A hybrid agent-based approach for modeling microbiological systems

Partial mean-field model for neurotransmission dynamics

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

An Eco-evolutionary Model on Surviving Lysogeny Through Grounding and Accumulation of Prophages

Temperate phages integrate into the bacterial genomes propagating along with the bacterial genomes. Multiple phage elements, representing diverse prophages, are present in most bacterial genomes. The evolutionary events and the ecological dynamics underlying the accumulation of prophage elements in bacterial genomes have yet to be understood. Here, we show that the local wastewater had 7% of lysogens (hosting mitomycin C-inducible prophages), and they showed resistance to superinfection by their corresponding lysates. Genomic analysis of four lysogens and four non-lysogens revealed the presence of multiple prophages (belonging to Myoviridae and Siphoviridae) in both lysogens and non-lysogens. For large-scale comparison, 2180 Escherichia coli genomes isolated from various sources across the globe and 523 genomes specifically isolated from diverse wastewaters were analyzed. A total of 15,279 prophages were predicted among 2180 E. coli genomes and 2802 prophages among 523 global wastewater isolates, with a mean of ~ 5 prophages per genome. These observations indicate that most putative prophages are relics of past bacteria-phage conflicts; they are "grounded" prophages that cannot excise from the bacterial genome. Prophage distribution analysis based on the sequence homology suggested the random distribution of E. coli prophages within and between E. coli clades. The independent occurrence pattern of these prophages indicates extensive horizontal transfers across the genomes. We modeled the eco-evolutionary dynamics to reconstruct the events that could have resulted in the prophage accumulation accounting for infection, superinfection immunity, and grounding. In bacteria-phage conflicts, the bacteria win by grounding the prophage, which could confer superinfection immunity.

Surrogate infection model predicts optimal alveolar macrophage number for clearance of Aspergillus fumigatus infections

The immune system has to fight off hundreds of microbial invaders every day, such as the human-pathogenic fungus Aspergillus fumigatus. The fungal conidia can reach the lower respiratory tract, swell and form hyphae within six hours causing life-threatening invasive aspergillosis. Invading pathogens are continuously recognized and eliminated by alveolar macrophages (AM). Their number plays an essential role, but remains controversial with measurements varying by a factor greater than ten for the human lung. We here investigate the impact of the AM number on the clearance of A. fumigatus conidia in humans and mice using analytical and numerical modeling approaches. A three-dimensional to-scale hybrid agent-based model (hABM) of the human and murine alveolus allowed us to simulate millions of virtual infection scenarios, and to gain quantitative insights into the infection dynamics for varying AM numbers and infection doses. Since hABM simulations are computationally expensive, we derived and trained an analytical surrogate infection model on the large dataset of numerical simulations. This enables reducing the number of hABM simulations while still providing (i) accurate and immediate predictions on infection progression, (ii) quantitative hypotheses on the infection dynamics under healthy and immunocompromised conditions, and (iii) optimal AM numbers for combating A. fumigatus infections in humans and mice.

Modeling endonuclease colicin-like bacteriocin operons as 'genetic arms' in plasmid-genome conflicts

Plasmids are acellular propagating entities that depend on bacteria, as molecular parasites, for propagation. A 'tussle' between bacteria and plasmid ensues; bacteria for riddance of the plasmid and plasmid for persistence within a live host. Plasmid-maintenance systems such as endonuclease Colicin-Like Bacteriocins (CLBs) ensure plasmid propagation within the population; (i) the plasmid-cured cells are killed by the CLBs; (ii) damaged cells lyse and release the CLBs that eliminate the competitors, and (iii) the released plasmids invade new bacteria. Surprisingly, endonuclease CLB operons occur on bacterial genomes whose significance is unknown. Here, we study genetics, eco-evolutionary drive, and physiological relevance of genomic endonuclease CLB operons. We investigated plasmidic and genomic endonuclease CLB operons using sequence analyses from an eco-evolutionary perspective. We found 1266 genomic and plasmidic endonuclease CLB operons across 30 bacterial genera. Although 51% of the genomes harbor endonuclease CLB operons, the majority of the genomic endonuclease CLB operons lacked a functional lysis gene, suggesting the negative selection of lethal genes. The immunity gene of the endonuclease CLB operon protects the plasmid-cured host, eliminating the metabolic burden. We show mutual exclusivity of endonuclease CLB operons on genomes and plasmids. We propose an anti-addiction hypothesis for genomic endonuclease CLB operons. Using a stochastic hybrid agent-based model, we show that the endonuclease CLB operons on genomes confer an advantage to the host genome in terms of immunity to the toxin and elimination of plasmid burden. The conflict between bacterial genome and plasmids allows the emergence of 'genetic arms' such as CLB operons that regulate the ecological interplay of bacterial genomes and plasmids.

Hybrid models of chemotaxis with application to leukocyte migration

Many chemical and biological systems involve reacting species with vastly different numbers of molecules/agents. Hybrid simulations model such phenomena by combining discrete (e.g., agent-based) and continuous (e.g., partial differential equation- or PDE-based) descriptors of the dynamics of reactants with small and large numbers of molecules/agents, respectively. We present a stochastic hybrid algorithm to model a stage of the immune response to inflammation, during which leukocytes reach a pathogen via chemotaxis. While large numbers of chemoattractant molecules justify the use of a PDE-based model to describe the spatiotemporal evolution of its concentration, relatively small numbers of leukocytes and bacteria involved in the process undermine the veracity of their continuum treatment by masking the effects of stochasticity and have to be treated discretely. Motility and interactions between leukocytes and bacteria are modeled via random walk and a stochastic simulation algorithm, respectively. Since the latter assumes the reacting species to be well mixed, the discrete component of our hybrid algorithm deploys stochastic operator splitting, in which the sequence of the diffusion and reaction operations is determined autonomously during each simulation step. We conduct a series of numerical experiments to ascertain the accuracy and computational efficiency of our hybrid simulations and, then, to demonstrate the importance of randomness for predicting leukocyte migration and fate during the immune response to inflammation.

Hybrid Agent-Based Modeling of Aspergillus fumigatus Infection to Quantitatively Investigate the Role of Pores of Kohn in Human Alveoli

The healthy state of an organism is constantly threatened by external cues. Due to the daily inhalation of hundreds of particles and pathogens, the immune system needs to constantly accomplish the task of pathogen clearance in order to maintain this healthy state. However, infection dynamics are highly influenced by the peculiar anatomy of the human lung. Lung alveoli that are packed in alveolar sacs are interconnected by so called Pores of Kohn. Mainly due to the lack of in vivo methods, the role of Pores of Kohn in the mammalian lung is still under debate and partly contradicting hypotheses remain to be investigated. Although it was shown by electron microscopy that Pores of Kohn may serve as passageways for immune cells, their impact on the infection dynamics in the lung is still unknown under in vivo conditions. In the present study, we apply a hybrid agent-based infection model to quantitatively compare three different scenarios and discuss the importance of Pores of Kohn during infections of Aspergillus fumigatus. A. fumigatus is an airborne opportunistic fungus with rising incidences causing severe infections in immunocompromised patients that are associated with high mortality rates. Our hybrid agent-based model incorporates immune cell dynamics of alveolar macrophages – the resident phagocytes in the lung – as well as molecular dynamics of diffusing chemokines that attract alveolar macrophages to the site of infection. Consequently, this model allows a quantitative comparison of three different scenarios and to study the importance of Pores of Kohn. This enables us to demonstrate how passaging of alveolar macrophages and chemokine diffusion affect A. fumigatus infection dynamics. We show that Pores of Kohn alter important infection clearance mechanisms, such as the spatial distribution of macrophages and the effect of chemokine signaling. However, despite these differences, a lack of passageways for alveolar macrophages does impede infection clearance only to a minor extend. Furthermore, we quantify the importance of recruited macrophages in comparison to resident macrophages.

On the efficiency of chemotactic pursuit - Comparing blind search with temporal and spatial gradient sensing

In chemotaxis, cells are modulating their migration patterns in response to concentration gradients of a guiding substance. Immune cells are believed to use such chemotactic sensing for remotely detecting and homing in on pathogens. Considering that immune cells may encounter a multitude of targets with vastly different migration properties, ranging from immobile to highly mobile, it is not clear which strategies of chemotactic pursuit are simultaneously efficient and versatile. We tackle this problem theoretically and define a tunable response function that maps temporal or spatial concentration gradients to migration behavior. The seven free parameters of this response function are optimized numerically with the objective of maximizing search efficiency against a wide spectrum of target cell properties. Finally, we reverse-engineer the best-performing parameter sets to uncover strategies of chemotactic pursuit that are efficient under different biologically realistic boundary conditions. Although strategies based on the temporal or spatial sensing of chemotactic gradients are significantly more efficient than unguided migration, such ‘blind search’ turns out to work surprisingly well, in particular if the immune cells are fast and directionally persistent. The resulting simulated data can be used for the design of chemotaxis experiments and for the development of algorithms that automatically detect and quantify goal oriented behavior in measured immune cell trajectories.

Spatially extended hybrid methods: a review

Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.

Deciphering chemokine properties by a hybrid agent-based model of Aspergillus fumigatus infection in human alveoli

The ubiquitous airborne fungal pathogen Aspergillus fumigatus is inhaled by humans every day. In the lung, it is able to quickly adapt to the humid environment and, if not removed within a time frame of 4–8 h, the pathogen may cause damage by germination and invasive growth. Applying a to-scale agent-based model of human alveoli to simulate early A. fumigatus infection under physiological conditions, we recently demonstrated that alveolar macrophages require chemotactic cues to accomplish the task of pathogen detection within the aforementioned time frame. The objective of this study is to specify our general prediction on the as yet unidentified chemokine by a quantitative analysis of its expected properties, such as the diffusion coefficient and the rates of secretion and degradation. To this end, the rule-based implementation of chemokine diffusion in the initial agent-based model is revised by numerically solving the spatio-temporal reaction-diffusion equation in the complex structure of the alveolus. In this hybrid agent-based model, alveolar macrophages are represented as migrating agents that are coupled to the interactive layer of diffusing molecule concentrations by the kinetics of chemokine receptor binding, internalization and re-expression. Performing simulations for more than a million virtual infection scenarios, we find that the ratio of secretion rate to the diffusion coefficient is the main indicator for the success of pathogen detection. Moreover, a subdivision of the parameter space into regimes of successful and unsuccessful parameter combination by this ratio is specific for values of the migration speed and the directional persistence time of alveolar macrophages, but depends only weakly on chemokine degradation rates.

Cell, isoform, and environment factors shape gradients and modulate chemotaxis

Chemokine gradient formation requires multiple processes that include ligand secretion and diffusion, receptor binding and internalization, and immobilization of ligand to surfaces. To understand how these events dynamically shape gradients and influence ensuing cell chemotaxis, we built a multi-scale hybrid agent-based model linking gradient formation, cell responses, and receptor-level information. The CXCL12/CXCR4/CXCR7 signaling axis is highly implicated in metastasis of many cancers. We model CXCL12 gradient formation as it is impacted by CXCR4 and CXCR7, with particular focus on the three most highly expressed isoforms of CXCL12. We trained and validated our model using data from an in vitro microfluidic source-sink device. Our simulations demonstrate how isoform differences on the molecular level affect gradient formation and cell responses. We determine that ligand properties specific to CXCL12 isoforms (binding to the migration surface and to CXCR4) significantly impact migration and explain differences in in vitro chemotaxis data. We extend our model to analyze CXCL12 gradient formation in a tumor environment and find that short distance, steep gradients characteristic of the CXCL12-γ isoform are effective at driving chemotaxis. We highlight the importance of CXCL12-γ in cancer cell migration: its high effective affinity for both extracellular surface sites and CXCR4 strongly promote CXCR4+ cell migration. CXCL12-γ is also more difficult to inhibit, and we predict that co-inhibition of CXCR4 and CXCR7 is necessary to effectively hinder CXCL12-γ-induced migration. These findings support the growing importance of understanding differences in protein isoforms, and in particular their implications for cancer treatment.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.

On the coupling of two models of the human immune response to an antigen

The development of mathematical models of the immune response allows a better understanding of the multifaceted mechanisms of the defense system. The main purpose of this work is to present a scheme for coupling distinct models of different scales and aspects of the immune system. As an example, we propose a new model where the local tissue inflammation processes are simulated with partial differential equations (PDEs) whereas a system of ordinary differential equations (ODEs) is used as a model for the systemic response. The simulation of distinct scenarios allows the analysis of the dynamics of various immune cells in the presence of an antigen. Preliminary results of this approach with a sensitivity analysis of the coupled model are shown but further validation is still required.

Travelling waves in hybrid chemotaxis models

Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations.

Multi-scale modeling predicts a balance of tumor necrosis factor-α and interleukin-10 controls the granuloma environment during Mycobacterium tuberculosis infection

Interleukin-10 (IL-10) and tumor necrosis factor-α (TNF-α) are key anti- and pro-inflammatory mediators elicited during the host immune response to Mycobacterium tuberculosis (Mtb). Understanding the opposing effects of these mediators is difficult due to the complexity of processes acting across different spatial (molecular, cellular, and tissue) and temporal (seconds to years) scales. We take an in silico approach and use multi-scale agent based modeling of the immune response to Mtb, including molecular scale details for both TNF-α and IL-10. Our model predicts that IL-10 is necessary to modulate macrophage activation levels and to prevent host-induced tissue damage in a granuloma, an aggregate of cells that forms in response to Mtb. We show that TNF-α and IL-10 parameters related to synthesis, signaling, and spatial distribution processes control concentrations of TNF-α and IL-10 in a granuloma and determine infection outcome in the long-term. We devise an overall measure of granuloma function based on three metrics - total bacterial load, macrophage activation levels, and apoptosis of resting macrophages - and use this metric to demonstrate a balance of TNF-α and IL-10 concentrations is essential to Mtb infection control, within a single granuloma, with minimal host-induced tissue damage. Our findings suggest that a balance of TNF-α and IL-10 defines a granuloma environment that may be beneficial for both host and pathogen, but perturbing the balance could be used as a novel therapeutic strategy to modulate infection outcomes.

Hybrid equation/agent-based model of ischemia-induced hyperemia and pressure ulcer formation predicts greater propensity to ulcerate in subjects with spinal cord injury

Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM) are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE) models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation.

Agent-based models of cellular systems

Software agents are particularly suitable for engineering models and simulations of cellular systems. In a very natural and intuitive manner, individual software components are therein delegated to reproduce "in silico" the behavior of individual components of alive systems at a given level of resolution. Individuals' actions and interactions among individuals allow complex collective behavior to emerge. In this chapter we first introduce the readers to software agents and multi-agent systems, reviewing the evolution of agent-based modeling of biomolecular systems in the last decade. We then describe the main tools, platforms, and methodologies available for programming societies of agents, possibly profiting also of toolkits that do not require advanced programming skills.

Systems biology of fungal infection

Elucidation of pathogenicity mechanisms of the most important human-pathogenic fungi, Aspergillus fumigatus and Candida albicans, has gained great interest in the light of the steadily increasing number of cases of invasive fungal infections. A key feature of these infections is the interaction of the different fungal morphotypes with epithelial and immune effector cells in the human host. Because of the high level of complexity, it is necessary to describe and understand invasive fungal infection by taking a systems biological approach, i.e., by a comprehensive quantitative analysis of the non-linear and selective interactions of a large number of functionally diverse, and frequently multifunctional, sets of elements, e.g., genes, proteins, metabolites, which produce coherent and emergent behaviors in time and space. The recent advances in systems biology will now make it possible to uncover the structure and dynamics of molecular and cellular cause-effect relationships within these pathogenic interactions. We review current efforts to integrate omics and image-based data of host-pathogen interactions into network and spatio-temporal models. The modeling will help to elucidate pathogenicity mechanisms and to identify diagnostic biomarkers and potential drug targets for therapy and could thus pave the way for novel intervention strategies based on novel antifungal drugs and cell therapy.

ImmunoGrid: towards agent-based simulations of the human immune system at a natural scale

The ultimate aim of the EU-funded ImmunoGrid project is to develop a natural-scale model of the human immune system-that is, one that reflects both the diversity and the relative proportions of the molecules and cells that comprise it-together with the grid infrastructure necessary to apply this model to specific applications in the field of immunology. These objectives present the ImmunoGrid Consortium with formidable challenges in terms of complexity of the immune system, our partial understanding about how the immune system works, the lack of reliable data and the scale of computational resources required. In this paper, we explain the key challenges and the approaches adopted to overcome them. We also consider wider implications for the present ambitious plans to develop natural-scale, integrated models of the human body that can make contributions to personalized health care, such as the European Virtual Physiological Human initiative. Finally, we ask a key question: How long will it take us to resolve these challenges and when can we expect to have fully functional models that will deliver health-care benefits in the form of personalized care solutions and improved disease prevention?

Multi-scale modelling in computational biomedicine

The inherent complexity of biomedical systems is well recognized; they are multi-scale, multi-science systems, bridging a wide range of temporal and spatial scales. This article reviews the currently emerging field of multi-scale modelling in computational biomedicine. Many exciting multi-scale models exist or are under development. However, an underpinning multi-scale modelling methodology seems to be missing. We propose a direction that complements the classic dynamical systems approach and introduce two distinct case studies, transmission of resistance in human immunodeficiency virus spreading and in-stent restenosis in coronary artery disease.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.