Individual-based modelling: an essential tool for microbiology

Real-time microbial growth curve (RMGC) system: an improved microplate reader with a graphical interface for automatic and high-throughput monitoring of microbial growth curves

The study of microbial growth curves is essential for comprehending microbial behavior and enhancing related processes. Current monitoring methods face limitations, including low automation, inefficient detection, and insufficient throughput. To address these challenges, we developed the Real-Time Microbial Growth Curve (RMGC) system, which offers fully automated and high-throughput monitoring of microbial growth through an Improved Microplate Reader (IMR) with a user-friendly graphical interface. By optimizing and calibrating the optical pathways, we achieve high-precision and consistent absorbance detection using LED light sources, surpassing traditional xenon lamp microplate readers, which lack continuous operation capabilities. We validated the RMGC system by cultivating 96 samples of Escherichia coli (E. coli) at a concentration of 105 CFU mL-1. After approximately 12 hours of continuous monitoring, the system exhibited a relative standard deviation (RSD) of less than 3.25% for optical density (OD) measurements and an RSD of 2.52% for the point of inflection (POI). These results indicate a similar level of precision but a longer monitoring time compared to conventional microplate readers, reflecting the effectiveness of the RMGC system in accurately monitoring microbial growth. The RMGC system showcases its versatility through various applications, such as microorganism gradient cultures, anaerobic microbial cultures, and antimicrobial susceptibility testing (AST). Its capabilities have important implications for multiple industries, including pharmaceuticals for antibiotic development, food safety for microbial contamination testing, and microbiological research.

Bacterial community dynamics as a result of growth-yield trade-off and multispecies metabolic interactions toward understanding the gut biofilm niche

Bacterial communities are ubiquitous, found in natural ecosystems, such as soil, and within living organisms, like the human microbiome. The dynamics of these communities in diverse environments depend on factors such as spatial features of the microbial niche, biochemical kinetics, and interactions among bacteria. Moreover, in many systems, bacterial communities are influenced by multiple physical mechanisms, such as mass transport and detachment forces. One example is gut mucosal communities, where dense, closely packed communities develop under the concurrent influence of nutrient transport from the lumen and fluid-mediated detachment of bacteria. In this study, we model a mucosal niche through a coupled agent-based and finite-volume modeling approach. This methodology enables us to model bacterial interactions affected by nutrient release from various sources while adjusting individual bacterial kinetics. We explored how the dispersion and abundance of bacteria are influenced by biochemical kinetics in different types of metabolic interactions, with a particular focus on the trade-off between growth rate and yield. Our findings demonstrate that in competitive scenarios, higher growth rates result in a larger share of the niche space. In contrast, growth yield plays a critical role in neutralism, commensalism, and mutualism interactions. When bacteria are introduced sequentially, they cause distinct spatiotemporal effects, such as deeper niche colonization in commensalism and mutualism scenarios driven by species intermixing effects, which are enhanced by high growth yields. Moreover, sub-ecosystem interactions dictate the dynamics of three-species communities, sometimes yielding unexpected outcomes. Competitive, fast-growing bacteria demonstrate robust colonization abilities, yet they face challenges in displacing established mutualistic systems. Bacteria that develop a cooperative relationship with existing species typically obtain niche residence, regardless of their growth rates, although higher growth yields significantly enhance their abundance. Our results underscore the importance of bacterial niche dynamics in shaping community properties and succession, highlighting a new approach to manipulating microbial systems.

Linking Methanogenesis in Low-Temperature Hydrothermal Vent Systems to Planetary Spectra: Methane Biosignatures on an Archean-Earth-like Exoplanet

In this work, the viability of the detection of methane produced by microbial activity in low-temperature hydrothermal vents on an Archean-Earth-like exoplanet in the habitable zone is explored via a simplified bottom-up approach using a toy model. By simulating methanogens at hydrothermal vent sites in the deep ocean, biological methane production for a range of substrate inflow rates was determined and compared to literature values. These production rates were then used, along with a range of ocean floor vent coverage fractions, to determine likely methane concentrations in the simplified atmosphere. At maximum production rates, a vent coverage of 4-15 × 10^-4 % (roughly 2000-6500 times that of modern Earth) is required to achieve 0.25% atmospheric methane. At minimum production rates, 100% vent coverage is not enough to produce 0.25% atmospheric methane. NASA's Planetary Spectrum Generator was then used to assess the detectability of methane features at various atmospheric concentrations. Even with future space-based observatory concepts (such as LUVOIR and HabEx), our results show the importance of both mirror size and distance to the observed planet. Planets with a substantial biomass of methanogens in hydrothermal vents can still lack a detectable, convincingly biological methane signature if they are beyond the scope of the chosen instrument. This work shows the value of coupling microbial ecological modeling with exoplanet science to better understand the constraints on biosignature gas production and its detectability.

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.

Individual-Based Modeling of Spatial Dynamics of Chemotactic Microbial Populations

One important direction of synthetic biology is to establish desired spatial structures from microbial populations. Underlying this structural development process are different driving factors, among which bacterial motility and chemotaxis serve as a major force. Here, we present an individual-based, biophysical computational framework for mechanistic and multiscale simulation of the spatiotemporal dynamics of motile and chemotactic microbial populations. The framework integrates cellular movement with spatial population growth, mechanical and chemical cellular interactions, and intracellular molecular kinetics. It is validated by a statistical comparison of single-cell chemotaxis simulations with reported experiments. The framework successfully captures colony range expansion of growing isogenic populations and also reveals chemotaxis-modulated, spatial patterns of a two-species amensal community. Partial differential equation-based models subsequently validate these simulation findings. This study provides a versatile computational tool to uncover the fundamentals of microbial spatial ecology as well as to facilitate the design of synthetic consortia for desired spatial patterns.

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'.

INDISIM-Denitrification, an individual-based model for study the denitrification process

Denitrification is one of the key processes of the global nitrogen (N) cycle driven by bacteria. It has been widely known for more than 100 years as a process by which the biogeochemical N-cycle is balanced. To study this process, we develop an individual-based model called INDISIM-Denitrification. The model embeds a thermodynamic model for bacterial yield prediction inside the individual-based model INDISIM and is designed to simulate in aerobic and anaerobic conditions the cell growth kinetics of denitrifying bacteria. INDISIM-Denitrification simulates a bioreactor that contains a culture medium with succinate as a carbon source, ammonium as nitrogen source and various electron acceptors. To implement INDISIM-Denitrification, the individual-based model INDISIM was used to give sub-models for nutrient uptake, stirring and reproduction cycle. Using a thermodynamic approach, the denitrification pathway, cellular maintenance and individual mass degradation were modeled using microbial metabolic reactions. These equations are the basis of the sub-models for metabolic maintenance, individual mass synthesis and reducing internal cytotoxic products. The model was implemented in the open-access platform NetLogo. INDISIM-Denitrification is validated using a set of experimental data of two denitrifying bacteria in two different experimental conditions. This provides an interactive tool to study the denitrification process carried out by any denitrifying bacterium since INDISIM-Denitrification allows changes in the microbial empirical formula and in the energy-transfer-efficiency used to represent the metabolic pathways involved in the denitrification process. The simulator can be obtained from the authors on request.

Modeling Microbial Communities: A Call for Collaboration between Experimentalists and Theorists

With our growing understanding of the impact of microbial communities, understanding how such communities function has become a priority. The influence of microbial communities is widespread. Human-associated microbiota impacts health, environmental microbes determine ecosystem sustainability, and microbe-driven industrial processes are expanding. This broad range of applications has led to a wide range of approaches to analyze and describe microbial communities. In particular, theoretical work based on mathematical modeling has been a steady source of inspiration for explaining and predicting microbial community processes. Here, we survey some of the modeling approaches used in different contexts. We promote classifying different approaches using a unified platform, and encourage cataloging the findings in a database. We believe that the synergy emerging from a coherent collection facilitates a better understanding of important processes that determine microbial community functions. We emphasize the importance of close collaboration between theoreticians and experimentalists in formulating, classifying, and improving models of microbial communities.

Dynamically analyzing cell interactions in biological environments using multiagent social learning framework

BACKGROUND

Biological environment is uncertain and its dynamic is similar to the multiagent environment, thus the research results of the multiagent system area can provide valuable insights to the understanding of biology and are of great significance for the study of biology. Learning in a multiagent environment is highly dynamic since the environment is not stationary anymore and each agent's behavior changes adaptively in response to other coexisting learners, and vice versa. The dynamics becomes more unpredictable when we move from fixed-agent interaction environments to multiagent social learning framework. Analytical understanding of the underlying dynamics is important and challenging.

RESULTS

In this work, we present a social learning framework with homogeneous learners (e.g., Policy Hill Climbing (PHC) learners), and model the behavior of players in the social learning framework as a hybrid dynamical system. By analyzing the dynamical system, we obtain some conditions about convergence or non-convergence. We experimentally verify the predictive power of our model using a number of representative games. Experimental results confirm the theoretical analysis.

CONCLUSION

Under multiagent social learning framework, we modeled the behavior of agent in biologic environment, and theoretically analyzed the dynamics of the model. We present some sufficient conditions about convergence or non-convergence and prove them theoretically. It can be used to predict the convergence of the system.

Heterogeneity in Pure Microbial Systems: Experimental Measurements and Modeling

Cellular heterogeneity influences bioprocess performance in ways that until date are not completely elucidated. In order to account for this phenomenon in the design and operation of bioprocesses, reliable analytical and mathematical descriptions are required. We present an overview of the single cell analysis, and the mathematical modeling frameworks that have potential to be used in bioprocess control and optimization, in particular for microbial processes. In order to be suitable for bioprocess monitoring, experimental methods need to be high throughput and to require relatively short processing time. One such method used successfully under dynamic conditions is flow cytometry. Population balance and individual based models are suitable modeling options, the latter one having in particular a good potential to integrate the various data collected through experimentation. This will be highly beneficial for appropriate process design and scale up as a more rigorous approach may prevent a priori unwanted performance losses. It will also help progressing synthetic biology applications to industrial scale.

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

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

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

Biodiversity has a critical impact on ecosystem functionality and stability, and thus the current biodiversity crisis has motivated many studies of the mechanisms that sustain biodiversity, a notable example being non-transitive or cyclic competition. We therefore extend existing microscopic models of communities with cyclic competition by incorporating resource dependence in demographic processes, characteristics of natural systems often oversimplified or overlooked by modellers. The spatially explicit nature of our individual-based model of three interacting species results in the formation of stable spatial structures, which have significant effects on community functioning, in agreement with experimental observations of pattern formation in microbial communities.

Sensitivity analysis of Repast computational ecology models with R/Repast

Computational ecology is an emerging interdisciplinary discipline founded mainly on modeling and simulation methods for studying ecological systems. Among the existing modeling formalisms, the individual‐based modeling is particularly well suited for capturing the complex temporal and spatial dynamics as well as the nonlinearities arising in ecosystems, communities, or populations due to individual variability. In addition, being a bottom‐up approach, it is useful for providing new insights on the local mechanisms which are generating some observed global dynamics. Of course, no conclusions about model results could be taken seriously if they are based on a single model execution and they are not analyzed carefully. Therefore, a sound methodology should always be used for underpinning the interpretation of model results. The sensitivity analysis is a methodology for quantitatively assessing the effect of input uncertainty in the simulation output which should be incorporated compulsorily to every work based on in‐silico experimental setup. In this article, we present R/Repast a GNU R package for running and analyzing Repast Simphony models accompanied by two worked examples on how to perform global sensitivity analysis and how to interpret the results.

INDISIM-Paracoccus, an individual-based and thermodynamic model for a denitrifying bacterium

We have developed an individual-based model for denitrifying bacteria. The model, called INDISIM-Paracoccus, embeds a thermodynamic model for bacterial yield prediction inside the individual-based model INDISIM, and is designed to simulate the bacterial cell population behavior and the product dynamics within the culture. The INDISIM-Paracoccus model assumes a culture medium containing succinate as a carbon source, ammonium as a nitrogen source and various electron acceptors such as oxygen, nitrate, nitrite, nitric oxide and nitrous oxide to simulate in continuous or batch culture the different nutrient-dependent cell growth kinetics of the bacterium Paracoccus denitrificans. The individuals in the model represent microbes and the individual-based model INDISIM gives the behavior-rules that they use for their nutrient uptake and reproduction cycle. Three previously described metabolic pathways for P. denitrificans were selected and translated into balanced chemical equations using a thermodynamic model. These stoichiometric reactions are an intracellular model for the individual behavior-rules for metabolic maintenance and biomass synthesis and result in the release of different nitrogen oxides to the medium. The model was implemented using the NetLogo platform and it provides an interactive tool to investigate the different steps of denitrification carried out by a denitrifying bacterium. The simulator can be obtained from the authors on request.

Local Inflammation, Dissemination and Coalescence of Lesions Are Key for the Progression toward Active Tuberculosis: The Bubble Model

The evolution of a tuberculosis (TB) infection toward active disease is driven by a combination of factors mostly related to the host response. The equilibrium between control of the bacillary load and the pathology generated is crucial as regards preventing the growth and proliferation of TB lesions. In addition, some experimental evidence suggests an important role of both local endogenous reinfection and the coalescence of neighboring lesions. Herein we propose a mathematical model that captures the essence of these factors by defining three hypotheses: (i) lesions grow logistically due to the inflammatory reaction; (ii) new lesions can appear as a result of extracellular bacilli or infected macrophages that escape from older lesions; and (iii) lesions can merge when they are close enough. This model was implemented in Matlab to simulate the dynamics of several lesions in a 3D space. It was also fitted to available microscopy data from infected C3HeB/FeJ mice, an animal model of active TB that reacts against Mycobacterium tuberculosis with an exaggerated inflammatory response. The results of the simulations show the dynamics observed experimentally, namely an initial increase in the number of lesions followed by fluctuations, and an exponential increase in the mean area of the lesions. In addition, further analysis of experimental and simulation results show a strong coincidence of the area distributions of lesions at day 21, thereby highlighting the consistency of the model. Three simulation series removing each one of the hypothesis corroborate their essential role in the dynamics observed. These results demonstrate that three local factors, namely an exaggerated inflammatory response, an endogenous reinfection, and a coalescence of lesions, are needed in order to progress toward active TB. The failure of one of these factors stops induction of the disease. This mathematical model may be used as a basis for developing strategies to stop the progression of infection toward disease in human lungs.

Individual-Based Model of Microbial Life on Hydrated Rough Soil Surfaces

Microbial life in soil is perceived as one of the most interesting ecological systems, with microbial communities exhibiting remarkable adaptability to vast dynamic environmental conditions. At the same time, it is a notoriously challenging system to understand due to its complexity including physical, chemical, and biological factors in synchrony. This study presents a spatially-resolved model of microbial dynamics on idealised rough soil surfaces represented as patches with different (roughness) properties that preserve the salient hydration physics of real surfaces. Cell level microbial interactions are considered within an individual-based formulation including dispersion and various forms of trophic dependencies (competition, mutualism). The model provides new insights into mechanisms affecting microbial community dynamics and gives rise to spontaneous formation of microbial community spatial patterns. The framework is capable of representing many interacting species and provides diversity metrics reflecting surface conditions and their evolution over time. A key feature of the model is its spatial scalability that permits representation of microbial processes from cell-level (micro-metric scales) to soil representative volumes at sub-metre scales. Several illustrative examples of microbial trophic interactions and population dynamics highlight the potential of the proposed modelling framework to quantitatively study soil microbial processes. The model is highly applicable in a wide range spanning from quantifying spatial organisation of multiple species under various hydration conditions to predicting microbial diversity residing in different soils.

Individual-Based Modeling of Tuberculosis in a User-Friendly Interface: Understanding the Epidemiological Role of Population Heterogeneity in a City

For millennia tuberculosis (TB) has shown a successful strategy to survive, making it one of the world’s deadliest infectious diseases. This resilient behavior is based not only on remaining hidden in most of the infected population, but also by showing slow evolution in most sick people. The course of the disease within a population is highly related to its heterogeneity. Thus, classic epidemiological approaches with a top-down perspective have not succeeded in understanding its dynamics. In the past decade a few individual-based models were built, but most of them preserved a top-down view that makes it difficult to study a heterogeneous population. We propose an individual-based model developed with a bottom-up approach to studying the dynamics of pulmonary TB in a certain population, considered constant. Individuals may belong to the following classes: healthy, infected, sick, under treatment, and treated with a probability of relapse. Several variables and parameters account for their age, origin (native or immigrant), immunodeficiency, diabetes, and other risk factors (smoking and alcoholism). The time within each infection state is controlled, and sick individuals may show a cavitated disease or not that conditions infectiousness. It was implemented in NetLogo because it allows non-modelers to perform virtual experiments with a user-friendly interface. The simulation was conducted with data from Ciutat Vella, a district of Barcelona with an incidence of 67 TB cases per 100,000 inhabitants in 2013. Several virtual experiments were performed to relate the disease dynamics with the structure of the infected subpopulation (e.g., the distribution of infected times). Moreover, the short-term effect of health control policies on modifying that structure was studied. Results show that the characteristics of the population are crucial for the local epidemiology of TB. The developed user-friendly tool is ready to test control strategies of disease in any city in the short-term.

Social dynamics within decomposer communities lead to nitrogen retention and organic matter build-up in soils

The chemical structure of organic matter has been shown to be only marginally important for its decomposability by microorganisms. The question of why organic matter does accumulate in the face of powerful microbial degraders is thus key for understanding terrestrial carbon and nitrogen cycling. Here we demonstrate, based on an individual-based microbial community model, that social dynamics among microbes producing extracellular enzymes (‘decomposers') and microbes exploiting the catalytic activities of others (‘cheaters') regulate organic matter turnover. We show that the presence of cheaters increases nitrogen retention and organic matter build-up by downregulating the ratio of extracellular enzymes to total microbial biomass, allowing nitrogen-rich microbial necromass to accumulate. Moreover, increasing catalytic efficiencies of enzymes are outbalanced by a strong negative feedback on enzyme producers, leading to less enzymes being produced at the community level. Our results thus reveal a possible control mechanism that may buffer soil CO₂ emissions in a future climate.

Microbial decomposers in soil provide the largest ecosystem flux of CO₂ to the atmosphere, but interactions at the microscale are poorly understood. Here, the authors use a computer modelling approach to show that social interactions among microbes buffer changing environmental conditions.

Synthetic Ecology of Microbes: Mathematical Models and Applications

As the indispensable role of natural microbial communities in many aspects of life on Earth is uncovered, the bottom-up engineering of synthetic microbial consortia with novel functions is becoming an attractive alternative to engineering single-species systems. Here, we summarize recent work on synthetic microbial communities with a particular emphasis on open challenges and opportunities in environmental sustainability and human health. We next provide a critical overview of mathematical approaches, ranging from phenomenological to mechanistic, to decipher the principles that govern the function, dynamics and evolution of microbial ecosystems. Finally, we present our outlook on key aspects of microbial ecosystems and synthetic ecology that require further developments, including the need for more efficient computational algorithms, a better integration of empirical methods and model-driven analysis, the importance of improving gene function annotation, and the value of a standardized library of well-characterized organisms to be used as building blocks of synthetic communities.

Modeling evolution of spatially distributed bacterial communities: a simulation with the haploid evolutionary constructor

Background

Multiscale approaches for integrating submodels of various levels of biological organization into a single model became the major tool of systems biology. In this paper, we have constructed and simulated a set of multiscale models of spatially distributed microbial communities and study an influence of unevenly distributed environmental factors on the genetic diversity and evolution of the community members.

Results

Haploid Evolutionary Constructor software http://evol-constructor.bionet.nsc.ru/ was expanded by adding the tool for the spatial modeling of a microbial community (1D, 2D and 3D versions). A set of the models of spatially distributed communities was built to demonstrate that the spatial distribution of cells affects both intensity of selection and evolution rate.

Conclusion

In spatially heterogeneous communities, the change in the direction of the environmental flow might be reflected in local irregular population dynamics, while the genetic structure of populations (frequencies of the alleles) remains stable. Furthermore, in spatially heterogeneous communities, the chemotaxis might dramatically affect the evolution of community members.

Simulating microbial community patterning using Biocellion

Mathematical modeling and computer simulation are important tools for understanding complex interactions between cells and their biotic and abiotic environment: similarities and differences between modeled and observed behavior provide the basis for hypothesis formation. Momeni et al. (Elife 2:e00230, 2013) investigated pattern formation in communities of yeast strains engaging in different types of ecological interactions, comparing the predictions of mathematical modeling, and simulation to actual patterns observed in wet-lab experiments. However, simulations of millions of cells in a three-dimensional community are extremely time consuming. One simulation run in MATLAB may take a week or longer, inhibiting exploration of the vast space of parameter combinations and assumptions. Improving the speed, scale, and accuracy of such simulations facilitates hypothesis formation and expedites discovery. Biocellion is a high-performance software framework for accelerating discrete agent-based simulation of biological systems with millions to trillions of cells. Simulations of comparable scale and accuracy to those taking a week of computer time using MATLAB require just hours using Biocellion on a multicore workstation. Biocellion further accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. Biocellion targets computational biologists who have mathematical modeling backgrounds and basic C++ programming skills. This chapter describes the necessary steps to adapt the original Momeni et al.'s model to the Biocellion framework as a case study.

Modeling the Growth of Filamentous Fungi at the Particle Scale in Solid-State Fermentation Systems

Solid-state fermentation (SSF) with filamentous fungi is a promising technique for the production of a range of biotechnological products and has the potential to play an important role in future biorefineries. The performance of such processes is intimately linked with the mycelial mode of growth of these fungi: Not only is the production of extracellular enzymes related to morphological characteristics, but also the mycelium can affect bed properties and, consequently, the efficiency of heat and mass transfer within the bed. A mathematical model that describes the development of the fungal mycelium in SSF systems at the particle scale would be a useful tool for investigating these phenomena, but, as yet, a sufficiently complete model has not been proposed. This review presents the biological and mass transfer phenomena that should be included in such a model and then evaluates how these phenomena have been modeled previously in the SSF and related literature. We conclude that a discrete lattice-based model that uses differential equations to describe the mass balances of the components within the system would be most appropriate and that mathematical expressions for describing the individual phenomena are available in the literature. It remains for these phenomena to be integrated into a complete model describing the development of fungal mycelia in SSF systems.

Biocellion: accelerating computer simulation of multicellular biological system models

MOTIVATION

Biological system behaviors are often the outcome of complex interactions among a large number of cells and their biotic and abiotic environment. Computational biologists attempt to understand, predict and manipulate biological system behavior through mathematical modeling and computer simulation. Discrete agent-based modeling (in combination with high-resolution grids to model the extracellular environment) is a popular approach for building biological system models. However, the computational complexity of this approach forces computational biologists to resort to coarser resolution approaches to simulate large biological systems. High-performance parallel computers have the potential to address the computing challenge, but writing efficient software for parallel computers is difficult and time-consuming.

RESULTS

We have developed Biocellion, a high-performance software framework, to solve this computing challenge using parallel computers. To support a wide range of multicellular biological system models, Biocellion asks users to provide their model specifics by filling the function body of pre-defined model routines. Using Biocellion, modelers without parallel computing expertise can efficiently exploit parallel computers with less effort than writing sequential programs from scratch. We simulate cell sorting, microbial patterning and a bacterial system in soil aggregate as case studies.

AVAILABILITY AND IMPLEMENTATION

Biocellion runs on x86 compatible systems with the 64 bit Linux operating system and is freely available for academic use. Visit http://biocellion.com for additional information.

From single cells to microbial population dynamics: modelling in biotechnology based on measurements of individual cells

The development of dynamic modelling of microbial populations in bioprocesses is reviewed. In the 1960s Arnold Fredrickson established the theoretical basis of such models, and other researchers have subsequently advanced them. This review explores the relationships that describe cell proliferation and evaluates the importance of the application of flow cytometry to the fundamental parameterisation of the models for their use in bioprocess engineering. The section "Individual-Based Modelling" discusses recent theoretical developments. Delay-differential equations are demonstrated to describe accurately temporal variation of the cell proliferation cycle and specialised approaches and related iconography are applied to stochastic and deterministic modelling of stages of cellular development. Synchronised cultures of the bacterium Cupriavidus necator were prepared and monitored using a flow cytometer. The data obtained demonstrate that cell proliferation could be simulated quantitatively using the developed model.

Biomimicry of quorum sensing using bacterial lifecycle model

BACKGROUND

Recent microbiologic studies have shown that quorum sensing mechanisms, which serve as one of the fundamental requirements for bacterial survival, exist widely in bacterial intra- and inter-species cell-cell communication. Many simulation models, inspired by the social behavior of natural organisms, are presented to provide new approaches for solving realistic optimization problems. Most of these simulation models follow population-based modelling approaches, where all the individuals are updated according to the same rules. Therefore, it is difficult to maintain the diversity of the population.

RESULTS

In this paper, we present a computational model termed LCM-QS, which simulates the bacterial quorum-sensing (QS) mechanism using an individual-based modelling approach under the framework of Agent-Environment-Rule (AER) scheme, i.e. bacterial lifecycle model (LCM). LCM-QS model can be classified into three main sub-models: chemotaxis with QS sub-model, reproduction and elimination sub-model and migration sub-model. The proposed model is used to not only imitate the bacterial evolution process at the single-cell level, but also concentrate on the study of bacterial macroscopic behaviour. Comparative experiments under four different scenarios have been conducted in an artificial 3-D environment with nutrients and noxious distribution. Detailed study on bacterial chemotatic processes with quorum sensing and without quorum sensing are compared. By using quorum sensing mechanisms, artificial bacteria working together can find the nutrient concentration (or global optimum) quickly in the artificial environment.

CONCLUSIONS

Biomimicry of quorum sensing mechanisms using the lifecycle model allows the artificial bacteria endowed with the communication abilities, which are essential to obtain more valuable information to guide their search cooperatively towards the preferred nutrient concentrations. It can also provide an inspiration for designing new swarm intelligence optimization algorithms, which can be used for solving the real-world problems.

Escherichia coli adapts to tetracycline resistance plasmid (pBR322) by mutating endogenous potassium transport: in silico hypothesis testing

Antibiotic resistance exerts a metabolic cost on bacteria and presumably a fitness disadvantage in the absence of antibiotics. However, several studies have shown that bacteria can evolve to eliminate this cost. Escherichia coli can adapt to the plasmid pBR322 carrying the tetA tetracycline-resistance gene (codes for the TetA efflux pump) by a chromosome mutation, which requires an intact tetA gene on the plasmid. The TetA pump can mediate potassium uptake. Here, the hypothesis that TetA replaces the endogenous K(+) uptake system Trk is explored using a multi-level modeling approach that explicitly resolves relevant intracellular processes (e.g., metabolism and K(+) uptake) and simulates individual bacteria in competition. The general behavior of the model is consistent with observations from the literature (e.g., growth rate and K(+) limitation). In competition experiments without tetracycline, the model correctly predicts the fitness advantage of naive susceptible over naive resistant, evolved resistant over naive resistant and evolved resistant over evolved susceptible strains. Trk takes up about 10 times the K(+) required, which costs energy. TetA takes up less K(+) , which is more efficient and leads to the evolution of the Trk mutant. The evolved Trk mutant relies on TetA to take up K(+) , and thus, carrying the plasmid is advantageous even in the absence of the antibiotic.

Microfluidic cell volume sensor with tunable sensitivity

We report the fabrication and validation of a microfluidic cell volume sensor integrated on a multi-layered polydimethylsiloxane (PDMS) microchip with a tunable detection volume for dynamic control of sensitivity, enabling the detection of individual Escherichia coli and microparticles.

Modeling microbial community structure and functional diversity across time and space

Microbial communities exhibit exquisitely complex structure. Many aspects of this complexity, from the number of species to the total number of interactions, are currently very difficult to examine directly. However, extraordinary efforts are being made to make these systems accessible to scientific investigation. While recent advances in high-throughput sequencing technologies have improved accessibility to the taxonomic and functional diversity of complex communities, monitoring the dynamics of these systems over time and space - using appropriate experimental design - is still expensive. Fortunately, modeling can be used as a lens to focus low-resolution observations of community dynamics to enable mathematical abstractions of functional and taxonomic dynamics across space and time. Here, we review the approaches for modeling bacterial diversity at both the very large and the very small scales at which microbial systems interact with their environments. We show that modeling can help to connect biogeochemical processes to specific microbial metabolic pathways.

A novel method for high-throughput data collection in predictive microbiology: optical density monitoring of colony growth as a function of time

Recently, the focus of predictive food microbiology has shifted towards more mechanistically-inspired modelling. Together with this trend, the need for methods that allow rapid data collection at the (intra)cellular level, as well as the intermediate subpopulation/colony level, has emerged. Although several experimental techniques are currently available to study colony dynamics in/on solid media, their widespread implementation as high-throughput methods remains a challenge. In this research, a novel method is presented to study colony growth based on optical density measurements performed in microtiter plates. An area scan procedure was applied to monitor individual Escherichia coli colonies in 48-well plates at 30 °C. Based on a fixed threshold value to separate the object (colony) from the background, the colony area was determined as a function of time. With this technique, expansion of the colony in radial direction could be monitored. Practical limitations (i.e., maximum achievable resolution and colony size) of the proposed method were investigated. A comparison was made with existing methods at the level of hardware requirements, data acquisition and data processing. Overall, the novel optical density method proved to be a flexible, high-throughput tool for monitoring (the mechanisms of) microbial colony growth in solid(like) systems.

Modeling microbial communities: current, developing, and future technologies for predicting microbial community interaction

Never has there been a greater opportunity for investigating microbial communities. Not only are the profound effects of microbial ecology on every aspect of Earth's geochemical cycles beginning to be understood, but also the analytical and computational tools for investigating microbial Earth are undergoing a rapid revolution. This environmental microbial interactome, the system of interactions between the microbiome and the environment, has shaped the planet's past and will undoubtedly continue to do so in the future. We review recent approaches for modeling microbial community structures and the interactions of microbial populations with their environments. Different modeling approaches consider the environmental microbial interactome from different aspects, and each provides insights to different facets of microbial ecology. We discuss the challenges and opportunities for the future of microbial modeling and describe recent advances in microbial community modeling that are extending current descriptive technologies into a predictive science.

Thermodynamic concepts in the study of microbial populations: age structure in Plasmodium falciparum infected red blood cells

Variability is a hallmark of microbial systems. On the one hand, microbes are subject to environmental heterogeneity and undergo changeable conditions in their immediate surroundings. On the other hand, microbial populations exhibit high cellular diversity. The relation between microbial diversity and variability of population dynamics is difficult to assess. This connection can be quantitatively studied from a perspective that combines in silico models and thermodynamic methods and interpretations. The infection process of Plasmodium falciparum parasitizing human red blood cells under laboratory cultivation conditions is used to illustrate the potential of Individual-based models in the context of predictive microbiology and parasitology. Experimental data from several in vitro cultures are compared to the outcome of an individual-based model and analysed from a thermodynamic perspective. This approach allows distinguishing between intrinsic and external constraints that give rise to the diversity in the infection forms, and it provides a criterion to quantitatively define transient and stationary regimes in the culture. Increasing the ability of models to discriminate between different states of microbial populations enhances their predictive capability which finally leads to a better the control over culture systems. The strategy here presented is of general application and it can substantially improve modelling of other types of microbial communities.

Spatial competition with Lactococcus lactis in mixed-species continuous-flow biofilms inhibits Listeria monocytogenes growth

Surfaces in industrial settings provide a home for resident biofilms that are likely to interact with the attachment, growth and survival of pathogens such as Listeria monocytogenes. Experimental results have indicated that L. monocytogenes cells were inhibited by the presence of a model resident flora (Lactococcus lactis) in dual-species continuous flow-biofilms, and are spatially restricted to the lower biofilm layers. Using a new, simplified individual-based model (IBM) that simulates bacterial cell growth in a three-dimensional space, the spatial arrangements of the two species were reconstructed and their cell counts successfully predicted. This model showed that the difference in generation times between L. monocytogenes and L. lactis cells during the initial stages of dual-species biofilm formation was probably responsible for the species spatialization observed and the subsequent inhibition of growth of the pathogen.

Analysis of the effect of inoculum characteristics on the first stages of a growing yeast population in beer fermentations by means of an individual-based model

The yeast Saccharomyces cerevisiae has a limited replicative lifespan. The cell mass at division is partitioned unequally between a larger, old parent cell and a smaller, new daughter cell. Industrial beer fermentations maintain and reuse yeast. At the end of fermentation a portion of the yeast is 'cropped' from the vessel for 'serial repitching'. Harvesting yeast may select a population with an imbalance of young and aged individuals, but the output of any bioprocess is dependent on the physiology of each single cell in the population. Unlike continuous models, individual-based modelling is an approach that considers each microbe as an individual, a unique and discrete entity, with characteristics that change throughout its life. The aim of this contribution is to explore, by means of individual-based simulations, the effects of inoculum size and cell genealogical age on the dynamics of virtual yeast fermentation, focussing on: (1) the first stages of population growth, (2) the mean biomass evolution of the population, (3) the rate of glucose uptake and ethanol production, and (4) the biomass and genealogical age distributions. The ultimate goal is to integrate these results in order to make progress in the understanding of the composition of yeast populations and their temporal evolution in beer fermentations. Simulation results show that there is a clear influence of these initial features of the inocula on the subsequent growth dynamics. By contrasting both the individual and global properties of yeast cells and populations, we gain insight into the interrelation between these two types of data, which helps us to deal with the macroscopic behaviour observed in experimental research.

Analysis of the lag phase to exponential growth transition by incorporating inoculum characteristics

During the last decade, individual-based modelling (IbM) has proven to be a valuable tool for modelling and studying microbial dynamics. As each individual is considered as an independent entity with its own characteristics, IbM enables the study of microbial dynamics and the inherent variability and heterogeneity. IbM simulations and (single-cell) experimental research form the basis to unravel individual cell characteristics underlying population dynamics. In this study, the IbM framework MICRODIMS, i.e., MICRObial Dynamics Individual-based Model/Simulator, is used to investigate the system dynamics (with respect to the model and the system modelled). First, the impact of the time resolution on the simulation accuracy is discussed. Second, the effect of the inoculum state and size on emerging individual dynamics, such as individual mass, individual age and individual generation time distribution dynamics, is studied. The distributions of individual characteristics are more informative during the lag phase and the transition to the exponential growth phase than during the exponential phase. The first generation time distributions are strongly influenced by the inoculum state. All inocula with a pronounced heterogeneity, except the inocula starting from a uniform distribution, exhibit commonly observed microbial behaviour, like a more spread first generation time distribution compared to following generations and a fast stabilisation of biomass and age distributions.

Exploring the lag phase and growth initiation of a yeast culture by means of an individual-based model

The performance of fermentation processes is greatly influenced by the size and quality of inocula. The characterization of the replicative age is decided by the number of birth scars each yeast exhibits on its cellular membrane. Yeast ageing and inoculum size are factors that affect industrial fermentation, particularly those processes in which the yeast cells are reused such as the production of beer. This process reuses yeast cropped at the end of one fermentation in the following one, in a process called "serial repitching". The aim of this study was to explore the effects of inoculum size and ageing on the first stages of the dynamics of yeast population growth. However, only Individual-based Models (IbMs) allow the study of small, well-characterized, microbial inocula. We used INDISIM-YEAST, based on the generic IbM simulator INDISIM, to carry out these studies. Several simulations were performed to analyze the effect of the inoculum size and genealogical age of the cells that made it up on the lag phase, first division time and specific growth rate. The shortest lag phase and time to the first division were obtained with largest inocula and with the youngest inoculated parent cells.