistence or cooperator dominance with expansion-collision dynamics, but only defector dominance otherwise. Also as predicted, the steady-state frequency of cooperators was determined by colonization density (the average initial cell-cell distance) and cost of cooperation. Lattice-based spatial simulations give good qualitative agreement with experiments, supporting our hypothesis that expansion-collision dynamics with costly public goods production is sufficient to generate stable cooperator-defector coexistence. This mechanism may be important for maintaining public-goods cooperation and conflict in microbial pioneer species living on surfaces.

The spatiotemporal system dynamics of acquired resistance in an engineered microecology

Great strides have been made in the understanding of complex networks; however, our understanding of natural microecologies is limited. Modelling of complex natural ecological systems has allowed for new findings, but these models typically ignore the constant evolution of species. Due to the complexity of natural systems, unanticipated interactions may lead to erroneous conclusions concerning the role of specific molecular components. To address this, we use a synthetic system to understand the spatiotemporal dynamics of growth and to study acquired resistance in vivo. Our system differs from earlier synthetic systems in that it focuses on the evolution of a microecology from a killer-prey relationship to coexistence using two different non-motile Escherichia coli strains. Using empirical data, we developed the first ecological model emphasising the concept of the constant evolution of species, where the survival of the prey species is dependent on location (distance from the killer) or the evolution of resistance. Our simple model, when expanded to complex microecological association studies under varied spatial and nutrient backgrounds may help to understand the complex relationships between multiple species in intricate natural ecological networks. This type of microecological study has become increasingly important, especially with the emergence of antibiotic-resistant pathogens.

Quantifying the strength of quorum sensing crosstalk within microbial communities

In multispecies microbial communities, the exchange of signals such as acyl-homoserine lactones (AHL) enables communication within and between species of Gram-negative bacteria. This process, commonly known as quorum sensing, aids in the regulation of genes crucial for the survival of species within heterogeneous populations of microbes. Although signal exchange was studied extensively in well-mixed environments, less is known about the consequences of crosstalk in spatially distributed mixtures of species. Here, signaling dynamics were measured in a spatially distributed system containing multiple strains utilizing homologous signaling systems. Crosstalk between strains containing the lux, las and rhl AHL-receptor circuits was quantified. In a distributed population of microbes, the impact of community composition on spatio-temporal dynamics was characterized and compared to simulation results using a modified reaction-diffusion model. After introducing a single term to account for crosstalk between each pair of signals, the model was able to reproduce the activation patterns observed in experiments. We quantified the robustness of signal propagation in the presence of interacting signals, finding that signaling dynamics are largely robust to interference. The ability of several wild isolates to participate in AHL-mediated signaling was investigated, revealing distinct signatures of crosstalk for each species. Our results present a route to characterize crosstalk between species and predict systems-level signaling dynamics in multispecies communities.