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

Agent-based modeling of cellular dynamics in adoptive cell therapy

Adoptive cell therapies (ACT) leverage tumor-immune interactions to cure cancer. Despite promising phase I/II clinical trials of chimeric-antigen-receptor natural killer (CAR-NK) cell therapies, molecular mechanisms and cellular properties required to achieve clinical benefits in broad cancer spectra remain underexplored. While in vitro and in vivo experiments are required in this endeavor, they are typically expensive, laborious, and limited to targeted investigations. Here, we present ABMACT (Agent-Based Model for Adoptive Cell Therapy), an in silico approach employing agent-based models (ABM) to simulate the continuous course and dynamics of an evolving tumor-immune ecosystem, consisting of heterogeneous "virtual cells" created based on knowledge and omics data observed in experiments and patients. Applying ABMACT in multiple therapeutic context indicates that to achieve optimal ACT efficacy, it is key to enhance immune cellular proliferation, cytotoxicity, and serial killing capacity. With ABMACT, in silico trials can be performed systematically to inform ACT product development and predict optimal treatment strategies.

A brief overview of mathematical modeling of the within-host dynamics of Mycobacterium tuberculosis

Tuberculosis (TB), a disease caused by bacteria Mycobacterium tuberculosis (Mtb), remains one of the major infectious diseases of humans with 10 million TB cases and 1.5 million deaths due to TB worldwide yearly. Upon exposure of a new host to Mtb, bacteria typically infect one local site in the lung, but over time, Mtb disseminates in the lung and in some cases to extrapulmonary sites. The contribution of various host components such as immune cells to Mtb dynamics in the lung, its dissemination in the lung and outside of the lung, remains incompletely understood. Here we overview different types of mathematical models used to gain insights in within-host dynamics of Mtb; these include models based on ordinary or partial differential equations (ODEs and PDEs), stochastic simulation models based on ODEs, agent-based models (ABMs), and hybrid models (ODE-based models linked to ABMs). We illustrate results from several of such models and identify areas for future resesarch.

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.

Designing combination therapies using multiple optimal controls

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

Spatio-temporal dynamics of Host-Virus competition: A model study of influenza A

We present results of a study of the early-time response of the innate immune system to influenza virus infection in an agent-based model (ABM) of epithelial cell layers. We find that the competition between the anti-viral immune response and viral antagonism can lead to viral titers non-monotonic in the initial infection fraction as found in experiments. Our model includes a coarse-grained version of intra-cellular processes and inter-cellular communication via cytokine and virion diffusion. We use ABM to follow the propagation of viral infection in the layer and the increase of the viral load as a function of time for different values of the multiplicity of infection (MOI), the initial number of viruses added per cell. We find that for moderately strong host immune response, the number of infected cells and viral load for a smaller MOI exceeds that for larger MOI, as seen in experiments. We elucidate the mechanism underlying this result as the synergistic action of cytokines secreted by infected cells in controlling viral amplification for larger MOI. We investigate the length and time scales that determine this non-monotonic behavior within the ABM. We study the diffusive spread of virions and cytokines from a single infected cell in an absorbing medium analytically and numerically and deduce the length scale that yields a good estimate of the MOI at which we find non-monotonicity. Detailed computations of the temporal behavior of averaged quantities and spatial measures provide further insights into host-viral interactions and connections to experimental observations.

Optimal control of acute myeloid leukaemia

Acute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

Microbiota and Dose Response: Evolving Paradigm of Health Triangle

SRA Dose-Response and Microbial Risk Analysis Specialty Groups jointly sponsored symposia that addressed the intersections between the "microbiome revolution" and dose response. Invited speakers presented on innovations and advances in gut and nasal microbiota (normal microbial communities) in the first decade after the Human Microbiome Project began. The microbiota and their metabolites are now known to influence health and disease directly and indirectly, through modulation of innate and adaptive immune systems and barrier function. Disruption of healthy microbiota is often associated with changes in abundance and diversity of core microbial species (dysbiosis), caused by stressors including antibiotics, chemotherapy, and disease. Nucleic-acid-based metagenomic methods demonstrated that the dysbiotic host microbiota no longer provide normal colonization resistance to pathogens, a critical component of innate immunity of the superorganism. Diverse pathogens, probiotics, and prebiotics were considered in human and animal models (in vivo and in vitro). Discussion included approaches for design of future microbial dose-response studies to account for the presence of the indigenous microbiota that provide normal colonization resistance, and the absence of the protective microbiota in dysbiosis. As NextGen risk analysis methodology advances with the "microbiome revolution," a proposed new framework, the Health Triangle, may replace the old paradigm based on the Disease Triangle (focused on host, pathogen, and environment) and germophobia. Collaborative experimental designs are needed for testing hypotheses about causality in dose-response relationships for pathogens present in our environments that clearly compete in complex ecosystems with thousands of bacterial species dominating the healthy superorganism.

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.

A mathematical model for a T cell fate decision algorithm during immune response

We formulate and analyze an algorithm of cell fate decision that describes the way in which division vs. apoptosis choices are made by individual T cells during an infection. Such model involves a minimal number of known biochemical mechanisms: it basically relies on the interplay between cell division and cell death inhibitors on one hand, and membrane receptors on the other. In spite of its simplicity, the proposed decision algorithm is able to account for some significant facts in immune response. At the individual level, the existence of T cells that continue to replicate in the absence of antigen and the possible occurrence of T cell apoptosis in the presence of antigen are predicted by the model. Moreover, the latter is shown to yield an emergent collective behavior, the observed delay in clonal contraction with respect to the end of antigen stimulation, which is shown to arise just from individual T cell decisions made according to the proposed mechanism.

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.

A quantitative model of transcriptional differentiation driving host-pathogen interactions

Despite our expanding knowledge about the biochemistry of gene regulation involved in host-pathogen interactions, a quantitative understanding of this process at a transcriptional level is still limited. We devise and assess a computational framework that can address this question. This framework is founded on a mixture model-based likelihood, equipped with functionality to cluster genes per dynamic and functional changes of gene expression within an interconnected system composed of the host and pathogen. If genes from the host and pathogen are clustered in the same group due to a similar pattern of dynamic profiles, they are likely to be reciprocally co-evolving. If genes from the two organisms are clustered in different groups, this means that they experience strong host-pathogen interactions. The framework can test the rates of change for individual gene clusters during pathogenic infection and quantify their impacts on host-pathogen interactions. The framework was validated by a pathological study of poplar leaves infected by fungal Marssonina brunnea in which co-evolving and interactive genes that determine poplar-fungus interactions are identified. The new framework should find its wide application to studying host-pathogen interactions for any other interconnected systems.

Computational modelling of maternal interactions with spermatozoa: potentials and prospects

Understanding the complex interactions between gametes, embryos and the maternal tract is required knowledge for combating infertility and developing new methods of contraception. Here we present some main aspects of spermatozoa interactions with the mammalian oviduct before fertilisation and discuss how computational modelling can be used as an invaluable aid to experimental investigation in this field. A complete predictive computational model of gamete and embryo interactions with the female reproductive tract is a long way off. However, the enormity of this task should not discourage us from working towards it. Computational modelling allows us to investigate aspects of maternal communication with gametes and embryos, which are financially, ethically or practically difficult to look at experimentally. In silico models of maternal communication with gametes and embryos can be used as tools to complement in vivo experiments, in the same way as in vitro and in situ models.

A state-time epidemiology model of tuberculosis: importance of re-infection

An epidemiological model is presented that considers five possible states of a population: susceptible (S), exposed (W), infectious (Y), in treatment (Z) and recovered (R). In certain instances transition rates (from one state to another) depend on the time spent in the state; therefore the states W, Y and Z depend on time and length of stay in that state - similar to age-structured models. The model is particularly amenable to describe delays of exposed persons to become infectious and re-infection of exposed persons. Other transitions that depend on state time include the case finding and diagnosis, increased death rate and treatment interruption. The mathematical model comprises of a set of partial differential and ordinary differential equations. Non-steady state solutions are first presented, followed by a bifurcation study of the stationary states.

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.

Rule-based modelling of iron homeostasis in tuberculosis

To establish itself within the host system, Mycobacterium tuberculosis (Mtb) has formulated various means of attacking the host system. One such crucial strategy is the exploitation of the iron resources of the host system. Obtaining and maintaining the required concentration of iron becomes a matter of contest between the host and the pathogen, both trying to achieve this through complex molecular networks. The extent of complexity makes it important to obtain a systems perspective of the interplay between the host and the pathogen with respect to iron homeostasis. We have reconstructed a systems model comprising 92 components and 85 protein-protein or protein-metabolite interactions, which have been captured as a set of 194 rules. Apart from the interactions, these rules also account for protein synthesis and decay, RBC circulation and bacterial production and death rates. We have used a rule-based modelling approach, Kappa, to simulate the system separately under infection and non-infection conditions. Various perturbations including knock-outs and dual perturbation were also carried out to monitor the behavioral change of important proteins and metabolites. From this, key components as well as the required controlling factors in the model that are critical for maintaining iron homeostasis were identified. The model is able to re-establish the importance of iron-dependent regulator (ideR) in Mtb and transferrin (Tf) in the host. Perturbations, where iron storage is increased, appear to enhance nutritional immunity and the analysis indicates how they can be harmful for the host. Instead, decreasing the rate of iron uptake by Tf may prove to be helpful. Simulation and perturbation studies help in identifying Tf as a possible drug target. Regulating the mycobactin (myB) concentration was also identified as a possible strategy to control bacterial growth. The simulations thus provide significant insight into iron homeostasis and also for identifying possible drug targets for tuberculosis.

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.

A systems biology perspective on plant-microbe interactions: biochemical and structural targets of pathogen effectors

Plants have biochemical defences against stresses from predators, parasites and pathogens. In this review we discuss the interaction of plant defences with microbial pathogens such as bacteria, fungi and oomycetes, and viruses. We examine principles of complex dynamic networks that allow identification of network components that are differentially and predictably sensitive to perturbation, thus making them likely effector targets. We relate these principles to recent developments in our understanding of known effector targets in plant-pathogen systems, and propose a systems-level framework for the interpretation and modelling of host-microbe interactions mediated by effectors. We describe this framework briefly, and conclude by discussing useful experimental approaches for populating this framework.

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.