BSim: an agent-based tool for modeling bacterial populations in systems and synthetic biology

Emergence of ion-channel-mediated electrical oscillations in Escherichia coli biofilms

Bacterial biofilms are communities of bacteria usually attached to solid strata and often differentiated into complex structures. Communication across biofilms has been shown to involve chemical signaling and, more recently, electrical signaling in Gram-positive biofilms. We report for the first time, community-level synchronized membrane potential dynamics in three-dimensional Escherichia coli biofilms. Two hyperpolarization events are observed in response to light stress. The first requires mechanically sensitive ion channels (MscK, MscL, and MscS) and the second needs the Kch-potassium channel. The channels mediated both local spiking of single E. coli biofilms and long-range coordinated electrical signaling in E. coli biofilms. The electrical phenomena are explained using Hodgkin-Huxley and 3D fire-diffuse-fire agent-based models. These data demonstrate that electrical wavefronts based on potassium ions are a mechanism by which signaling occurs in Gram-negative biofilms and as such may represent a conserved mechanism for communication across biofilms.

Disentangling the feedback loops driving spatial patterning in microbial communities

The properties of multispecies biofilms are determined by how species are arranged in space. How these patterns emerge is a complex and largely unsolved problem. Here, we synthesize the known factors affecting pattern formation, identify the interdependencies and feedback loops coupling them, and discuss approaches to disentangle their effects. Finally, we propose an interdisciplinary research program that could create a predictive understanding of pattern formation in microbial communities.

Harnessing microbial division of labor for biomanufacturing: a review of laboratory and formal modeling approaches

Bioprocess industries aim to meet the increasing demand for product complexity by designing enhanced cellular and metabolic capabilities for the host. Monocultures, standard biomanufacturing workhorses, are often restricted in their capability to meet these demands, and the solution often involves the genetic modification of the host. Synthetic microbial communities are a promising alternative to monocultures because they exhibit division of labor, enabling efficient resource utilization and pathway modularity. This specialization minimizes metabolic burden and enhances robustness to perturbations, providing a competitive advantage. Despite this potential, their utilization in biotechnological or bioprocessing applications remains limited. The recent emergence of new and innovative community design tools and strategies, particularly those harnessing the division of labor, holds promise to change this outlook. Understanding the microbial interactions governing natural microbial communities can be used to identify complementary partners, informing synthetic community design. Therefore, we particularly consider engineering division of labor in synthetic microbial communities as a viable solution to accelerate progress in the field. This review presents the current understanding of how microbial interactions enable division of labor and how this information can be used to design synthetic microbial communities to perform tasks otherwise unfeasible to individual organisms. We then evaluate laboratory and formal modeling approaches specifically developed to: elucidate microbial community physiology, guide experimental design, and improve our understanding of complex community interactions assisting synthetic community design. By synthesizing these insights, we aim to present a comprehensive framework that advances the use of microbial communities in biomanufacturing applications.

Electrical signaling in three-dimensional bacterial biofilms using an agent-based fire-diffuse-fire model

Agent-based models were used to describe electrical signaling in bacterial biofilms in three dimensions. Specifically, wavefronts of potassium ions in Escherichia coli biofilms subjected to stress from blue light were modeled from experimental data. Electrical signaling occurs only when the biofilms grow beyond a threshold size, which we have shown to vary with the K^{+} ion diffusivity, and the K^{+} ion threshold concentration, which triggered firing in the fire-diffuse-fire model. The transport of the propagating wavefronts shows superdiffusive scaling on time. K^{+} ion diffusivity is the main factor that affects the wavefront velocity. The K^{+} ion diffusivity and the firing threshold also affect the anomalous exponent for the propagation of the wavefront determining whether the wavefront is subdiffusive or superdiffusive. The geometry of the biofilm and its relation to the mean-square displacement (MSD) of the wavefront as a function of time was investigated for spherical, cylindrical, cubical, and mushroom-like structures. The MSD varied significantly with geometry; an additional regime to the kinetics occurred when the potassium wavefront leaves the biofilm. Adding cylindrical defects to the biofilm, which are known to occur in E. coli biofilms, also gave an extra kinetic regime to the wavefront MSD for the propagation through the defect.

Optimization of periodic treatment strategies for bacterial biofilms using an agent-based in silico approach

Biofilms are responsible for most chronic infections and are highly resistant to antibiotic treatments. Previous studies have demonstrated that periodic dosing of antibiotics can help sensitize persistent subpopulations and reduce the overall dosage required for treatment. Because the dynamics and mechanisms of biofilm growth and the formation of persister cells are diverse and are affected by environmental conditions, it remains a challenge to design optimal periodic dosing regimens. Here, we develop a computational agent-based model to streamline this process and determine key parameters for effective treatment. We used our model to test a broad range of persistence switching dynamics and found that if periodic antibiotic dosing was tuned to biofilm dynamics, the dose required for effective treatment could be reduced by nearly 77%. The biofilm architecture and its response to antibiotics were found to depend on the dynamics of persister cells. Despite some differences in the response of biofilm governed by different persister switching rates, we found that a general optimized periodic treatment was still effective in significantly reducing the required antibiotic dose. As persistence becomes better quantified and understood, our model has the potential to act as a foundation for more effective strategies to target bacterial infections.

Is it selfish to be filamentous in biofilms? Individual-based modeling links microbial growth strategies with morphology using the new and modular iDynoMiCS 2.0

Microbial communities are found in all habitable environments and often occur in assemblages with self-organized spatial structures developing over time. This complexity can only be understood, predicted, and managed by combining experiments with mathematical modeling. Individual-based models are particularly suited if individual heterogeneity, local interactions, and adaptive behavior are of interest. Here we present the completely overhauled software platform, the individual-based Dynamics of Microbial Communities Simulator, iDynoMiCS 2.0, which enables researchers to specify a range of different models without having to program. Key new features and improvements are: (1) Substantially enhanced ease of use (graphical user interface, editor for model specification, unit conversions, data analysis and visualization and more). (2) Increased performance and scalability enabling simulations of up to 10 million agents in 3D biofilms. (3) Kinetics can be specified with any arithmetic function. (4) Agent properties can be assembled from orthogonal modules for pick and mix flexibility. (5) Force-based mechanical interaction framework enabling attractive forces and non-spherical agent morphologies as an alternative to the shoving algorithm. The new iDynoMiCS 2.0 has undergone intensive testing, from unit tests to a suite of increasingly complex numerical tests and the standard Benchmark 3 based on nitrifying biofilms. A second test case was based on the "biofilms promote altruism" study previously implemented in BacSim because competition outcomes are highly sensitive to the developing spatial structures due to positive feedback between cooperative individuals. We extended this case study by adding morphology to find that (i) filamentous bacteria outcompete spherical bacteria regardless of growth strategy and (ii) non-cooperating filaments outcompete cooperating filaments because filaments can escape the stronger competition between themselves. In conclusion, the new substantially improved iDynoMiCS 2.0 joins a growing number of platforms for individual-based modeling of microbial communities with specific advantages and disadvantages that we discuss, giving users a wider choice.

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.

Novel Ground-Up 3D Multicellular Simulators for Synthetic Biology CAD Integrating Stochastic Gillespie Simulations Benchmarked with Topologically Variable SBML Models

The elevation of Synthetic Biology from single cells to multicellular simulations would be a significant scale-up. The spatiotemporal behavior of cellular populations has the potential to be prototyped in silico for computer assisted design through ergonomic interfaces. Such a platform would have great practical potential across medicine, industry, research, education and accessible archiving in bioinformatics. Existing Synthetic Biology CAD systems are considered limited regarding population level behavior, and this work explored the in silico challenges posed from biological and computational perspectives. Retaining the connection to Synthetic Biology CAD, an extension of the Infobiotics Workbench Suite was considered, with potential for the integration of genetic regulatory models and/or chemical reaction networks through Next Generation Stochastic Simulator (NGSS) Gillespie algorithms. These were executed using SBML models generated by in-house SBML-Constructor over numerous topologies and benchmarked in association with multicellular simulation layers. Regarding multicellularity, two ground-up multicellular solutions were developed, including the use of Unreal Engine 4 contrasted with CPU multithreading and Blender visualization, resulting in a comparison of real-time versus batch-processed simulations. In conclusion, high-performance computing and client-server architectures could be considered for future works, along with the inclusion of numerous biologically and physically informed features, whilst still pursuing ergonomic solutions.

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.

Unravelling microbial efflux through mathematical modelling

AbstractMathematical modelling is a useful tool that is increasingly used in the life sciences to understand and predict the behaviour of biological systems. This review looks at how this interdisciplinary approach has advanced our understanding of microbial efflux, the process by which microbes expel harmful substances. The discussion is largely in the context of antimicrobial resistance, but applications in synthetic biology are also touched upon. The goal of this paper is to spark further fruitful collaborations between modellers and experimentalists in the efflux community and beyond.

Even allocation of benefits stabilizes microbial community engaged in metabolic division of labor

Microbial communities execute metabolic pathways to drive global nutrient cycles. Within a community, functionally specialized strains can perform different yet complementary steps within a linear pathway, a phenomenon termed metabolic division of labor (MDOL). However, little is known about how such metabolic behaviors shape microbial communities. Here, we derive a theoretical framework to define the assembly of a community that degrades an organic compound through MDOL. The framework indicates that to ensure community stability, the strains performing the initial steps should hold a growth advantage (m) over the "private benefit" (n) of the strain performing the last step. The steady-state frequency of the last strain is then determined by the quotient of n and m. Our experiments show that the framework accurately predicts the assembly of our synthetic consortia that degrade naphthalene through MDOL. Our results provide insights for designing and managing stable microbial systems for metabolic pathway optimization.

Ratiometric control of cell phenotypes in monostrain microbial consortia

We address the problem of regulating and keeping at a desired balance the relative numbers between cells exhibiting a different phenotype within a monostrain microbial consortium. We propose a strategy based on the use of external control inputs, assuming each cell in the community is endowed with a reversible, bistable memory mechanism. Specifically, we provide a general analytical framework to guide the design of external feedback control strategies aimed at balancing the ratio between cells whose memory is stabilized at either one of two equilibria associated with different cell phenotypes. We demonstrate the stability and robustness properties of the control laws proposed and validate them in silico, implementing the memory element via a genetic toggle-switch. The proposed control framework may be used to allow long-term coexistence of different populations, with both industrial and biotechnological applications. As a representative example, we consider the realistic agent-based implementation of our control strategy to enable cooperative bioproduction of a dimer in a monostrain microbial consortium.

A Self-Controlled and Self-Healing Model of Bacterial Cells

A new kind of self-assembly model, morphogenetic (M) systems, assembles spatial units into larger structures through local interactions of simpler components and enables discovery of new principles for cellular membrane assembly, development, and its interface function. The model is based on interactions among three kinds of constitutive objects such as tiles and protein-like elements in discrete time and continuous 3D space. It was motivated by achieving a balance between three conflicting goals: biological, physical-chemical, and computational realism. A recent example is a unified model of morphogenesis of a single biological cell, its membrane and cytoskeleton formation, and finally, its self-reproduction. Here, a family of dynamic M systems (Mbac) is described with similar characteristics, modeling the process of bacterial cell formation and division that exhibits bacterial behaviors of living cells at the macro-level (including cell growth that is self-controlled and sensitive to the presence/absence of nutrients transported through membranes), as well as self-healing properties. Remarkably, it consists of only 20 or so developmental rules. Furthermore, since the model exhibits membrane formation and septic mitosis, it affords more rigorous definitions of concepts such as injury and self-healing that enable quantitative analyses of these kinds of properties. Mbac shows that self-assembly and interactions of living organisms with their environments and membrane interfaces are critical for self-healing, and that these properties can be defined and quantified more rigorously and precisely, despite their complexity.

Control-Based Continuation: A New Approach to Prototype Synthetic Gene Networks

Control-Based Continuation (CBC) is a general and systematic method to carry out the bifurcation analysis of physical experiments. CBC does not rely on a mathematical model and thus overcomes the uncertainty introduced when identifying bifurcation curves indirectly through modeling and parameter estimation. We demonstrate, in silico, CBC applicability to biochemical processes by tracking the equilibrium curve of a toggle switch, which includes additive process noise and exhibits bistability. We compare the results obtained when CBC uses a model-free and model-based control strategy and show that both can track stable and unstable solutions, revealing bistability. We then demonstrate CBC in conditions more representative of an in vivo experiment using an agent-based simulator describing cell growth and division, cell-to-cell variability, spatial distribution, and diffusion of chemicals. We further show how the identified curves can be used for parameter estimation and discuss how CBC can significantly accelerate the prototyping of synthetic gene regulatory networks.

A Graph-based Molecular Communications Model Analysis of the Human Gut Bacteriome

Alterations in the human Gut Bacteriome (GB) can be associated with human health issues, such as type-2 diabetes and obesity. Both external and internal factors can drive changes in the composition and in interactions of the human GB, impacting negatively on the host cells. This paper focuses on the human GB metabolism and proposes a two-layer network system to investigate its dynamics. Furthermore, we develop an in-silico simulation model (virtual GB), allowing us to study the impact of the metabolite exchange through molecular communications in the human GB network system. Our results show that regulation of molecular inputs strongly affect bacterial population growth and create an unbalanced network, as shown by shifts in the node weights based on the produced molecular signals. Additionally, we show that the metabolite molecular communication production is greatly affected when directly manipulating the composition of the human GB network in the virtual GB. These results indicate that our human GB interaction model can help to identify hidden behaviors of the human GB depending on molecular signal interactions. Moreover, the virtual GB can support the research and development of novel medical treatments based on the accurate control of bacterial population growth and exchange of metabolites.

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.

Integrating Systems and Synthetic Biology to Understand and Engineer Microbiomes

Microbiomes are complex and ubiquitous networks of microorganisms whose seemingly limitless chemical transformations could be harnessed to benefit agriculture, medicine, and biotechnology. The spatial and temporal changes in microbiome composition and function are influenced by a multitude of molecular and ecological factors. This complexity yields both versatility and challenges in designing synthetic microbiomes and perturbing natural microbiomes in controlled, predictable ways. In this review, we describe factors that give rise to emergent spatial and temporal microbiome properties and the meta-omics and computational modeling tools that can be used to understand microbiomes at the cellular and system levels. We also describe strategies for designing and engineering microbiomes to enhance or build novel functions. Throughout the review, we discuss key knowledge and technology gaps for elucidating the networks and deciphering key control points for microbiome engineering, and highlight examples where multiple omics and modeling approaches can be integrated to address these gaps.

Simulating ATO Mechanism and EGFR Signaling with Fuzzy Logic and Petri Net

BACKGROUND

Interactions of many key proteins or genes in signalling pathway have been studied qualitatively in the literature, but only little quantitative information is available.

OBJECTIVE

Although much has been done to clarify the biochemistry of transcriptional dynamics in signalling pathway, it remains difficult to find out and predict quantitative responses. The aim of this study is to construct a computational model of epidermal growth factor receptor (EGFR) signalling pathway as one of hallmarks of cancer so as to predict quantitative responses.

MATERIAL AND METHODS

In this analytical study, we presented a computational model to investigate EGFR signalling pathway. Interaction of Arsenic trioxide (ATO) with EGFR signalling pathway factors has been elicited by systematic search in data bases, as ATO is one of the mysterious chemotherapy agents that control EGFR expression in cancer. ATO has dichotomous manner in vivo, dependent on its concentration. According to fuzzy rules based upon qualitative knowledge and Petri Net, we can construct a quantitative model to describe ATO mechanism in EGFR signalling pathway.

RESULTS

By Fuzzy Logic models that have the potential to trade with the loss of quantitative information on how different species interact, along with Petri net quantitatively describe the dynamics of EGFR signalling pathway. By this model the dynamic of different factors in EGFR signalling pathway is achieved.

CONCLUSION

The use of Fuzzy Logic and PNs in biological network modelling causes a deeper understanding and comprehensive analysis of the biological networks.

Toward Engineering Biosystems With Emergent Collective Functions

Many complex behaviors in biological systems emerge from large populations of interacting molecules or cells, generating functions that go beyond the capabilities of the individual parts. Such collective phenomena are of great interest to bioengineers due to their robustness and scalability. However, engineering emergent collective functions is difficult because they arise as a consequence of complex multi-level feedback, which often spans many length-scales. Here, we present a perspective on how some of these challenges could be overcome by using multi-agent modeling as a design framework within synthetic biology. Using case studies covering the construction of synthetic ecologies to biological computation and synthetic cellularity, we show how multi-agent modeling can capture the core features of complex multi-scale systems and provide novel insights into the underlying mechanisms which guide emergent functionalities across scales. The ability to unravel design rules underpinning these behaviors offers a means to take synthetic biology beyond single molecules or cells and toward the creation of systems with functions that can only emerge from collectives at multiple scales.

Agent-Based Models Predict Emergent Behavior of Heterogeneous Cell Populations in Dynamic Microenvironments

Computational models are most impactful when they explain and characterize biological phenomena that are non-intuitive, unexpected, or difficult to study experimentally. Countless equation-based models have been built for these purposes, but we have yet to realize the extent to which rules-based models offer an intuitive framework that encourages computational and experimental collaboration. We develop ARCADE, a multi-scale agent-based model to interrogate emergent behavior of heterogeneous cell agents within dynamic microenvironments and demonstrate how complexity of intracellular metabolism and signaling modules impacts emergent dynamics. We perform in silico case studies on context, competition, and heterogeneity to demonstrate the utility of our model for gaining computational and experimental insight. Notably, there exist (i) differences in emergent behavior between colony and tissue contexts, (ii) linear, non-linear, and multimodal consequences of parameter variation on competition in simulated co-cultures, and (iii) variable impact of cell and population heterogeneity on emergent outcomes. Our extensible framework is easily modified to explore numerous biological systems, from tumor microenvironments to microbiomes.

Easybiotics: a GUI for 3D physical modelling of multi-species bacterial populations

MOTIVATION

3D physical modelling is a powerful computational technique that allows for the simulation of complex systems such as consortia of mixed bacterial species. The complexities in physical modelling reside in the knowledge intensive model building process and the computational expense in calculating their numerical solutions. These models can offer insights into microbiology, both in understanding natural systems and as design tools for developing novel synthetic bacterial systems. Developing a robust synthetic system typically requires multiple iterations around the specify→design→build→test cycle to meet specifications. This process is laborious and expensive for both the computational and laboratory aspects, hence any improvement in any of the workflow steps would be welcomed. We have previously introduced Simbiotics, a powerful and flexible platform for designing and analyzing 3D simulations of mixed species bacterial populations. Simbiotics requires programming experience to use which creates barriers to entry for use of the tool.

RESULTS

In the spirit of enabling biologists who may not have programming skills to install and utilize Simbiotics, we present in this application note Easybiotics, a user-friendly graphical user interface for Simbiotics. Users may design, simulate and analyze models from within the graphical user interface, with features such as live graph plotting and parameter sweeps. Easybiotics provides full access to all of Simbiotics simulation features, such as cell growth, motility and gene regulation.

AVAILABILITY AND IMPLEMENTATION

Easybiotics and Simbiotics are free to use under the GPL3.0 licence, and can be found at: http://ico2s.org/software/simbiotics.html. We also provide readily downloadable virtual machine sandboxes to facilitate rapid installation.

Balancing Cell Populations Endowed with a Synthetic Toggle Switch via Adaptive Pulsatile Feedback Control

The problem of controlling cells endowed with a genetic toggle switch has been recently highlighted as a benchmark problem in synthetic biology. It has been shown that a carefully selected periodic forcing can balance a population of such cells in an undifferentiated state. The effectiveness of these control strategies, however, can be hindered by the presence of stochastic perturbations and uncertainties typically observed in biological systems and is therefore not robust. Here, we propose the use of feedback control strategies to enhance robustness and performance of the balancing action by selecting in real-time both the amplitude and the duty-cycle of the pulsatile inputs affecting the toggle switch behavior. We show, via in silico experiments and realistic agent-based simulations, the effectiveness of the proposed strategies even in the presence of uncertainties, stochastic effects, cell growth, and inducer diffusion. In so doing, we confirm previous observations made in the literature about coherence of the population when pulsatile forcing inputs are used, but, contrary to what was proposed in the past, we leverage feedback control techniques to endow the balancing strategy with unprecedented robustness and stability properties. We compare via in silico experiments different external control solutions and show their advantages and limitations from an in vivo implementation viewpoint.

Modelling bacterial chemotaxis for indirectly binding attractants

In bacterial chemotaxis, chemoattractant molecules may bind either directly or indirectly with receptors within the cell periplasmic space. The indirect binding mechanism, which involves an intermediate periplasmic binding protein, has been reported to increase sensitivity to dilute attractant concentrations as well as range of response. Current mathematical models for bacterial chemotaxis at the population scale do not appear to take the periplasmic binding protein (BP) concentration or the indirect binding mechanics into account. We formulate an indirect binding extension to the existing Rivero equation for chemotactic velocity based on fundamental reversible enzyme kinetics. The formulated indirect binding expression accounts for the periplasmic BP concentration and the dissociation constants for binding between attractant and periplasmic BP, as well as between BP and chemoreceptor. We validate the indirect-binding model using capillary assay simulations of the chemotactic responses of E. coli to the indirectly-binding attractants maltose and AI-2. The predicted response agrees well with experimental data from a number of maltose capillary assay studies conducted in previous literature. The model is also able to achieve good agreement with AI-2 capillary assay data of one study out of two tested. The chemotactic response of E. coli towards AI-2 appears to be of higher complexity due to reports of variable periplasmic BP concentration as well as the low concentration of periplasmic BP relative to the total receptor concentration. Our current model is thus suitable for indirect binding chemotactic response systems with constant periplasmic BP concentration that is significantly larger than the total receptor concentration, such as the response of E. coli towards maltose. Further considerations may be taken into account to model the chemotactic response towards AI-2 with greater accuracy.

Hybrid Model of Bacterial Biofilm Growth

Bacterial biofilms play a critical role in environmental processes, water treatment, human health, and food processing. They exhibit highly complex dynamics due to the interactions between the bacteria and the extracellular polymeric substance (EPS), water, and nutrients and minerals that make up the biofilm. We present a hybrid computational model in which the dynamics of discrete bacterial cells are simulated within a multiphase continuum, consisting of EPS and water as separate interacting phases, through which nutrients and minerals diffuse. Bacterial cells in our model consume water and nutrients in order to grow, divide, and produce EPS. Consequently, EPS flows outward from the bacterial colony, while water flows inward. The model predicts bacterial colony formation as a treelike structure. The distribution of bacterial growth and EPS production is found to be sensitive to the pore spacing between bacteria and the consumption of nutrients within the bacterial colony. Forces that are sometimes neglected in biofilm simulations, such as lubrication force between nearby bacterial cells and osmotic (swelling) pressure force resulting from gradients in EPS concentration, are observed to have an important effect on biofilm growth via their influence on bacteria pore spacing and associated water/nutrient percolation into the bacterial colony.

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

Pathways to cellular supremacy in biocomputing

Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found.

Synthetic biology uses cells as its computing substrate, often based on the genetic circuit concept. In this Perspective, the authors argue that existing synthetic biology approaches based on classical models of computation limit the potential of biocomputing, and propose that living organisms have under-exploited capabilities.

GutLogo: Agent-based modeling framework to investigate spatial and temporal dynamics in the gut microbiome

Knowledge of the spatial and temporal dynamics of the gut microbiome is essential to understanding the state of human health, as over a hundred diseases have been correlated with changes in microbial populations. Unfortunately, due to the complexity of the microbiome and the limitations of in vivo and in vitro experiments, studying spatial and temporal dynamics of gut bacteria in a biological setting is extremely challenging. Thus, in silico experiments present an excellent alternative for studying such systems. In consideration of these issues, we have developed a user-friendly agent-based model, GutLogo, that captures the spatial and temporal development of four representative bacterial genera populations in the ileum. We demonstrate the utility of this model by simulating population responses to perturbations in flow rate, nutrition, and probiotics. While our model predicts distinct changes in population levels due to these perturbations, most of the simulations suggest that the gut populations will return to their original steady states once the disturbance is removed. We hope that, in the future, the GutLogo model is utilized and customized by interested parties, as GutLogo can serve as a basic modeling framework for simulating a variety of physiological scenarios and can be extended to capture additional complexities of interest.

A Multiscale Agent-Based Model for the Investigation of E. coli K12 Metabolic Response During Biofilm Formation

Bacterial biofilm formation is an organized collective response to biochemical cues that enables bacterial colonies to persist and withstand environmental insults. We developed a multiscale agent-based model that characterizes the intracellular, extracellular, and cellular scale interactions that modulate Escherichia coli MG1655 biofilm formation. Each bacterium's intracellular response and cellular state were represented as an outcome of interactions with the environment and neighboring bacteria. In the intracellular model, environment-driven gene expression and metabolism were captured using statistical regression and Michaelis-Menten kinetics, respectively. In the cellular model, growth, death, and type IV pili- and flagella-dependent movement were based on the bacteria's intracellular state. We implemented the extracellular model as a three-dimensional diffusion model used to describe glucose, oxygen, and autoinducer 2 gradients within the biofilm and bulk fluid. We validated the model by comparing simulation results to empirical quantitative biofilm profiles, gene expression, and metabolic concentrations. Using the model, we characterized and compared the temporal metabolic and gene expression profiles of sessile versus planktonic bacterial populations during biofilm formation and investigated correlations between gene expression and biofilm-associated metabolites and cellular scale phenotypes. Based on our in silico studies, planktonic bacteria had higher metabolite concentrations in the glycolysis and citric acid cycle pathways, with higher gene expression levels in flagella and lipopolysaccharide-associated genes. Conversely, sessile bacteria had higher metabolite concentrations in the autoinducer 2 pathway, with type IV pili, autoinducer 2 export, and cellular respiration genes upregulated in comparison with planktonic bacteria. Having demonstrated results consistent with in vitro static culture biofilm systems, our model enables examination of molecular phenomena within biofilms that are experimentally inaccessible and provides a framework for future exploration of how hypothesized molecular mechanisms impact bulk community behavior.

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.

Agent-Based Modeling in Molecular Systems Biology

Molecular systems orchestrating the biology of the cell typically involve a complex web of interactions among various components and span a vast range of spatial and temporal scales. Computational methods have advanced our understanding of the behavior of molecular systems by enabling us to test assumptions and hypotheses, explore the effect of different parameters on the outcome, and eventually guide experiments. While several different mathematical and computational methods are developed to study molecular systems at different spatiotemporal scales, there is still a need for methods that bridge the gap between spatially-detailed and computationally-efficient approaches. In this review, we summarize the capabilities of agent-based modeling (ABM) as an emerging molecular systems biology technique that provides researchers with a new tool in exploring the dynamics of molecular systems/pathways in health and disease.

BSim 2.0: An Advanced Agent-Based Cell Simulator

Agent-based models (ABMs) provide a number of advantages relative to traditional continuum modeling approaches, permitting incorporation of great detail and realism into simulations, allowing in silico tracking of single-cell behaviors and correlation of these with emergent effects at the macroscopic level. In this study we present BSim 2.0, a radically new version of BSim, a computational ABM framework for modeling dynamics of bacteria in typical experimental environments including microfluidic chemostats. This is facilitated through the implementation of new methods including cells with capsular geometry that are able to physically and chemically interact with one another, a realistic model of cellular growth, a delay differential equation solver, and realistic environmental geometries.

A New Improved and Extended Version of the Multicell Bacterial Simulator gro

gro is a cell programming language developed in Klavins Lab for simulating colony growth and cell-cell communication. It is used as a synthetic biology prototyping tool for simulating multicellular biocircuits and microbial consortia. In this work, we present several extensions made to gro that improve the performance of the simulator, make it easier to use, and provide new functionalities. The new version of gro is between 1 and 2 orders of magnitude faster than the original version. It is able to grow microbial colonies with up to 10⁵ cells in less than 10 min. A new library, CellEngine, accelerates the resolution of spatial physical interactions between growing and dividing cells by implementing a new shoving algorithm. A genetic library, CellPro, based on Probabilistic Timed Automata, simulates gene expression dynamics using simplified and easy to compute digital proteins. We also propose a more convenient language specification layer, ProSpec, based on the idea that proteins drive cell behavior. CellNutrient, another library, implements Monod-based growth and nutrient uptake functionalities. The intercellular signaling management was improved and extended in a library called CellSignals. Finally, bacterial conjugation, another local cell-cell communication process, was added to the simulator. To show the versatility and potential outreach of this version of gro, we provide studies and novel examples ranging from synthetic biology to evolutionary microbiology. We believe that the upgrades implemented for gro have made it into a powerful and fast prototyping tool capable of simulating a large variety of systems and synthetic biology designs.

A mechanistic Individual-based Model of microbial communities

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

Simbiotics: A Multiscale Integrative Platform for 3D Modeling of Bacterial Populations

Simbiotics is a spatially explicit multiscale modeling platform for the design, simulation and analysis of bacterial populations. Systems ranging from planktonic cells and colonies, to biofilm formation and development may be modeled. Representation of biological systems in Simbiotics is flexible, and user-defined processes may be in a variety of forms depending on desired model abstraction. Simbiotics provides a library of modules such as cell geometries, physical force dynamics, genetic circuits, metabolic pathways, chemical diffusion and cell interactions. Model defined processes are integrated and scheduled for parallel multithread and multi-CPU execution. A virtual lab provides the modeler with analysis modules and some simulated lab equipment, enabling automation of sample interaction and data collection. An extendable and modular framework allows for the platform to be updated as novel models of bacteria are developed, coupled with an intuitive user interface to allow for model definitions with minimal programming experience. Simbiotics can integrate existing standards such as SBML, and process microscopy images to initialize the 3D spatial configuration of bacteria consortia. Two case studies, used to illustrate the platform flexibility, focus on the physical properties of the biosystems modeled. These pilot case studies demonstrate Simbiotics versatility in modeling and analysis of natural systems and as a CAD tool for synthetic biology.

Perspectives and Challenges in Microbial Communities Metabolic Modeling

Bacteria have evolved to efficiently interact each other, forming complex entities known as microbial communities. These "super-organisms" play a central role in maintaining the health of their eukaryotic hosts and in the cycling of elements like carbon and nitrogen. However, despite their crucial importance, the mechanisms that influence the functioning of microbial communities and their relationship with environmental perturbations are obscure. The study of microbial communities was boosted by tremendous advances in sequencing technologies, and in particular by the possibility to determine genomic sequences of bacteria directly from environmental samples. Indeed, with the advent of metagenomics, it has become possible to investigate, on a previously unparalleled scale, the taxonomical composition and the functional genetic elements present in a specific community. Notwithstanding, the metagenomic approach per se suffers some limitations, among which the impossibility of modeling molecular-level (e.g., metabolic) interactions occurring between community members, as well as their effects on the overall stability of the entire system. The family of constraint-based methods, such as flux balance analysis, has been fruitfully used to translate genome sequences in predictive, genome-scale modeling platforms. Although these techniques have been initially developed for analyzing single, well-known model organisms, their recent improvements allowed engaging in multi-organism in silico analyses characterized by a considerable predictive capability. In the face of these advances, here we focus on providing an overview of the possibilities and challenges related to the modeling of metabolic interactions within a bacterial community, discussing the feasibility and the perspectives of this kind of analysis in the (near) future.

Agent-based modelling in synthetic biology

Biological systems exhibit complex behaviours that emerge at many different levels of organization. These span the regulation of gene expression within single cells to the use of quorum sensing to co-ordinate the action of entire bacterial colonies. Synthetic biology aims to make the engineering of biology easier, offering an opportunity to control natural systems and develop new synthetic systems with useful prescribed behaviours. However, in many cases, it is not understood how individual cells should be programmed to ensure the emergence of a required collective behaviour. Agent-based modelling aims to tackle this problem, offering a framework in which to simulate such systems and explore cellular design rules. In this article, I review the use of agent-based models in synthetic biology, outline the available computational tools, and provide details on recently engineered biological systems that are amenable to this approach. I further highlight the challenges facing this methodology and some of the potential future directions.

Towards Concurrent Data Transmission: Exploiting Plasmid Diversity by Bacterial Conjugation

The progress of molecular communication (MC) is tightly connected to the progress of nanomachine design. State-of-the-art states that nanomachines can be built either from novel nanomaterials by the help of nanotechnology or they can be built from living cells which are modified to function as intended by synthetic biology. With the growing need of the biomedical applications of MC, we focus on developing bio-compatible communication systems by engineering the cells to become MC nanomachines. Since this approach relies on modifying cellular functions, the improvements in the performance can only be achieved by integrating new biological properties. A previously proposed model for molecular communication is using bacteria as information carriers between transmitters and receivers, also known as bacterial nanonetworks. This approach has suggested encoding information into the plasmids inserted into the bacteria which leads to extra overhead for the receivers to decode and analyze the plasmids to obtain the encoded information. Another scheme, which is proposed in this paper, is to determine the digital information transmitted based on the quantity of bacteria emitted. While this scheme has its simplicity, the major drawback is the low-data rate resulting from the long propagation of the bacteria. To improve the performance, this paper proposes a distributed modulation scheme utilizing three bacterial properties, namely, engineering of plasmids, conjugation, and bacterial motility. In particular, genetic engineering allows us to engineer the different combinations of genes representing the different series of bits. When compared with binary density modulation and the M-ary density modulation, it is shown that the distributed modulation scheme outperforms the other two approaches in terms of bit error probability as well as the achievable rate for varying quantity of bacteria transmitted, distances, as well as time slot length.

BacArena: Individual-based metabolic modeling of heterogeneous microbes in complex communities

Recent advances focusing on the metabolic interactions within and between cellular populations have emphasized the importance of microbial communities for human health. Constraint-based modeling, with flux balance analysis in particular, has been established as a key approach for studying microbial metabolism, whereas individual-based modeling has been commonly used to study complex dynamics between interacting organisms. In this study, we combine both techniques into the R package BacArena (https://cran.r-project.org/package=BacArena) to generate novel biological insights into Pseudomonas aeruginosa biofilm formation as well as a seven species model community of the human gut. For our P. aeruginosa model, we found that cross-feeding of fermentation products cause a spatial differentiation of emerging metabolic phenotypes in the biofilm over time. In the human gut model community, we found that spatial gradients of mucus glycans are important for niche formations which shape the overall community structure. Additionally, we could provide novel hypothesis concerning the metabolic interactions between the microbes. These results demonstrate the importance of spatial and temporal multi-scale modeling approaches such as BacArena.

In nature, organisms are typically found in near proximity to each other, forming symbiotic relationships. Particularly bacteria are often part of highly organized communities such as biofilms. In this study, we integrate the detailed knowledge about the metabolic capabilities of individual organisms into an individual-based modeling approach for simulating the dynamics of local interactions. We provide a fast and flexible framework, in which established computational models for individual organisms can be simulated in communities. Nutrients can diffuse in an area where cells move, divide, and die. The resulting spatial as well as temporal dynamics and metabolic interactions can be analyzed as well as visualized and subsequently compared to experimental findings. We demonstrate how our approach can be used to gain novel insights on dynamics in single species biofilm formation and multi-species intestinal microbial communities.

In-Silico Analysis and Implementation of a Multicellular Feedback Control Strategy in a Synthetic Bacterial Consortium

Living organisms employ endogenous negative feedback loops to maintain homeostasis despite environmental fluctuations. A pressing open challenge in Synthetic Biology is to design and implement synthetic circuits to control host cells' behavior, in order to regulate and maintain desired conditions. To cope with the high degree of circuit complexity required to accomplish this task and the intrinsic modularity of classical control schemes, we suggest the implementation of synthetic endogenous feedback loops across more than one cell population. The distribution of the sensing, computation, and actuation functions required to achieve regulation across different cell populations within a consortium allows the genetic engineering in a particular cell to be reduced, increases the robustness, and makes it possible to reuse the synthesized modules for different control applications. Here, we analyze, in-silico, the design of a synthetic feedback controller implemented across two cell populations in a consortium. We study the effects of distributing the various functions required to build a control system across two populations, prove the robustness and modularity of the strategy described, and provide a computational proof-of-concept of its feasibility.

How Behaviour and the Environment Influence Transmission in Mobile Groups

The movement of individuals living in groups leads to the formation of physical interaction networks over which signals such as information or disease can be transmitted. Direct contacts represent the most obvious opportunities for a signal to be transmitted. However, because signals that persist after being deposited into the environment may later be acquired by other group members, indirect environmentally-mediated transmission is also possible. To date, studies of signal transmission within groups have focused on direct physical interactions and ignored the role of indirect pathways. Here, we use an agent-based model to study how the movement of individuals and characteristics of the signal being transmitted modulate transmission. By analysing the dynamic interaction networks generated from these simulations, we show that the addition of indirect pathways speeds up signal transmission, while the addition of physically-realistic collisions between individuals in densely packed environments hampers it. Furthermore, the inclusion of spatial biases that induce the formation of individual territories, reveals the existence of a trade-off such that optimal signal transmission at the group level is only achieved when territories are of intermediate sizes. Our findings provide insight into the selective pressures guiding the evolution of behavioural traits in natural groups, and offer a means by which multi-agent systems can be engineered to achieve desired transmission capabilities.

Agent-Based Modelling in Multicellular Systems Biology

This chapter aims at discussing the content of multi-agent based simulation (MABS) applied to computational biology i.e., to modelling and simulating biological systems by means of computational models, methodologies, and frameworks. In particular, the adoption of agent-based modelling (ABM) in the field of multicellular systems biology is explored, focussing on the challenging scenarios of developmental biology. After motivating why agent-based abstractions are critical in representing multicellular systems behaviour, MABS is discussed as the source of the most natural and appropriate mechanism for analysing the self-organising behaviour of systems of cells. As a case study, an application of MABS to the development of Drosophila Melanogaster is finally presented, which exploits the ALCHEMIST platform for agent-based simulation.

A mechanistic Individual-based Model of microbial communities

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