INDISIM, an individual-based discrete simulation model to study bacterial cultures

Stochastic Gene Expression in Proliferating Cells: Differing Noise Intensity in Single-Cell and Population Perspectives

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth, and the protein inhibits growth at high concentrations, establishing a positive feedback loop. For a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the commonly used single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

Coupling Cell Size Regulation and Proliferation Dynamics of C. glutamicum Reveals Cell Division Based on Surface Area

Single cells actively coordinate growth and division to regulate their size, yet how this size homeostasis at the single-cell level propagates over multiple generations to impact clonal expansion remains fundamentally unexplored. Classical timer models for cell proliferation (where the duration of the cell cycle is an independent variable) predict that the stochastic variation in colony size will increase monotonically over time. In stark contrast, implementing size control according to adder strategy (where on average a fixed size added from cell birth to division) leads to colony size variations that eventually decay to zero. While these results assume a fixed size of the colony-initiating progenitor cell, further analysis reveals that the magnitude of the intercolony variation in population number is sensitive to heterogeneity in the initial cell size. We validate these predictions by tracking the growth of isogenic microcolonies of Corynebacterium glutamicum in microfluidic chambers. Approximating their cell shape to a capsule, we observe that the degree of random variability in cell size is different depending on whether the cell size is quantified as per length, surface area, or volume, but size control remains an adder regardless of these size metrics. A comparison of the observed variability in the colony population with the predictions suggests that proliferation matches better with a cell division based on the cell surface. In summary, our integrated mathematical-experimental approach bridges the paradigms of single-cell size regulation and clonal expansion at the population levels. This innovative approach provides elucidation of the mechanisms of size homeostasis from the stochastic dynamics of colony size for rod-shaped microbes.

Review: The prevailing mathematical modeling classifications and paradigms to support the advancement of sustainable animal production

Mathematical modeling is typically framed as the art of reductionism of scientific knowledge into an arithmetical layout. However, most untrained people get the art of modeling wrong and end up neglecting it because modeling is not simply about writing equations and generating numbers through simulations. Models tell not only about a story; they are spoken to by the circumstances under which they are envisioned. They guide apprentice and experienced modelers to build better models by preventing known pitfalls and invalid assumptions in the virtual world and, most importantly, learn from them through simulation and identify gaps in pushing scientific knowledge further. The power of the human mind is well-documented for idealizing concepts and creating virtual reality models, and as our hypotheses grow more complicated and more complex data become available, modeling earns more noticeable footing in biological sciences. The fundamental modeling paradigms include discrete-events, dynamic systems, agent-based (AB), and system dynamics (SD). The source of knowledge is the most critical step in the model-building process regardless of the paradigm, and the necessary expertise includes (a) clear and concise mental concepts acquired through different ways that provide the fundamental structure and expected behaviors of the model and (b) numerical data necessary for statistical analysis, not for building the model. The unreasonable effectiveness of models to grow scientific learning and knowledge in sciences arise because different researchers would model the same problem differently, given their knowledge and experiential background, leading to choosing different variables and model structures. Secondly, different researchers might use different paradigms and even unalike mathematics to resolve the same problem; thus, model needs are intrinsic to their perceived assumptions and structures. Thirdly, models evolve as the scientific community knowledge accumulates and matures over time, hopefully resulting in improved modeling efforts; thus, the perfect model is fictional. Some paradigms are most appropriate for macro, high abstraction with less detailed-oriented scenarios, while others are most suitable for micro, low abstraction with higher detailed-oriented strategies. Modern hybridization aggregating artificial intelligence (AI) to mathematical models can become the next technological wave in modeling. AI can be an integral part of the SD/AB models and, before long, write the model code by itself. Success and failures in model building are more related to the ability of the researcher to interpret the data and understand the underlying principles and mechanisms to formulate the correct relationship among variables rather than profound mathematical knowledge.

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

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

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

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

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

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

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.

Spatiotemporal establishment of dense bacterial colonies growing on hard agar

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

A low-complexity metabolic network model for the respiratory and fermentative metabolism of Escherichia coli

Over the last decades, predictive microbiology has made significant advances in the mathematical description of microbial spoiler and pathogen dynamics in or on food products. Recently, the focus of predictive microbiology has shifted from a (semi-)empirical population-level approach towards mechanistic models including information about the intracellular metabolism in order to increase model accuracy and genericness. However, incorporation of this subpopulation-level information increases model complexity and, consequently, the required run time to simulate microbial cell and population dynamics. In this paper, results of metabolic flux balance analyses (FBA) with a genome-scale model are used to calibrate a low-complexity linear model describing the microbial growth and metabolite secretion rates of Escherichia coli as a function of the nutrient and oxygen uptake rate. Hence, the required information about the cellular metabolism (i.e., biomass growth and secretion of cell products) is selected and included in the linear model without incorporating the complete intracellular reaction network. However, the applied FBAs are only representative for microbial dynamics under specific extracellular conditions, viz., a neutral medium without weak acids at a temperature of 37℃. Deviations from these reference conditions lead to metabolic shifts and adjustments of the cellular nutrient uptake or maintenance requirements. This metabolic dependency on extracellular conditions has been taken into account in our low-complex metabolic model. In this way, a novel approach is developed to take the synergistic effects of temperature, pH, and undissociated acids on the cell metabolism into account. Consequently, the developed model is deployable as a tool to describe, predict and control E. coli dynamics in and on food products under various combinations of environmental conditions. To emphasize this point,three specific scenarios are elaborated: (i) aerobic respiration without production of weak acid extracellular metabolites, (ii) anaerobic fermentation with secretion of mixed acid fermentation products into the food environment, and (iii) respiro-fermentative metabolic regimes in between the behaviors at aerobic and anaerobic conditions.

Dynamic Modeling of Streptococcus pneumoniae Competence Provides Regulatory Mechanistic Insights Into Its Tight Temporal Regulation

In the human pathogen Streptococcus pneumoniae, the gene regulatory circuit leading to the transient state of competence for natural transformation is based on production of an auto-inducer that activates a positive feedback loop. About 100 genes are activated in two successive waves linked by a central alternative sigma factor ComX. This mechanism appears to be fundamental to the biological fitness of S. pneumoniae. We have developed a knowledge-based model of the competence cycle that describes average cell behavior. It reveals that the expression rates of the two competence operons, comAB and comCDE, involved in the positive feedback loop must be coordinated to elicit spontaneous competence. Simulations revealed the requirement for an unknown late com gene product that shuts of competence by impairing ComX activity. Further simulations led to the predictions that the membrane protein ComD bound to CSP reacts directly to pH change of the medium and that blindness to CSP during the post-competence phase is controlled by late DprA protein. Both predictions were confirmed experimentally.

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

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

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

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

MbT-Tool: An open-access tool based on Thermodynamic Electron Equivalents Model to obtain microbial-metabolic reactions to be used in biotechnological process

Modelling cellular metabolism is a strategic factor in investigating microbial behaviour and interactions, especially for bio-technological processes. A key factor for modelling microbial activity is the calculation of nutrient amounts and products generated as a result of the microbial metabolism. Representing metabolic pathways through balanced reactions is a complex and time-consuming task for biologists, ecologists, modellers and engineers. A new computational tool to represent microbial pathways through microbial metabolic reactions (MMRs) using the approach of the Thermodynamic Electron Equivalents Model has been designed and implemented in the open-access framework NetLogo. This computational tool, called MbT-Tool (Metabolism based on Thermodynamics) can write MMRs for different microbial functional groups, such as aerobic heterotrophs, nitrifiers, denitrifiers, methanogens, sulphate reducers, sulphide oxidizers and fermenters. The MbT-Tool's code contains eighteen organic and twenty inorganic reduction-half-reactions, four N-sources (NH4 (+), NO3 (-), NO2 (-), N2) to biomass synthesis and twenty-four microbial empirical formulas, one of which can be determined by the user (CnHaObNc). MbT-Tool is an open-source program capable of writing MMRs based on thermodynamic concepts, which are applicable in a wide range of academic research interested in designing, optimizing and modelling microbial activity without any extensive chemical, microbiological and programing experience.

Developmental Design of Synthetic Bacterial Architectures by Morphogenetic Engineering

Synthetic biology is an emerging scientific field that promotes the standardized manufacturing of biological components without natural equivalents. Its goal is to create artificial living systems that can meet various needs in health care or energy domains. While most works are focused on the individual bacterium as a chemical reactor, our project, SynBioTIC, addresses a novel and more complex challenge: shape engineering; that is, the redesign of natural morphogenesis toward a new kind of developmental 3D printing. Potential applications include organ growth, natural computing in biocircuits, or future vegetal houses. To create in silico multicellular organisms that exhibit specific shapes, we construe their development as an iterative process combining fundamental collective phenomena such as homeostasis, patterning, segmentation, and limb growth. Our numerical experiments rely on the existing Escherichia coli simulator Gro, a physicochemical computation platform offering reaction-diffusion and collision dynamics solvers. The synthetic bioware of our model executes a set of rules, or genome, in each cell. Cells can differentiate into several predefined types associated with specific actions (divide, emit signal, detect signal, die). Transitions between types are triggered by conditions involving internal and external sensors that detect various protein levels inside and around the cell. Indirect communication between bacteria is relayed by morphogen diffusion and the mechanical constraints of 2D packing. Starting from a single bacterium, the overall architecture emerges in a purely endogenous fashion through a series of developmental stages, inlcuding proliferation, differentiation, morphogen diffusion, and synchronization. The genome can be parametrized to control the growth and features of appendages individually. As exemplified by the L and T shapes that we obtain, certain precursor cells can be inhibited while others can create limbs of varying size (divergence of the homology). Such morphogenetic phenotypes open the way to more complex shapes made of a recursive array of core bodies and limbs and, most importantly, to an evolutionary developmental exploration of unplanned functional forms.

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.

A modelling approach to explore the critical environmental parameters influencing the growth and establishment of the invasive seaweed Undaria pinnatifida in Europe

A key factor to determine the expansion dynamics and future distribution of non-native species is their physiological response to abiotic factors and their changes over time. For this study we developed a spatially explicit, agent-based model of population growth to represent the complex population dynamics of invasive marine macroalgae with heteromorphic biphasic life cycles. The model framework represents this complex life cycle by treating the individual developmental stages (gametophytes/sporophytes) as autonomous agents with unique behaviour/growth parameters. It was parameterised to represent a well-documented invasive algal species, the Asian kelp Undaria pinnatifida, and validated against field results from an in situ population in Brittany, France, showing good quantitative agreement in terms of seasonal changes in abundance/recruitment and growth dynamics. It was then used to explore how local environmental parameters (light availability, temperature and day length) affect the population dynamics of the individual developmental stages and the overall population growth. This type of modelling approach represents a promising tool for understanding the population dynamics of macroalgae from the bottom-up in terms of the individual interactions between the independent life history stages (both microscopic and macroscopic). It can be used to trace back the behaviour of the population as a whole to the underlying physiological and environmental processes impacting each developmental stage and give insights into the roles these play in invasion success.

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.

An individual-based modeling approach to simulate the effects of cellular nutrient competition on Escherichia coli K-12 MG1655 colony behavior and interactions in aerobic structured food systems

Traditional kinetic models in predictive microbiology reliably predict macroscopic dynamics of planktonically-growing cell cultures in homogeneous liquid food systems. However, most food products have a semi-solid structure, where microorganisms grow locally in colonies. Individual colony cells exhibit strongly different and non-normally distributed behavior due to local nutrient competition. As a result, traditional models considering average population behavior in a homogeneous system do not describe colony dynamics in full detail. To incorporate local resource competition and individual cell differences, an individual-based modeling approach has been applied to Escherichia coli K-12 MG1655 colonies, considering the microbial cell as modeling unit. The first contribution of this individual-based model is to describe single colony growth under nutrient-deprived conditions. More specifically, the linear and stationary phase in the evolution of the colony radius, the evolution from a disk-like to branching morphology, and the emergence of a starvation zone in the colony center are simulated and compared to available experimental data. These phenomena occur earlier at more severe nutrient depletion conditions, i.e., at lower nutrient diffusivity and initial nutrient concentration in the medium. Furthermore, intercolony interactions have been simulated. Higher inoculum densities lead to stronger intercolony interactions, such as colony merging and smaller colony sizes, due to nutrient competition. This individual-based model contributes to the elucidation of characteristic experimentally observed colony behavior from mechanistic information about cellular physiology and interactions.

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.

The relevance of conditional dispersal for bacterial colony growth and biodegradation

Bacterial degradation is an ecosystem service that offers a promising method for the remediation of contaminated soils. To assess the dynamics and efficiency of bacterial degradation, reliable microbial simulation models, along with the relevant processes, are required. We present an approach aimed at improving reliability by studying the relevance and implications of an important concept from theoretical ecology in the context of a bacterial system: conditional dispersal denoting that the dispersal strategy depends on environmental conditions. Different dispersal strategies, which either incorporate or neglect this concept, are implemented in a bacterial model and results are compared to data obtained from laboratory experiments with Pseudomonas putida colonies growing on glucose agar. Our results show that, with respect to the condition of resource uptake, the model's correspondence to experimental data is significantly higher for conditional than for unconditional bacterial dispersal. In particular, these results support the hypothesis that bacteria disperse less when resources are abundant. We also show that the dispersal strategy has a considerable impact on model predictions for bacterial degradation of resources: disregarding conditional bacterial dispersal can lead to overestimations when assessing the performance of this ecosystem service.

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.

A theoretical analysis of the prodrug delivery system for treating antibiotic-resistant bacteria

Simulations were carried out to analyze a promising new antimicrobial treatment strategy for targeting antibiotic-resistant bacteria called the β-lactamase-dependent prodrug delivery system. In this system, the antibacterial drugs are delivered as inactive precursors that only become activated after contact with an enzyme characteristic of many species of antibiotic-resistant bacteria (β-lactamase enzyme). The addition of an activation step contributes an extra layer of complexity to the system that can lead to unexpected emergent behavior. In order to optimize for treatment success and minimize the risk of resistance development, there must be a clear understanding of the system dynamics taking place and how they impact on the overall response. It makes sense to use a systems biology approach to analyze this method because it can facilitate a better understanding of the complex emergent dynamics arising from diverse interactions in populations. This paper contains an initial theoretical examination of the dynamics of this system of activation and an assessment of its therapeutic potential from a theoretical standpoint using an agent-based modeling approach. It also contains a case study comparison with real-world results from an experimental study carried out on two prodrug candidate compounds in the literature.

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.

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.

A computational model of antibiotic-resistance mechanisms in methicillin-resistant Staphylococcus aureus (MRSA)

An agent-based model of bacteria-antibiotic interactions has been developed that incorporates the antibiotic-resistance mechanisms of Methicillin-Resistant Staphylococcus aureus (MRSA). The model, called the Micro-Gen Bacterial Simulator, uses information about the cell biology of bacteria to produce global information about population growth in different environmental conditions. It facilitates a detailed systems-level investigation of the dynamics involved in bacteria-antibiotic interactions and a means to relate this information to traditional high-level properties such as the Minimum Inhibitory Concentration (MIC) of an antibiotic. The two main resistance strategies against beta-lactam antibiotics employed by MRSA were incorporated into the model: beta-lactamase enzymes, which hydrolytically cleave antibiotic molecules, and penicillin-binding proteins (PBP2a) with reduced binding affinities for antibiotics. Initial tests with three common antibiotics (penicillin, ampicillin and cephalothin) indicate that the model can be used to generate quantitatively accurate predictions of MICs for antibiotics against different strains of MRSA from basic cellular and biochemical information. Furthermore, by varying key parameters in the model, the relative impact of different kinetic parameters associated with the two resistance mechanisms to beta-lactam antibiotics on cell survival in the presence of antibiotics was investigated.

Individual-based modelling: an essential tool for microbiology

Micro-organisms play a central role in every ecosystem and in the global biomass cycle. They are strongly involved in many fields of human interest, from medicine to the food industry and waste control. Nevertheless, most micro-organisms remain almost unknown, and nearly 99% of them have not yet been successfully cultured in vitro. Therefore, new approaches and new tools must be developed in order to understand the collective behaviour of microbial communities in any natural or artificial setting. In particular, theoretical and practical methodologies to deal with such systems at a mesoscopic level of description (covering the range from 100 to 10(8) cells) are required. Individual-based modelling (IBM) has become a widely used tool for describing complex systems made up of autonomous entities, such as ecosystems and social networks. Individual-based models (IBMs) provide some advantages over the traditional whole-population models: (a) they are bottom-up approaches, so they describe the behaviour of a system as a whole by establishing procedural rules for the individuals and for their interactions, and thus allow more realistic assumptions for the model of the individuals than population models do; (b) they permit the introduction of randomness and individual variability, so they can reproduce the diversity found in real systems; and (c) they can account for individual adaptive behaviour to their environmental conditions, so the evolution of the whole system arises from the dynamics that govern individuals in their pursuit of optimal fitness. However, they also present some drawbacks: they lack the clarity of continuous models and may easily become rambling, which makes them difficult to analyse and communicate. All in all, IBMs supply a holistic description of microbial systems and their emerging properties. They are specifically appropriate to deal with microbial communities in non-steady states, and spatially explicit IBMs are particularly appropriate to study laboratory and natural microbiological systems with spatial heterogeneity. In this paper, we review IBM methodology applied to microbiology. We also present some results obtained from the application of Individual Discrete Simulations, an IBM of ours, to the study of bacterial communities, yeast cultures and Plasmodium falciparum-infected erythrocytes in vitro cultures of Plasmodium falciparum-infected erythrocytes.

Analysis and IbM simulation of the stages in bacterial lag phase: basis for an updated definition

The lag phase is the initial phase of a culture that precedes exponential growth and occurs when the conditions of the culture medium differ from the pre-inoculation conditions. It is usually defined by means of cell density because the number of individuals remains approximately constant or slowly increases, and it is quantified with the lag parameter lambda. The lag phase has been studied through mathematical modelling and by means of specific experiments. In recent years, Individual-based Modelling (IbM) has provided helpful insights into lag phase studies. In this paper, the definition of lag phase is thoroughly examined. Evolution of the total biomass and the total number of bacteria during lag phase is tackled separately. The lag phase lasts until the culture reaches a maximum growth rate both in biomass and cell density. Once in the exponential phase, both rates are constant over time and equal to each other. Both evolutions are split into an initial phase and a transition phase, according to their growth rates. A population-level mathematical model is presented to describe the transitional phase in cell density. INDividual DIScrete SIMulation (INDISIM) is used to check the outcomes of this analysis. Simulations allow the separate study of the evolution of cell density and total biomass in a batch culture, they provide a depiction of different observed cases in lag evolution at the individual-cell level, and are used to test the population-level model. The results show that the geometrical lag parameter lambda is not appropriate as a universal definition for the lag phase. Moreover, the lag phase cannot be characterized by a single parameter. For the studied cases, the lag phases of both the total biomass and the population are required to fully characterize the evolution of bacterial cultures. The results presented prove once more that the lag phase is a complex process that requires a more complete definition. This will be possible only after the phenomena governing the population dynamics at an individual level of description, and occurring during the lag and exponential growth phases, are well understood.

Rule-based modelling of conjugative plasmid transfer and incompatibility

COSMIC-rules, an individual-based model for bacterial adaptation and evolution, has been used to study virtual transmission of plasmids within bacterial populations, in an environment varying between supportive and inhibitory. The simulations demonstrate spread of antibiotic resistance (R) plasmids, both compatible and incompatible, by the bacterial gene transfer process of conjugation. This paper describes the behaviour of virtual plasmids, their modes of exchange within bacterial populations and the impact of antibiotics, together with the rules governing plasmid transfer. Three case studies are examined: transfer of an R plasmid within an antibiotic-susceptible population, transfer of two incompatible R plasmids and transfer of two compatible R plasmids. R plasmid transfer confers antibiotic resistance on recipients. For incompatible plasmids, one or other plasmid could be maintained in bacterial cells and only that portion of the population acquiring the appropriate plasmid-encoded resistance survives exposure to the antibiotics. By contrast, the compatible plasmids transfer and mix freely within the bacterial population that survives in its entirety in the presence of the antibiotics. These studies are intended to inform models for examining adaptive evolution in bacteria. They provide proof of principle in simple systems as a platform for predicting the behaviour of bacterial populations in more complex situations, for example in response to changing environments or in multi-species bacterial assemblages.

Rule-based computing system for microbial interactions and communications: evolution in virtual bacterial populations

We have developed a novel rule-based computing system of microbial interactions and communications, referred to as COSMIC-Rules, for simulating evolutionary processes within populations of virtual bacteria. The model incorporates three levels: the bacterial genome, the bacterial cell and an environment inhabited by such cells. The virtual environment in COSMIC-Rules can contain multiple substances, whose relative toxicity or nutrient status is specified by the genome of the bacterium. Each substance may be distributed uniformly or in a user-defined manner. The organisms in COSMIC-Rules possess individually-defined physical locations, size, cell division status and genomes. Genes and/or gene systems are represented by abstractions that may summate sometimes complex phenotypes. Central to COSMIC-Rules is a simplified representation of bacterial species, each containing a functional genome including, where desired, extrachromosomal elements such as plasmids and/or bacteriophages. A widely applicable computer representation of biological recognition systems based on bit string matching is essential to the model. This representation permits, for example, the modelling of protein-protein interactions, receptor-ligand interactions and DNA-DNA transactions. COSMIC-Rules is intended to inform studies on bacterial adaptation and evolution, and to predict behaviour of populations of pathogenic bacteria and their viruses. The framework is constructed for parallel execution across a large number of machines and efficiently utilises a 64 processor development cluster. It will run on any Grid system and has successfully tested simulations with millions of bacteria, of multiple species and utilising multiple substrates. The model may be used for large-scale simulations where a genealogical record for individual organisms is required.

Individual-based model and simulation of Plasmodium falciparum infected erythrocyte in vitro cultures

Malaria is still one of the most fatal diseases in the world. Development of an effective treatment or vaccine requires the cultivation of the parasite that causes it: Plasmodium falciparum. Several methods for in vitro cultivation of P. falciparum infected erythrocytes have been successfully developed and described in the last 30 years. Some problems arising from the current harvests are the low parasitaemia and daily human supervision requirements. The lack of a suitable model for global culture behavior makes the assay of new methodologies a costly and tenuous task. In this paper we present a model and simulation tool for these systems. We use the INDividual DIScrete SIMulation protocol (INDISIM) to qualitatively reproduce the temporal evolution of the erythrocyte and merozoite populations. Whole system dynamics are inferred by setting the rules of behavior for each individual red blood cell, such as the nutrient uptake, metabolism and infection processes, as well as the properties and rules for the culture medium: composition, diffusion and external manipulation. We set the individual description parameters according to the values in published data, and allow population heterogeneity. Cells are arranged in a three-dimensional grid and the study is focused on the geometric constraints and physical design of experimental sets. Several published experimental cultures have been reproduced with computer simulations of this model, showing that the observed experimental behavior can be explained by means of individual interactions and statistical laws.

An object simulation model for modeling hypothetical disease epidemics - EpiFlex

BACKGROUND

EpiFlex is a flexible, easy to use computer model for a single computer, intended to be operated by one user who need not be an expert. Its purpose is to study in-silico the epidemic behavior of a wide variety of diseases, both known and theoretical, by simulating their spread at the level of individuals contracting and infecting others. To understand the system fully, this paper must be read together in conjunction with study of the software and its results. EpiFlex is evaluated using results from modeling influenza A epidemics and comparing them with a variety of field data sources and other types of modeling. EpiFlex is an object-oriented Monte Carlo system, allocating entities to correspond to individuals, disease vectors, diseases, and the locations that hosts may inhabit. EpiFlex defines eight different contact types available for a disease. Contacts occur inside locations within the model. Populations are composed of demographic groups, each of which has a cycle of movement between locations. Within locations, superspreading is defined by skewing of contact distributions.

RESULTS

EpiFlex indicates three phenomena of interest for public health: (1) R0 is variable, and the smaller the population, the larger the infected fraction within that population will be; (2) significant compression/synchronization between cities by a factor of roughly 2 occurs between the early incubation phase of a multi-city epidemic and the major manifestation phase; (3) if better true morbidity data were available, more asymptomatic hosts would be seen to spread disease than we currently believe is the case for influenza. These results suggest that field research to study such phenomena, while expensive, should be worthwhile.

CONCLUSION

Since EpiFlex shows all stages of disease progression, detailed insight into the progress of epidemics is possible. EpiFlex shows the characteristic multimodality and apparently random variation characteristic of real world data, but does so as an emergent property of a carefully constructed model of disease dynamics and is not simply a stochastic system. EpiFlex can provide a better understanding of infectious diseases and strategies for response.

Individual-based modelling of bacterial cultures to study the microscopic causes of the lag phase

The lag phase has been widely studied for years in an effort to contribute to the improvement of food safety. Many analytical models have been built and tested by several authors. The use of Individual-based Modelling (IbM) allows us to probe deeper into the behaviour of individual cells; it is a bridge between theories and experiments when needed. INDividual DIScrete SIMulation (INDISIM) has been developed and coded by our group as an IbM simulator and used to study bacterial growth, including the microscopic causes of the lag phase. First of all, the evolution of cellular masses, specifically the mean mass and biomass distribution, is shown to be a determining factor in the beginning of the exponential phase. Secondly, whenever there is a need for an enzyme synthesis, its rate has a direct effect on the lag duration. The variability of the lag phase with different factors is also studied. The known decrease of the lag phase with an increase in the temperature is also observed in the simulations. An initial study of the relationship between individual and collective lag phases is presented, as a complement to the studies already published. One important result is the variability of the individual lag times and generation times. It has also been found that the mean of the individual lags is greater than the population lag. This is the first in a series of studies of the lag phase that we are carrying out. Therefore, the present work addresses a generic system by making a simple set of assumptions.

A rule-based approach to the modelling of bacterial ecosystems

This paper presents an approach to ecological/evolutionary modelling that is inspired by natural bacterial ecosystems and bacterial evolution. An individual-based artificial ecosystem model is proposed, which is designed to explore the evolvability of adaptive behavioural strategies in artificial bacteria represented by rule-based learning classifier systems. The proposed ecosystem model consists of a n-dimensional environmental grid, which can contain different types of artificial resources in arbitrary arrangements. The resources provide the energy that is necessary for the organisms to sustain life, and can trigger different types of behaviour in the organisms, such as movement towards nutrients and away from toxic substances, growth, and the controlled release of signalling resources. The balance between energy and material is modelled carefully to ensure that the ecosystem is dissipative. Those organisms that are able to efficiently exploit the available resources gradually accumulate enough energy to reproduce (by binary fission) and generate copies of themselves in the environment. Organisms are also able to produce their own resources, which can potentially be used as markers to send signals to other organisms (a behaviour known as quorum sensing). The complex relationships between stimuli and actions in the organisms are stochastically altered by means of mutations, thus enabling the organisms to adapt to their environment and maximise their lifespan and reproductive success. In this paper, the proposed bacterial ecosystem model is defined formally and its structure is discussed in detail. This is followed by results from simulation experiments that illustrate the model's operation and how it can be used in evolutionary modelling/computing scenarios.

Flocculation in brewing yeasts: a computer simulation study

A new simulator, INDISIM-FLOC, based on the individual-based simulator INDISIM, is used to examine the predictions of two different models of yeast flocculation. The first, proposed by Calleja is known as the "addition" model. The second, proposed by Stratford is known as the "cascade" model. The simulations show that the latter exhibits a better qualitative agreement with available experimental data.

An agent-based and spatially explicit model of pathogen dissemination in the intensive care unit*

OBJECTIVE

To develop and disseminate a spatially explicit model of contact transmission of pathogens in the intensive care unit.

DESIGN

A model simulating the spread of a pathogen transmitted by direct contact (such as methicillin-resistant Staphylococcus aureus or vancomycin-resistant Enterococcus) was constructed. The modulation of pathogen dissemination attending changes in clinically relevant pathogen- and institution-specific factors was then systematically examined.

SETTING AND PATIENTS

The model was configured as a hypothetical 24-bed intensive care unit. The model can be parameterized with different pathogen transmissibilities, durations of caregiver and/or patient contamination, and caregiver allocation and flow patterns.

INTERVENTIONS

Pathogen- and institution-specific factors examined included pathogen transmissibility, duration of caregiver contamination, regional cohorting of contaminated or infected patients, delayed detection and isolation of newly contaminated patients, reduction of the number of caregiver visits, and alteration of caregiver allocation among patients.

MEASUREMENTS AND MAIN RESULTS

The model predicts the probability that a given fraction of the population will become contaminated or infected with the pathogen of interest under specified spatial, initial prevalence, and dynamic conditions. Per-encounter pathogen acquisition risk and the duration of caregiver pathogen carriage most strongly affect dissemination. Regional cohorting and rapid detection and isolation of contaminated patients each markedly diminish the likelihood of dissemination even absent other interventions. Strategies reducing "crossover" between caregiver domains diminish the likelihood of more widespread dissemination.

CONCLUSIONS

Spatially explicit discrete element models, such as the model presented, may prove useful for analyzing the transmission of pathogens within the intensive care unit.

Individual-based spatially-explicit model of an herbivore and its resource: the effect of habitat reduction and fragmentation

We present an individual-based, spatially-explicit model of the dynamics of a small mammal and its resource. The life histories of each individual animal are modeled separately. The individuals can have the status of residents or wanderers and belong to behaviorally differing groups of juveniles or adults and males or females. Their territory defending and monogamous behavior is taken into consideration. The resource, green vegetation, grows depending on seasonal climatic characteristics and is diminished due to the herbivore's grazing. Other specifics such as a varying personal energetic level due to feeding and starvation of the individuals, mating preferences, avoidance of competitors, dispersal of juveniles, as a result of site overgrazing, etc., are included in the model. We determined model parameters from real data for the species Microtus ochrogaster (prairie vole). The simulations are done for a case of an enclosed habitat without predators or other species competitors. The goal of the study is to find the relation between size of habitat and population persistence. The experiments with the model show the populations go extinct due to severe overgrazing, but that the length of population persistence depends on the area of the habitat as well as on the presence of fragmentation. Additionally, the total population size of the vole population obtained during the simulations exhibits yearly fluctuations as well as multi-yearly peaks of fluctuations. This dynamics is similar to the one observed in prairie vole field studies.

Dynamic modeling of microbial cell populations

Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Recent advances have been made in cell population modeling, which allow the effects of cell heterogeneity on culture dynamics and metabolite production to be predicted. If the intracellular state can be captured with a few variables, the population balance equation framework is a viable modeling approach. The cell ensemble modeling technique is better suited for the development of population models that include more detailed descriptions of cellular metabolism and/or cell-cycle progression.