Mathematical and computational approaches can complement experimental studies of host-pathogen interactions

Transcriptional differentiation driving Cucumis sativus-Botrytis cinerea interactions based on the Skellam model and Bayesian networks

Robust statistical tools such as the Skellam model and Bayesian networks can capture the count properties of transcriptome sequencing data and clusters of genes among treatments, thereby improving our knowledge of gene functions and networks. In this study, we successfully implemented a model to analyze a transcriptome dataset of Cucumis sativus and Botrytis cinerea before and after their interaction. First, 4200 differentially expressed genes (DEGs) from C. sativus were clustered into 17 distinct groups, and 670 DEGs from B. cinerea were clustered into 12 groups. Gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses were applied on these DEGs to assess the interactions between C. sativus and B. cinerea. In C. sativus, more DEGs were divided into terms in the molecular function and biological process domains than into cellular components, and 277 DEGs were allocated to 19 KEGG pathways. In B. cinerea, more DEGs were divided into terms in the biological process and cellular component domains than into molecular functions, and 150 DEGs were allocated to 26 KEGG pathways. In this study, we constructed networks of genes that interact with each other to screen hub genes based on a directed graphical model known as Bayesian networks. Through a detailed GO analysis, we excavated hub genes which were biologically meaningful. These results verify that availability of Skellam model and Bayesian networks in clustering gene expression data and sorting out hub genes. These models are instrumental in increasing our knowledge of gene functions and networks in plant–pathogen interaction.

Heterogeneity in tuberculosis

Infection with Mycobacterium tuberculosis, the causative agent of tuberculosis (TB), results in a range of clinical presentations in humans. Most infections manifest as a clinically asymptomatic, contained state that is termed latent TB infection (LTBI); a smaller subset of infected individuals present with symptomatic, active TB. Within these two seemingly binary states, there is a spectrum of host outcomes that have varying symptoms, microbiologies, immune responses and pathologies. Recently, it has become apparent that there is diversity of infection even within a single individual. A good understanding of the heterogeneity that is intrinsic to TB - at both the population level and the individual level - is crucial to inform the development of intervention strategies that account for and target the unique, complex and independent nature of the local host-pathogen interactions that occur in this infection. In this Review, we draw on model systems and human data to discuss multiple facets of TB biology and their relationship to the overall heterogeneity observed in the human disease.

Modeling Rabbit Responses to Single and Multiple Aerosol Exposures of Bacillus anthracis Spores

Survival models are developed to predict response and time-to-response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple-dose data set to predict the probability of death through specifying functions of dose response and the time between exposure and the time-to-death (TTD). Among the models developed, the best-fitting survival model (baseline model) is an exponential dose-response model with a Weibull TTD distribution. Alternative models assessed use different underlying dose-response functions and use the assumption that, in a multiple-dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this article. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high-dose rabbit data sets. More accurate survival models depend upon future development of dose-response data sets specifically designed to assess potential multiple-dose effects on response and time-to-response. The process used in this article to develop the best-fitting survival model for exposure of rabbits to multiple aerosol doses of B. anthracis spores should have broad applicability to other host-pathogen systems and dosing schedules because the empirical modeling approach is based upon pathogen-specific empirically-derived parameters.

Modeling Lymph Flow and Fluid Exchange with Blood Vessels in Lymph Nodes

BACKGROUND

Lymph nodes (LNs) are positioned strategically throughout the body as critical mediators of lymph filtration and immune response. Lymph carries cytokines, antigens, and cells to the downstream LNs, and their effective delivery to the correct location within the LN directly impacts the quality and quantity of immune response. Despite the importance of this system, the flow patterns in LN have never been quantified, in part because experimental characterization is so difficult.

METHODS AND RESULTS

To achieve a more quantitative knowledge of LN flow, a computational flow model has been developed based on the mouse popliteal LN, allowing for a parameter sensitivity analysis to identify the important system characteristics. This model suggests that about 90% of the lymph takes a peripheral path via the subcapsular and medullary sinuses, while fluid perfusing deeper into the paracortex is sequestered by parenchymal blood vessels. Fluid absorption by these blood vessels under baseline conditions was driven mainly by oncotic pressure differences between lymph and blood, although the magnitude of fluid transfer is highly dependent on blood vessel surface area. We also predict that the hydraulic conductivity of the medulla, a parameter that has never been experimentally measured, should be at least three orders of magnitude larger than that of the paracortex to ensure physiologic pressures across the node.

CONCLUSIONS

These results suggest that structural changes in the LN microenvironment, as well as changes in inflow/outflow conditions, dramatically alter the distribution of lymph, cytokines, antigens, and cells within the LN, with great potential for modulating immune response.

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

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

Computational Identification of Mechanistic Factors That Determine the Timing and Intensity of the Inflammatory Response

Timely resolution of inflammation is critical for the restoration of homeostasis in injured or infected tissue. Chronic inflammation is often characterized by a persistent increase in the concentrations of inflammatory cells and molecular mediators, whose distinct amount and timing characteristics offer an opportunity to identify effective therapeutic regulatory targets. Here, we used our recently developed computational model of local inflammation to identify potential targets for molecular interventions and to investigate the effects of individual and combined inhibition of such targets. This was accomplished via the development and application of computational strategies involving the simulation and analysis of thousands of inflammatory scenarios. We found that modulation of macrophage influx and efflux is an effective potential strategy to regulate the amount of inflammatory cells and molecular mediators in both normal and chronic inflammatory scenarios. We identified three molecular mediators − tumor necrosis factor-α (TNF-α), transforming growth factor-β (TGF-β), and the chemokine CXCL8 − as potential molecular targets whose individual or combined inhibition may robustly regulate both the amount and timing properties of the kinetic trajectories for neutrophils and macrophages in chronic inflammation. Modulation of macrophage flux, as well as of the abundance of TNF-α, TGF-β, and CXCL8, may improve the resolution of chronic inflammation.

A recent approach to quantitatively characterize the timing and intensity of the inflammatory response relies on the use of four quantities termed inflammation indices. The values of the inflammation indices may reflect the differences between normal and pathological inflammation, and may be used to gauge the effects of therapeutic interventions aimed to control inflammation. Yet, the specific inflammatory mechanisms that can be targeted to selectively control these indices remain unknown. Here, we developed and applied a computational strategy to identify potential target mechanisms to regulate such indices. We used our recently developed model of local inflammation to simulate thousands of inflammatory scenarios. We then subjected the corresponding inflammation index values to sensitivity and correlation analysis. We found that the inflammation indices may be significantly influenced by the macrophage influx and efflux rates, as well as by the degradation rates of three specific molecular mediators. These results suggested that the indices can be effectively regulated by individual or combined inhibition of those molecular mediators, which we confirmed by computational experiments. Taken together, our results highlight possible targets of therapeutic intervention that can be used to control both the timing and the intensity of the inflammatory response.

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

The long subclinical phase of Mycobacterium avium ssp. paratuberculosis infections explained without adaptive immunity

Mycobacterium avium ssp. paratuberculosis (MAP) is an infection of the ruminant intestine. In cows, a long subclinical phase with no or low intermittent shedding precedes the clinical phase with high shedding. It is generally considered that an adaptive cell-mediated immune response controls the infection during the subclinical phase, followed by unprotective antibodies later in life. Based on recent observations, we challenge the importance of adaptive immunity and instead suggest a role of the structural organization of infected macrophages in localized granulomatous lesions. We investigated this hypothesis by mathematical modelling. Our first model describes infection in a villus, assuming a constant lesion volume. This model shows the existence of two threshold parameters, the MAP reproduction ratio R_MAP determining if a lesion can develop, and the macrophage replacement ratio R_MF determining if recruitment of macrophages is sufficient for unlimited growth. We show that changes in R_MF during a cow’s life – i.e. changes in the innate immune response – can cause intermittent shedding. Our second model describes infection in a granuloma, assuming a growing lesion volume. This model confirms the results of the villus model, and can explain early slow granuloma development: small granulomas grow slower because bacteria leave the granuloma quickly through the relatively large surface area. In conclusion, our models show that the long subclinical period of MAP infection can result from the structural organization of the infection in granulomatous lesions with an important role for innate rather than adaptive immunity. It thus provides a reasonable hypothesis that needs further investigation.

Mining large-scale response networks reveals 'topmost activities' in Mycobacterium tuberculosis infection

Mycobacterium tuberculosis owes its high pathogenic potential to its ability to evade host immune responses and thrive inside the macrophage. The outcome of infection is largely determined by the cellular response comprising a multitude of molecular events. The complexity and inter-relatedness in the processes makes it essential to adopt systems approaches to study them. In this work, we construct a comprehensive network of infection-related processes in a human macrophage comprising 1888 proteins and 14,016 interactions. We then compute response networks based on available gene expression profiles corresponding to states of health, disease and drug treatment. We use a novel formulation for mining response networks that has led to identifying highest activities in the cell. Highest activity paths provide mechanistic insights into pathogenesis and response to treatment. The approach used here serves as a generic framework for mining dynamic changes in genome-scale protein interaction networks.

Harnessing the heterogeneity of T cell differentiation fate to fine-tune generation of effector and memory T cells

Recent studies show that naïve T cells bearing identical T cell receptors experience heterogeneous differentiation and clonal expansion processes. The factors controlling this outcome are not well characterized, and their contributions to immune cell dynamics are similarly poorly understood. In this study, we develop a computational model to elaborate mechanisms occurring within and between two important physiological compartments, lymph nodes and blood, to determine how immune cell dynamics are controlled. Our multi-organ (multi-compartment) model integrates cellular and tissue level events and allows us to examine the heterogeneous differentiation of individual precursor cognate naïve T cells to generate both effector and memory T lymphocytes. Using this model, we simulate a hypothetical immune response and reproduce both primary and recall responses to infection. Increased numbers of antigen-bearing dendritic cells (DCs) are predicted to raise production of both effector and memory T cells, and distinct “sweet spots” of peptide-MHC levels on those DCs exist that favor CD4+ or CD8+ T cell differentiation toward either effector or memory cell phenotypes. This has important implications for vaccine development and immunotherapy.

Latent Tuberculosis: Models, Computational Efforts and the Pathogen's Regulatory Mechanisms during Dormancy

Latent tuberculosis is a clinical syndrome that occurs after an individual has been exposed to the Mycobacterium tuberculosis (Mtb) Bacillus, the infection has been established and an immune response has been generated to control the pathogen and force it into a quiescent state. Mtb can exit this quiescent state where it is unresponsive to treatment and elusive to the immune response, and enter a rapid replicating state, hence causing infection reactivation. It remains a gray area to understand how the pathogen causes a persistent infection and it is unclear whether the organism will be in a slow replicating state or a dormant non-replicating state. The ability of the pathogen to adapt to changing host immune response mechanisms, in which it is exposed to hypoxia, low pH, nitric oxide (NO), nutrient starvation, and several other anti-microbial effectors, is associated with a high metabolic plasticity that enables it to metabolize under these different conditions. Adaptive gene regulatory mechanisms are thought to coordinate how the pathogen changes their metabolic pathways through mechanisms that sense changes in oxygen tension and other stress factors, hence stimulating the pathogen to make necessary adjustments to ensure survival. Here, we review studies that give insights into latency/dormancy regulatory mechanisms that enable infection persistence and pathogen adaptation to different stress conditions. We highlight what mathematical and computational models can do and what they should do to enhance our current understanding of TB latency.

Spartan: a comprehensive tool for understanding uncertainty in simulations of biological systems

Integrating computer simulation with conventional wet-lab research has proven to have much potential in furthering the understanding of biological systems. Success requires the relationship between simulation and the real-world system to be established: substantial aspects of the biological system are typically unknown, and the abstract nature of simulation can complicate interpretation of in silico results in terms of the biology. Here we present spartan (Simulation Parameter Analysis RToolkit ApplicatioN), a package of statistical techniques specifically designed to help researchers understand this relationship and provide novel biological insight. The tools comprising spartan help identify which simulation results can be attributed to the dynamics of the modelled biological system, rather than artefacts of biological uncertainty or parametrisation, or simulation stochasticity. Statistical analyses reveal the influence that pathways and components have on simulation behaviour, offering valuable biological insight into aspects of the system under study. We demonstrate the power of spartan in providing critical insight into aspects of lymphoid tissue development in the small intestine through simulation. Spartan is released under a GPLv2 license, implemented within the open source R statistical environment, and freely available from both the Comprehensive R Archive Network (CRAN) and http://www.cs.york.ac.uk/spartan. The techniques within the package can be applied to traditional ordinary or partial differential equation simulations as well as agent-based implementations. Manuals, comprehensive tutorials, and example simulation data upon which spartan can be applied are available from the website.

Intracellular bacillary burden reflects a burst size for Mycobacterium tuberculosis in vivo

We previously reported that Mycobacterium tuberculosis triggers macrophage necrosis in vitro at a threshold intracellular load of ∼25 bacilli. This suggests a model for tuberculosis where bacilli invading lung macrophages at low multiplicity of infection proliferate to burst size and spread to naïve phagocytes for repeated cycles of replication and cytolysis. The current study evaluated that model in vivo, an environment significantly more complex than in vitro culture. In the lungs of mice infected with M. tuberculosis by aerosol we observed three distinct mononuclear leukocyte populations (CD11b⁻ CD11c^+/hi, CD11b^+/lo CD11c^lo/−, CD11b^+/hi CD11c^+/hi) and neutrophils hosting bacilli. Four weeks after aerosol challenge, CD11b^+/hi CD11c^+/hi mononuclear cells and neutrophils were the predominant hosts for M. tuberculosis while CD11b^+/lo CD11c^lo/− cells assumed that role by ten weeks. Alveolar macrophages (CD11b⁻ CD11c^+/hi) were a minority infected cell type at both time points. The burst size model predicts that individual lung phagocytes would harbor a range of bacillary loads with most containing few bacilli, a smaller proportion containing many bacilli, and few or none exceeding a burst size load. Bacterial load per cell was enumerated in lung monocytic cells and neutrophils at time points after aerosol challenge of wild type and interferon-γ null mice. The resulting data fulfilled those predictions, suggesting a median in vivo burst size in the range of 20 to 40 bacilli for monocytic cells. Most heavily burdened monocytic cells were nonviable, with morphological features similar to those observed after high multiplicity challenge in vitro: nuclear condensation without fragmentation and disintegration of cell membranes without apoptotic vesicle formation. Neutrophils had a narrow range and lower peak bacillary burden than monocytic cells and some exhibited cell death with release of extracellular neutrophil traps. Our studies suggest that burst size cytolysis is a major cause of infection-induced mononuclear cell death in tuberculosis.

Macrophages patrol the lung to ingest and destroy inhaled microbes. Mycobacterium tuberculosis, the bacteria causing tuberculosis, can survive within macrophages and use them as a protected environment for growth. Macrophages by themselves are poorly equipped to kill M. tuberculosis but may undergo programmed cell death (apoptosis) to limit bacterial replication. Virulent M. tuberculosis has evolved the capacity to inhibit macrophage apoptosis, thereby protecting the replication niche. In previous studies we showed that upon reaching a threshold intracellular number (burst size), virulent M. tuberculosis kills macrophages by necrosis and escapes for spreading infection. The present study was designed to test whether this mechanism seen in vitro operates during pulmonary tuberculosis in vivo. The distribution of M. tuberculosis numbers inside lung phagocytes of mice with tuberculosis conformed to predictions based on the burst size hypothesis, as did the appearance of dying cells. We identified four different types of phagocytes hosting intracellular M. tuberculosis. The distribution of M. tuberculosis load within individual phagocytes and between different types of phagocyte changed over the course of tuberculosis disease. These studies reveal the complexity of host defense in tuberculosis that must be considered as new therapies are sought.

Tracing personalized health curves during infections

By concentrating on the relationship between health and microbe number over the course of infections, most pathogenic and mutualistic infections can be summarized by a small alphabet of curves, which has implications not only for basic research but for how we might treat patients.

It is difficult to describe host–microbe interactions in a manner that deals well with both pathogens and mutualists. Perhaps a way can be found using an ecological definition of tolerance, where tolerance is defined as the dose response curve of health versus parasite load. To plot tolerance, individual infections are summarized by reporting the maximum parasite load and the minimum health for a population of infected individuals and the slope of the resulting curve defines the tolerance of the population. We can borrow this method of plotting health versus microbe load in a population and make it apply to individuals; instead of plotting just one point that summarizes an infection in an individual, we can plot the values at many time points over the course of an infection for one individual. This produces curves that trace the course of an infection through phase space rather than over a more typical timeline. These curves highlight relationships like recovery and point out bifurcations that are difficult to visualize with standard plotting techniques. Only nine archetypical curves are needed to describe most pathogenic and mutualistic host–microbe interactions. The technique holds promise as both a qualitative and quantitative approach to dissect host–microbe interactions of all kinds.

Systems biology approaches for understanding cellular mechanisms of immunity in lymph nodes during infection

Adaptive immunity is initiated in secondary lymphoid tissues when naive T cells recognize foreign antigen presented as MHC-bound peptide on the surface of dendritic cells. Only a small fraction of T cells in the naive repertoire will express T cell receptors specific for a given epitope, but antigen recognition triggers T cell activation and proliferation, thus greatly expanding antigen-specific clones. Expanded T cells can serve a helper function for B cell responses or traffic to sites of infection to secrete cytokines or kill infected cells. Over the past decade, two-photon microscopy of lymphoid tissues has shed important light on T cell development, antigen recognition, cell trafficking and effector functions. These data have enabled the development of sophisticated quantitative and computational models that, in turn, have been used to test hypotheses in silico that would otherwise be impossible or difficult to explore experimentally. Here, we review these models and their principal findings and highlight remaining questions where modeling approaches are poised to advance our understanding of complex immunological systems.

Dynamic models of immune responses: what is the ideal level of detail?

Background

One of the goals of computational immunology is to facilitate the study of infectious diseases. Dynamic modeling is a powerful tool to integrate empirical data from independent sources, make novel predictions, and to foresee the gaps in the current knowledge. Dynamic models constructed to study the interactions between pathogens and hosts' immune responses have revealed key regulatory processes in the infection.

Optimum complexity and dynamic modeling

We discuss the usability of various deterministic dynamic modeling approaches to study the progression of infectious diseases. The complexity of these models is dependent on the number of components and the temporal resolution in the model. We comment on the specific use of simple and complex models in the study of the progression of infectious diseases.

Conclusions

Models of sub-systems or simplified immune response can be used to hypothesize phenomena of host-pathogen interactions and to estimate rates and parameters. Nevertheless, to study the pathogenesis of an infection we need to develop models describing the dynamics of the immune components involved in the progression of the disease. Incorporation of the large number and variety of immune processes involved in pathogenesis requires tradeoffs in modeling.

A systems immunology approach to plasmacytoid dendritic cell function in cytopathic virus infections

Plasmacytoid dendritic cell (pDC)-mediated protection against cytopathic virus infection involves various molecular, cellular, tissue-scale, and organism-scale events. In order to better understand such multiscale interactions, we have implemented a systems immunology approach focusing on the analysis of the structure, dynamics and operating principles of virus-host interactions which constrain the initial spread of the pathogen. Using high-resolution experimental data sets coming from the well-described mouse hepatitis virus (MHV) model, we first calibrated basic modules including MHV infection of its primary target cells, i.e. pDCs and macrophages (Mphis). These basic building blocks were used to generate and validate an integrative mathematical model for in vivo infection dynamics. Parameter estimation for the system indicated that on a per capita basis, one infected pDC secretes sufficient type I IFN to protect 10(3) to 10(4) Mphis from cytopathic viral infection. This extremely high protective capacity of pDCs secures the spleen's capability to function as a 'sink' for the virus produced in peripheral organs such as the liver. Furthermore, our results suggest that the pDC population in spleen ensures a robust protection against virus variants which substantially down-modulate IFN secretion. However, the ability of pDCs to protect against severe disease caused by virus variants exhibiting an enhanced liver tropism and higher replication rates appears to be rather limited. Taken together, this systems immunology analysis suggests that antiviral therapy against cytopathic viruses should primarily limit viral replication within peripheral target organs.

Tuberculosis: global approaches to a global disease

Mycobacterium tuberculosis is a remarkably successful human pathogen. The interaction with the human host is complex and much remains unknown. Recent advances in systems biology have allowed the integration of data from humans and animal models into computational approaches. For example, mathematical models provide a platform for in silico manipulation of host-pathogen interactions to gain insight into this infection across temporal and biologic scales. Here, we review recent studies on global approaches toward identifying comprehensive responses of both host and bacillus during infection, and the potential for incorporation of these data into many types of useful computational systems. Systems biology approaches provide a unique opportunity to study interventions that may improve therapy and vaccines against this major killer.

Tuberculosis research: going forward with a powerful "translational systems biology" approach

Due to the complexity of the immune response to a Mycobacterium tuberculosis infection, identifying new, effective therapies and vaccines to combat it has been a problematic issue. Although many advances have been made in understanding particular mechanisms involved, they have, to date, proved insufficient to provide real breakthroughs in this area of tuberculosis research. The term "Translational Systems Biology" has been formally proposed to describe the use of experimental findings combined with mathematical modeling and/or engineering principles to understand complex biological processes in an integrative fashion for the purpose of enhancing clinical practice. This opinion piece discusses the importance of using a Translational Systems Biology approach for tuberculosis research as a means by which to go forward with the potential for significant breakthroughs to occur.