The human immune response to Mycobacterium tuberculosis in lung and lymph node

Mathematical model of MMC chemotherapy for non-invasive bladder cancer treatment

Mitomycin-C (MMC) chemotherapy is a well-established anti-cancer treatment for non-muscle-invasive bladder cancer (NMIBC). However, despite comprehensive biological research, the complete mechanism of action and an ideal regimen of MMC have not been elucidated. In this study, we present a theoretical investigation of NMIBC growth and its treatment by continuous administration of MMC chemotherapy. Using temporal ordinary differential equations (ODEs) to describe cell populations and drug molecules, we formulated the first mathematical model of tumor-immune interactions in the treatment of MMC for NMIBC, based on biological sources. Several hypothetical scenarios for NMIBC under the assumption that tumor size correlates with cell count are presented, depicting the evolution of tumors classified as small, medium, and large. These scenarios align qualitatively with clinical observations of lower recurrence rates for tumor size ≤ 30[mm] with MMC treatment, demonstrating that cure appears up to a theoretical x[mm] tumor size threshold, given specific parameters within a feasible biological range. The unique use of mole units allows to introduce a new method for theoretical pre-treatment assessments by determining MMC drug doses required for a cure. In this way, our approach provides initial steps toward personalized MMC chemotherapy for NMIBC patients, offering the possibility of new insights and potentially holding the key to unlocking some of its mysteries.

Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations

Although infectious disease dynamics are often analyzed at the macro-scale, increasing numbers of drug-resistant infections highlight the importance of within-host modeling that simultaneously solves across multiple scales to effectively respond to epidemics. We review multiscale modeling approaches for complex, interconnected biological systems and discuss critical steps involved in building, analyzing, and applying such models within the discipline of model credibility. We also present our two tools: CaliPro, for calibrating multiscale models (MSMs) to datasets, and tunable resolution, for fine- and coarse-graining sub-models while retaining insights. We include as an example our work simulating infection with Mycobacterium tuberculosis to demonstrate modeling choices and how predictions are made to generate new insights and test interventions. We discuss some of the current challenges of incorporating novel datasets, rigorously training computational biologists, and increasing the reach of MSMs. We also offer several promising future research directions of incorporating within-host dynamics into applications ranging from combinatorial treatment to epidemic response.

Quantitative Systems Pharmacology Modeling Framework of Autophagy in Tuberculosis: Application to Adjunctive Metformin Host-Directed Therapy

Quantitative systems pharmacology (QSP) modeling of the host immune response against Mycobacterium tuberculosis can inform the rational design of host-directed therapies (HDTs). We aimed to develop a QSP framework to evaluate the effects of metformin-associated autophagy induction in combination with antibiotics. A QSP framework for autophagy was developed by extending a model for host immune response to include adenosine monophosphate-activated protein kinase (AMPK)-mTOR-autophagy signaling. This model was combined with pharmacokinetic-pharmacodynamic models for metformin and antibiotics against M. tuberculosis. We compared the model predictions to mice infection experiments and derived predictions for the pathogen- and host-associated dynamics in humans treated with metformin in combination with antibiotics. The model adequately captured the observed bacterial load dynamics in mice M. tuberculosis infection models treated with metformin. Simulations for adjunctive metformin therapy in newly diagnosed patients suggested a limited yet dose-dependent effect of metformin on reduction of the intracellular bacterial load when the overall bacterial load is low, late during antibiotic treatment. We present the first QSP framework for HDTs against M. tuberculosis, linking cellular-level autophagy effects to disease progression and adjunctive HDT treatment response. This framework may be extended to guide the design of HDTs against M. tuberculosis.

Mathematical Modeling and Analysis of CD200-CD200R in Cancer Treatment

CD200 is a cell membrane protein that binds to its receptor, CD200 receptor (CD200R). The CD200 positive tumor cells inhibit the cellular functions of M1 and M2 macrophages and dendritic cells (DCs) through the CD200-CD200R complex, resulting in downregulation of Interleukin-10 and Interleukin-12 productions and affecting the activation of cytotoxic T lymphocytes. In this work, we provide two ordinary differential equation models, one complete model and one simplified model, to investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200-CD200R complex in tumor growth. Our simulations demonstrate that (i) the impact of the CD200-CD200R complex on tumor promotion or inhibition highly depends on the binding affinity of the CD200R on M2 macrophages and DCs to the CD200 on tumor cells, and (ii) a stronger binding affinity of the CD200R on M1 macrophages or DCs to the CD200 on tumor cells induces a higher tumor cell density in the CD200 positive tumor. Thus, the CD200 blockade would be an efficient treatment method in this case. Moreover, the simplified model shows that the binding affinity of CD200R on macrophages is the major factor to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are significantly different to each other. On the other hand, both the binding affinity of CD200R and the population of macrophages are the major factors to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are close to each other. We also analyze the simplified model to investigate the dynamics of the positive and trivial equilibria of the CD200 positive tumor case and the CD200 deficient tumor case. The bifurcation diagrams show that when M1 macrophages dominate the population, the tumor cell density of the CD200 positive tumor is higher than the one of CD200 deficient tumor. Moreover, the dynamics of tumor cell density change from tumor elimination to tumor persistence to oscillation, as the maximal proliferation rate of tumor cells increases.

Deterministic and stochastic in-host tuberculosis models for bacterium-directed and host-directed therapy combination

Mycobacterium tuberculosis (TB) infection can involve all immune system components and can result in different disease outcomes. The antibiotic TB drugs require strict adherence to prevent both disease relapse and mutation of drug- and multidrug-resistant strains. To overcome the constraints of pathogen-directed therapy, host-directed therapy has attracted more attention in recent years as an adjunct therapy to enhance host immunity to fight against this intractable pathogen. The goal of this paper is to investigate in-host TB models to provide insights into therapy development. Focusing on therapy-targeting parameters, the parameter regions for different disease outcomes are identified from an established ODE model. Interestingly, the ODE model also demonstrates that the immune responses can both benefit and impede disease progression, depending on the number of bacteria engulfed and released by macrophages. We then develop two Itô SDE models, which consider the impact of demographic variations at the cellular level and environmental variations during therapies along with demographic variations. The SDE model with demographic variation suggests that stochastic fluctuations at the cellular level have significant influences on (1) the T-cell population in all parameter regions, (2) the bacterial population when parameters located in the region with multiple disease outcomes and (3) the uninfected macrophage population in the parameter region representing active disease. Further, considering environmental variations from therapies, the second SDE model suggests that disease progression can slow down if therapies (1) can have fast return rates and (2) can bring parameter values into the disease clearance regions.

A virtual host model of Mycobacterium tuberculosis infection identifies early immune events as predictive of infection outcomes

Tuberculosis (TB), caused by infection with Mycobacterium tuberculosis (Mtb), is one of the world's deadliest infectious diseases and remains a significant global health burden. TB disease and pathology can present clinically across a spectrum of outcomes, ranging from total sterilization of infection to active disease. Much remains unknown about the biology that drives an individual towards various clinical outcomes as it is challenging to experimentally address specific mechanisms driving clinical outcomes. Furthermore, it is unknown whether numbers of immune cells in the blood accurately reflect ongoing events during infection within human lungs. Herein, we utilize a systems biology approach by developing a whole-host model of the immune response to Mtb across multiple physiologic and time scales. This model, called HostSim, tracks events at the cellular, granuloma, organ, and host scale and represents the first whole-host, multi-scale model of the immune response following Mtb infection. We show that this model can capture various aspects of human and non-human primate TB disease and predict that biomarkers in the blood may only faithfully represent events in the lung at early time points after infection. We posit that HostSim, as a first step toward personalized digital twins in TB research, offers a powerful computational tool that can be used in concert with experimental approaches to understand and predict events about various aspects of TB disease and therapeutics.

Mathematical Modeling of the Gut-Bone Axis and Implications of Butyrate Treatment on Osteoimmunology

Butyrate, a short-chain fatty acid produced by the gut microbiota, has pivotal roles in the regulation of the immune system. Recent studies have revealed that butyrate increases the differentiation of peripheral regulatory T cells in the gut-bone axis and promotes osteoblasts' bone forming activity. However, the mechanism of the therapeutic benefit of butyrate in bone remodeling remains incompletely understood. Here, we develop a multicompartment mathematical model to quantitatively predict the contribution of butyrate on the expansion of regulatory T cells in the gut, blood, and bone compartments. We investigate the interplay between regulatory T cell-derived TGF-β and CD8+ T cell-derived Wnt-10b with changes in gut butyrate concentration. In addition, we connect our model to a detailed model of bone metabolism to study the impacts of butyrate and Wnt-10b on trabecular bone volume. Our results indicate both direct and indirect immune-mediated impacts of butyrate on bone metabolism.

Host-directed therapies for tuberculosis: quantitative systems pharmacology approaches

Host-directed therapies (HDTs) that modulate host-pathogen interactions offer an innovative strategy to combat Mycobacterium tuberculosis (Mtb) infections. When combined with tuberculosis (TB) antibiotics, HDTs could contribute to improving treatment outcomes, reducing treatment duration, and preventing resistance development. Translation of the interplay of host-pathogen interactions leveraged by HDTs towards therapeutic outcomes in patients is challenging. Quantitative understanding of the multifaceted nature of the host-pathogen interactions is vital to rationally design HDT strategies. Here, we (i) provide an overview of key Mtb host-pathogen interactions as basis for HDT strategies; and (ii) discuss the components and utility of quantitative systems pharmacology (QSP) models to inform HDT strategies. QSP models can be used to identify and optimize treatment targets, to facilitate preclinical to human translation, and to design combination treatment strategies.

Modeling the immune response to Salmonella during typhoid

Several facets of the host immune response to Salmonella infection have been studied independently at great depths to understand the progress and pathogenesis of Salmonella infection. The circumstances under which a Salmonella-infected individual succumbs to an active disease, evolves as a persister or clears the infection are not understood in detail. We have adopted a system-level approach to develop a continuous-time mechanistic model. We considered key interactions of the immune system state variables with Salmonella in the mesenteric lymph node to determine the final disease outcome deterministically and exclusively temporally. The model accurately predicts the disease outcomes and immune response trajectories operational during typhoid. The results of the simulation confirm the role of anti-inflammatory (M2) macrophages as a site for persistence and relapsing infection. Global sensitivity analysis highlights the importance of both bacterial and host attributes in influencing the disease outcome. It also illustrates the importance of robust phagocytic and anti-microbial potential of M1 macrophages and dendritic cells (DCs) in controlling the disease. Finally, we propose therapeutic strategies for both antibiotic-sensitive and antibiotic-resistant strains (such as IFN-γ therapy, DC transfer and phagocytic potential stimulation). We also suggest prevention strategies such as improving the humoral response and macrophage carrying capacity, which could complement current vaccination schemes for enhanced efficiency.

An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis

Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steady-state transitions can be the occurrence of transcritical and saddle-node bifurcations, which are induced by slowly changing parameters. Transcritical bifurcation, occurring when the basic reproduction number equals to one, determines whether the infection clears or spreads. Saddle-node bifurcation is the key mechanism to create and destroy steady states. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyses on transcritical bifurcation conditions and saddle-node bifurcation conditions. The sensitivity analysis results suggest that the macrophage apoptosis rate is the most significant factor affecting the transition in disease outcomes. This result agrees with the discovery that the programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interplay. Sensitivity analysis narrows down the parameters of interest, but cannot answer how these parameters influence the model outcomes. To do this, we employ bifurcation analysis and numerical simulation to unfold various disease outcomes induced by the variation of macrophage apoptosis rate. Our findings support the hypothesis that the regulation mechanism of macrophage apoptosis affects the host immunity against tuberculosis infection and tuberculosis virulence. Moreover, our mathematical results suggest that new treatments and/or vaccines that regulate macrophage apoptosis in combination with weakening bacillary viability and/or promoting adaptive immunity could have therapeutic value.

Modelling the effects of environmental heterogeneity within the lung on the tuberculosis life-cycle

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In silico model of TB in the lung incorporating environmental heterogeneity.

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Preferential conditions at the apex of lung localise post-primary disease there.

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Analysis of the key influences driving disease at different regions of the lung.

Progress in shortening the duration of tuberculosis (TB) treatment is hampered by the lack of a predictive model that accurately reflects the diverse environment within the lung. This is important as TB has been shown to produce distinct localisations to different areas of the lung during different disease stages, with the environmental heterogeneity within the lung of factors such as air ventilation, blood perfusion and oxygen tension believed to contribute to the apical localisation witnessed during the post-primary form of the disease.

Building upon our previous model of environmental lung heterogeneity, we present a networked metapopulation model that simulates TB across the whole lung, incorporating these notions of environmental heterogeneity across the whole TB life-cycle to show how different stages of the disease are influenced by different environmental and immunological factors. The alveolar tissue in the lung is divided into distinct patches, with each patch representing a portion of the total tissue and containing environmental attributes that reflect the internal conditions at that location. We include populations of bacteria and immune cells in various states, and events are included which determine how the members of the model interact with each other and the environment. By allowing some of these events to be dependent on environmental attributes, we create a set of heterogeneous dynamics, whereby the location of the tissue within the lung determines the disease pathological events that occur there.

Our results show that the environmental heterogeneity within the lung is a plausible driving force behind the apical localisation during post-primary disease. After initial infection, bacterial levels will grow in the initial infection location at the base of the lung until an adaptive immune response is initiated. During this period, bacteria are able to disseminate and create new lesions throughout the lung. During the latent stage, the lesions that are situated towards the apex are the largest in size, and once a post-primary immune-suppressing event occurs, it is the uppermost lesions that reach the highest levels of bacterial proliferation. Our sensitivity analysis also shows that it is the differential in blood perfusion, causing reduced immune activity towards the apex, which has the biggest influence of disease outputs.

Stability Analysis of Delayed Tumor-Antigen-ActivatedImmune Response in Combined BCG and IL-2Immunotherapy of Bladder Cancer

We use a system biology approach to translate the interaction of Bacillus Calmette-Gurin (BCG) + interleukin 2 (IL-2) for the treatment of bladder cancer into a mathematical model. The main goal of this research is to predict the outcome of BCG + IL-2 treatment combinations. We examined whether the delay effect caused by the proliferation of tumor antigen-specific effector cells after the immune system destroys BCG-infected urothelium cells after BCG and IL-2 immunotherapy influences success in bladder cancer treatment. To do this, we introduce a system of differential equations where the variables are the main participants in the immune response after BCG installations to fight cancer: the number of tumor cells, BCG cells, immune cells, and cytokines involved in the tumor-immune response. The relevant parameters describing the dynamics of the system are taken from a variety of biological, clinical literature and estimated using the mathematical models. We examine the local stability analysis of non-negative equilibrium states of the model. In theory, treatment could improve system stability, and we analyze the stability of all equilibria using the method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). Our results prove that the period for the proliferation of tumor antigen-specific effector cells does not influence to the success of the non-responsive patients after an intensified combined BCG + IL-2 treatment.

Mathematical model and tool to explore shorter multi-drug therapy options for active pulmonary tuberculosis

Standard treatment for active tuberculosis (TB) requires drug treatment with at least four drugs over six months. Shorter-duration therapy would mean less need for strict adherence, and reduced risk of bacterial resistance. A system pharmacology model of TB infection, and drug therapy was developed and used to simulate the outcome of different drug therapy scenarios. The model incorporated human immune response, granuloma lesions, multi-drug antimicrobial chemotherapy, and bacterial resistance. A dynamic population pharmacokinetic/pharmacodynamic (PK/PD) simulation model including rifampin, isoniazid, pyrazinamide, and ethambutol was developed and parameters aligned with previous experimental data. Population therapy outcomes for simulations were found to be generally consistent with summary results from previous clinical trials, for a range of drug dose and duration scenarios. An online tool developed from this model is released as open source software. The TB simulation tool could support analysis of new therapy options, novel drug types, and combinations, incorporating factors such as patient adherence behavior.

A comprehensive in-silico model of pulmonary tuberculosis successfully predicted previous clinical trials and could simulate future therapeutics.

The ups and downs of S. aureus nasal carriage

Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model's behaviour were made including interacting effects of the bacteria's growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.

A mathematical model shows macrophages delay Staphylococcus aureus replication, but limitations in microbicidal capacity restrict bacterial clearance

S. aureus is a leading cause of bacterial infection. Macrophages, the first line of defence in the human immune response, phagocytose and kill S. aureus but the pathogen can evade these responses. Therefore, the exact role of macrophages is incompletely defined. We develop a mathematical model of macrophage - S. aureus dynamics, built on recent experimental data. We demonstrate that, while macrophages may not clear infection, they significantly delay its growth and potentially buy time for recruitment of further cells. We find that macrophage killing is a major obstacle to controlling infection and ingestion capacity also limits the response. We find bistability such that the infection can be limited at low doses. Our combination of experimental data, mathematical analysis and model fitting provide important insights in to the early stages of S. aureus infections, showing macrophages play an important role limiting bacterial replication but can be overwhelmed with large inocula.

Integrating mathematical models with experimental data to investigate the within-host dynamics of bacterial infections

Bacterial infections still constitute a major cause of mortality and morbidity worldwide. The unavailability of therapeutics, antimicrobial resistance and the chronicity of infections due to incomplete clearance contribute to this phenomenon. Despite the progress in antimicrobial and vaccine development, knowledge about the effect that therapeutics have on the host–bacteria interactions remains incomplete. Insights into the characteristics of bacterial colonization and migration between tissues and the relationship between replication and host- or therapeutically induced killing can enable efficient design of treatment approaches. Recently, innovative experimental techniques have generated data enabling the qualitative characterization of aspects of bacterial dynamics. Here, we argue that mathematical modeling as an adjunct to experimental data can enrich the biological insight that these data provide. However, due to limited interdisciplinary training, efforts to combine the two remain limited. To promote this dialogue, we provide a categorization of modeling approaches highlighting their relationship to data generated by a range of experimental techniques in the area of in vivo bacterial dynamics. We outline common biological themes explored using mathematical models with case studies across all pathogen classes. Finally, this review advocates multidisciplinary integration to improve our mechanistic understanding of bacterial infections and guide the use of existing or new therapies.

Stochastic dynamics of Francisella tularensis infection and replication

We study the pathogenesis of Francisella tularensis infection with an experimental mouse model, agent-based computation and mathematical analysis. Following inhalational exposure to Francisella tularensis SCHU S4, a small initial number of bacteria enter lung host cells and proliferate inside them, eventually destroying the host cell and releasing numerous copies that infect other cells. Our analysis of disease progression is based on a stochastic model of a population of infectious agents inside one host cell, extending the birth-and-death process by the occurrence of catastrophes: cell rupture events that affect all bacteria in a cell simultaneously. Closed expressions are obtained for the survival function of an infected cell, the number of bacteria released as a function of time after infection, and the total bacterial load. We compare our mathematical analysis with the results of agent-based computation and, making use of approximate Bayesian statistical inference, with experimental measurements carried out after murine aerosol infection with the virulent SCHU S4 strain of the bacterium Francisella tularensis, that infects alveolar macrophages. The posterior distribution of the rate of replication of intracellular bacteria is consistent with the estimate that the time between rounds of bacterial division is less than 6 hours in vivo.

Infecting a host cell is required for the replication of many types of bacteria and viruses. In some cases, infected cells release new infectious agents continuously over their lifetime. In others, such as the Francisella tularensis bacterium studied here, they are released in a single burst that coincides with the cell’s death. We show how a stochastic model, the birth-and-death process with catastrophe, can be used to characterise infection in a single cell, thereby allowing us to account for burst events and quantify the kinetics of pathogenesis in the lung, the initial site of infection, as well as in other organs that the infection spreads to. We learn about the parameters of the mathematical model of Francisella tularensis infection making use of the experimental measurements of bacterial loads, together with approximate Bayesian statistical inference methods. The most important parameter describing the pathogenesis is the rate of replication of intracellular bacteria.

Alveolar macrophages generate a noncanonical NRF2-driven transcriptional response to Mycobacterium tuberculosis in vivo

Alveolar macrophages (AMs) are the first cells to be infected during Mycobacterium tuberculosis (M.tb.) infection. Thus, the AM response to infection is the first of many steps leading to initiation of the adaptive immune response required for efficient control of infection. A hallmark of M.tb. infection is the slow initiation of the adaptive response, yet the mechanisms responsible for this are largely unknown. To study the initial AM response to infection, we developed a system to identify, sort, and analyze M.tb.-infected AMs from the lung within the first 10 days of infection. In contrast to what has been previously described using in vitro systems, M.tb.-infected AMs up-regulate a cell-protective antioxidant transcriptional signature that is dependent on the lung environment but not bacterial virulence. Computational approaches including pathway analysis and transcription factor motif enrichment analysis identify NRF2 as a master regulator of the response. Using knockout mouse models, we demonstrate that NRF2 drives expression of the cell-protective signature in AMs and impairs the control of early bacterial growth. AMs up-regulate a substantial pro-inflammatory response to M.tb. infection only 10 days after infection, yet comparisons with bystander AMs from the same infected animals demonstrate that M.tb.-infected AMs generate a less robust inflammatory response than the uninfected cells around them. Our findings demonstrate that the initial macrophage response to M.tb. in the lung is far less inflammatory than has previously been described by in vitro systems and may impede the overall host response to infection.

The Role of Dimensionality in Understanding Granuloma Formation

Within the first 2-3 months of a Mycobacterium tuberculosis (Mtb) infection, 2-4 mm spherical structures called granulomas develop in the lungs of the infected hosts. These are the hallmark of tuberculosis (TB) infection in humans and non-human primates. A cascade of immunological events occurs in the first 3 months of granuloma formation that likely shapes the outcome of the infection. Understanding the main mechanisms driving granuloma development and function is key to generating treatments and vaccines. In vitro, in vivo, and in silico studies have been performed in the past decades to address the complexity of granuloma dynamics. This study builds on our previous 2D spatio-temporal hybrid computational model of granuloma formation in TB (GranSim) and presents for the first time a more realistic 3D implementation. We use uncertainty and sensitivity analysis techniques to calibrate the new 3D resolution to non-human primate (NHP) experimental data on bacterial levels per granuloma during the first 100 days post infection. Due to the large computational cost associated with running a 3D agent-based model, our major goal is to assess to what extent 2D and 3D simulations differ in predictions for TB granulomas and what can be learned in the context of 3D that is missed in 2D. Our findings suggest that in terms of major mechanisms driving bacterial burden, 2D and 3D models return very similar results. For example, Mtb growth rates and molecular regulation mechanisms are very important both in 2D and 3D, as are cellular movement and modulation of cell recruitment. The main difference we found was that the 3D model is less affected by crowding when cellular recruitment and movement of cells are increased. Overall, we conclude that the use of a 2D resolution in GranSim is warranted when large scale pilot runs are to be performed and if the goal is to determine major mechanisms driving infection outcome (e.g., bacterial load). To comprehensively compare the roles of model dimensionality, further tests and experimental data will be needed to expand our conclusions to molecular scale dynamics and multi-scale resolutions.

Dynamic balance of pro- and anti-inflammatory signals controls disease and limits pathology

Immune responses to pathogens are complex and not well understood in many diseases, and this is especially true for infections by persistent pathogens. One mechanism that allows for long-term control of infection while also preventing an over-zealous inflammatory response from causing extensive tissue damage is for the immune system to balance pro- and anti-inflammatory cells and signals. This balance is dynamic and the immune system responds to cues from both host and pathogen, maintaining a steady state across multiple scales through continuous feedback. Identifying the signals, cells, cytokines, and other immune response factors that mediate this balance over time has been difficult using traditional research strategies. Computational modeling studies based on data from traditional systems can identify how this balance contributes to immunity. Here we provide evidence from both experimental and mathematical/computational studies to support the concept of a dynamic balance operating during persistent and other infection scenarios. We focus mainly on tuberculosis, currently the leading cause of death due to infectious disease in the world, and also provide evidence for other infections. A better understanding of the dynamically balanced immune response can help shape treatment strategies that utilize both drugs and host-directed therapies.

A spatially heterogeneous network-based metapopulation software model applied to the simulation of a pulmonary tuberculosis infection

Tuberculosis (TB) is an ancient disease that, although curable, still accounts for over 1 million deaths worldwide. Shortening treatment time is an important area of research but is hampered by the lack of models that mimic the full range of human pathology. TB shows distinct localisations during different stages of infection, the reasons for which are poorly understood. Greater understanding of how heterogeneity within the human lung influences disease progression may hold the key to improving treatment efficiency and reducing treatment times. In this work, we present a novel in silico software model which uses a networked metapopulation incorporating both spatial heterogeneity and dissemination possibilities to simulate a TB infection over the whole lung and associated lymphatics. The entire population of bacteria and immune cells is split into a network of patches: members interact within patches and are able to move between them. Patches and edges of the lung network include their own environmental attributes which influence the dynamics of interactions between the members of the subpopulations of the patches and the translocation of members along edges. In this work, we detail the initial findings of a whole-organ model that incorporates distinct spatial heterogeneity features which are not present in standard differential equation approaches to tuberculosis modelling. We show that the inclusion of heterogeneity within the lung landscape when modelling TB disease progression has significant outcomes on the bacterial load present: a greater differential of oxygen, perfusion and ventilation between the apices and the basal regions of the lungs creates micro-environments at the apex that are more preferential for bacteria, due to increased oxygen availability and reduced immune activity, leading to a greater overall bacterial load present once latency is established. These findings suggest that further whole-organ modelling incorporating more sophisticated heterogeneities within the environment and complex lung topologies will provide more insight into the environments in which TB bacteria persist and thus help develop new treatments which are factored towards these environmental conditions.

Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma

In this work we formulate a model for the population dynamics of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB). Our main interest is to assess the impact of the competition among bacteria on the infection prevalence. For this end, we assume that Mtb population has two types of growth. The first one is due to bacteria produced in the interior of each infected macrophage, and it is assumed that is proportional to the number of infected macrophages. The second one is of logistic type due to the competition among free bacteria released by the same infected macrophages. The qualitative analysis and numerical results suggests the existence of forward, backward and S-shaped bifurcations when the associated reproduction number R0 of the Mtb is less unity. In addition, qualitative analysis of the model shows that there may be up to three bacteria-present equilibria, two locally asymptotically stable, and one unstable.

Deletion of TGF-β1 Increases Bacterial Clearance by Cytotoxic T Cells in a Tuberculosis Granuloma Model

Mycobacterium tuberculosis is the pathogenic bacterium that causes tuberculosis (TB), one of the most lethal infectious diseases in the world. The only vaccine against TB is minimally protective, and multi-drug resistant TB necessitates new therapeutics to treat infection. Developing new therapies requires a better understanding of the complex host immune response to infection, including dissecting the processes leading to formation of granulomas, the dense cellular lesions associated with TB. In this work, we pair experimental and computational modeling studies to explore cytokine regulation in the context of TB. We use our next-generation hybrid multi-scale model of granuloma formation (GranSim) to capture molecular, cellular, and tissue scale dynamics of granuloma formation. We identify TGF-β1 as a major inhibitor of cytotoxic T-cell effector function in granulomas. Deletion of TGF-β1 from the system results in improved bacterial clearance and lesion sterilization. We also identify a novel dichotomous regulation of cytotoxic T cells and macrophages by TGF-β1 and IL-10, respectively. These findings suggest that increasing cytotoxic T-cell effector functions may increase bacterial clearance in granulomas and highlight potential new therapeutic targets for treating TB.

Identifying mechanisms driving formation of granuloma-associated fibrosis during Mycobacterium tuberculosis infection

Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB), is a pulmonary pathogen of major global concern. A key feature of Mtb infection in primates is the formation of granulomas, dense cellular structures surrounding infected lung tissue. These structures serve as the main site of host-pathogen interaction in TB, and thus to effectively treat TB we must clarify mechanisms of granuloma formation and their function in disease. Fibrotic granulomas are associated with both good and bad disease outcomes. Fibrosis can serve to isolate infected tissue from healthy tissue, but it can also cause difficulty breathing as it leaves scars. Little is known about fibrosis in TB, and data from non-human primates is just beginning to clarify the picture. This work focuses on constructing a hybrid multi-scale model of fibrotic granuloma formation, in order to identify mechanisms driving development of fibrosis in Mtb infected lungs. We combine dynamics of molecular, cellular, and tissue scale models from previously published studies to characterize the formation of two common sub-types of fibrotic granulomas: peripherally fibrotic, with a cuff of collagen surrounding granulomas, and centrally fibrotic, with collagen throughout granulomas. Uncertainty and sensitivity analysis, along with large simulation sets, enable us to identify mechanisms differentiating centrally versus peripherally fibrotic granulomas. These findings suggest that heterogeneous cytokine environments exist within granulomas and may be responsible for driving tissue scale morphologies. Using this model we are primed to better understand the complex structure of granulomas, a necessity for developing successful treatments for TB.

A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment

Tuberculosis (TB) is an ancient and deadly disease characterized by complex host-pathogen dynamics playing out over multiple time and length scales and physiological compartments. Computational modeling can be used to integrate various types of experimental data and suggest new hypotheses, mechanisms, and therapeutic approaches to TB. Here, we offer a first-time comprehensive review of work on within-host TB models that describe the immune response of the host to infection, including the formation of lung granulomas. The models include systems of ordinary and partial differential equations and agent-based models as well as hybrid and multi-scale models that are combinations of these. Many aspects of M. tuberculosis infection, including host dynamics in the lung (typical site of infection for TB), granuloma formation, roles of cytokine and chemokine dynamics, and bacterial nutrient availability have been explored. Finally, we survey applications of these within-host models to TB therapy and prevention and suggest future directions to impact this global disease.

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

A Multi-Compartment Hybrid Computational Model Predicts Key Roles for Dendritic Cells in Tuberculosis Infection

Tuberculosis (TB) is a world-wide health problem with approximately 2 billion people infected with Mycobacterium tuberculosis (Mtb, the causative bacterium of TB). The pathologic hallmark of Mtb infection in humans and Non-Human Primates (NHPs) is the formation of spherical structures, primarily in lungs, called granulomas. Infection occurs after inhalation of bacteria into lungs, where resident antigen-presenting cells (APCs), take up bacteria and initiate the immune response to Mtb infection. APCs traffic from the site of infection (lung) to lung-draining lymph nodes (LNs) where they prime T cells to recognize Mtb. These T cells, circulating back through blood, migrate back to lungs to perform their immune effector functions. We have previously developed a hybrid agent-based model (ABM, labeled GranSim) describing in silico immune cell, bacterial (Mtb) and molecular behaviors during tuberculosis infection and recently linked that model to operate across three physiological compartments: lung (infection site where granulomas form), lung draining lymph node (LN, site of generation of adaptive immunity) and blood (a measurable compartment). Granuloma formation and function is captured by a spatio-temporal model (i.e., ABM), while LN and blood compartments represent temporal dynamics of the whole body in response to infection and are captured with ordinary differential equations (ODEs). In order to have a more mechanistic representation of APC trafficking from the lung to the lymph node, and to better capture antigen presentation in a draining LN, this current study incorporates the role of dendritic cells (DCs) in a computational fashion into GranSim.

Modeling and Hemofiltration Treatment of Acute Inflammation

The body responds to endotoxins by triggering the acute inflammatory response system to eliminate the threat posed by gram-negative bacteria (endotoxin) and restore health. However, an uncontrolled inflammatory response can lead to tissue damage, organ failure, and ultimately death; this is clinically known as sepsis. Mathematical models of acute inflammatory disease have the potential to guide treatment decisions in critically ill patients. In this work, an 8-state (8-D) differential equation model of the acute inflammatory response system to endotoxin challenge was developed. Endotoxin challenges at 3 and 12 mg/kg were administered to rats, and dynamic cytokine data for interleukin (IL)-6, tumor necrosis factor (TNF), and IL-10 were obtained and used to calibrate the model. Evaluation of competing model structures was performed by analyzing model predictions at 3, 6, and 12 mg/kg endotoxin challenges with respect to experimental data from rats. Subsequently, a model predictive control (MPC) algorithm was synthesized to control a hemoadsorption (HA) device, a blood purification treatment for acute inflammation. A particle filter (PF) algorithm was implemented to estimate the full state vector of the endotoxemic rat based on time series cytokine measurements. Treatment simulations show that: (i) the apparent primary mechanism of HA efficacy is white blood cell (WBC) capture, with cytokine capture a secondary benefit; and (ii) differential filtering of cytokines and WBC does not provide substantial improvement in treatment outcomes vs. existing HA devices.

Systems Medicine for Lung Diseases: Phenotypes and Precision Medicine in Cancer, Infection, and Allergy

Lung diseases cause an enormous socioeconomic burden. Four of them are among the ten most important causes of deaths worldwide: Pneumonia has the highest death toll of all infectious diseases, lung cancer kills the most people of all malignant proliferative disorders, chronic obstructive pulmonary disease (COPD) ranks third in mortality among the chronic noncommunicable diseases, and tuberculosis is still one of the most important chronic infectious diseases. Despite all efforts, for example, by the World Health Organization and clinical and experimental researchers, these diseases are still highly prevalent and harmful. This is in part due to the specific organization of tissue homeostasis, architecture, and immunity of the lung. Recently, several consortia have formed and aim to bring together clinical and molecular data from big cohorts of patients with lung diseases with novel experimental setups, biostatistics, bioinformatics, and mathematical modeling. This "systems medicine" concept will help to match the different disease modalities with adequate therapeutic and possibly preventive strategies for individual patients in the sense of precision medicine.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Quantifying Limits on Replication, Death, and Quiescence of Mycobacterium tuberculosis in Mice

When an individual is exposed to Mycobacterium tuberculosis (Mtb) three outcomes are possible: bacterial clearance, active disease, or latent infection. It is generally believed that most individuals exposed to Mtb become latently infected and carry the mycobacteria for life. How Mtb is maintained during this latent infection remains largely unknown. During an Mtb infection in mice, there is a phase of rapid increase in bacterial numbers in the murine lungs within the first 3 weeks, and then bacterial numbers either stabilize or increase slowly over the period of many months. It has been debated whether the relatively constant numbers of bacteria in the chronic infection result from latent (dormant, quiescent), non-replicating bacteria, or whether the observed Mtb cell numbers are due to balance between rapid replication and death. A recent study of mice, infected with a Mtb strain carrying an unstable plasmid, showed that during the chronic phase, Mtb was replicating at significant rates. Using experimental data from this study and mathematical modeling we investigated the limits of the rates of bacterial replication, death, and quiescence during Mtb infection of mice. First, we found that to explain the data the rates of bacterial replication and death could not be constant and had to decrease with time since infection unless there were large changes in plasmid segregation probability over time. While a decrease in the rate of Mtb replication with time since infection was expected due to depletion of host's resources, a decrease in the Mtb death rate was counterintuitive since Mtb-specific immune response, appearing in the lungs 3–4 weeks after infection, should increase removal of bacteria. Interestingly, we found no significant correlation between estimated rates of Mtb replication and death suggesting the decline in these rates was driven by independent mechanisms. Second, we found that the data could not be explained by assuming that bacteria do not die, suggesting that some removal of bacteria from lungs of these mice had to occur even though the total bacterial counts in these mice always increased over time. Third and finally, we showed that to explain the data the majority of bacterial cells (at least ~60%) must be replicating in the chronic phase of infection further challenging widespread belief of nonreplicating Mtb in latency. Our predictions were robust to some changes in the structure of the model, for example, when the loss of plasmid-bearing cells was mainly due to high fitness cost of the plasmid. Further studies should determine if more mechanistic models for Mtb dynamics are also able to accurately explain these data.

Mathematical modeling and systems pharmacology of tuberculosis: Isoniazid as a case study

Tuberculosis (TB) treatment needs to be optimized as it is currently long and associated with increasing drug resistance. The antimycobacterial effect of isoniazid (INH) is characterized by a biphasic kill curve, whose causes are still debated. In this work, we developed a complete mathematical model describing the time-course of TB infection and its treatment by INH in human lung. This model was based on a pharmacokinetic model, a pharmacodynamic model and a pathophysiological model. It was used to simulate the antibacterial effect of INH during the first days of therapy. This full model adequately reproduced some qualitative and quantitative properties of the early bactericidal activity of INH observed in TB patients. The kill curves simulated with the model reproduced the biphasic killing effect of INH and the predicted declines in extracellular bacteria were comparable to clinical data. A sensitivity analysis provided interesting insights regarding the biphasic kill curve. The first phase appeared to be essentially driven by the drug effect. In the second phase, while drug pharmacology was the major determinant of the antibacterial effect, a slight influence of the dynamics of infected macrophages was also observed. This work permits to formulate hypotheses for optimizing the efficacy of TB drug candidates and confirms the utility of mathematical modeling to generate new assumptions for TB research.

Third-Kind Encounters in Biomedicine: Immunology Meets Mathematics and Informatics to Become Quantitative and Predictive

The understanding of the immune response is right now at the center of biomedical research. There are growing expectations that immune-based interventions will in the midterm provide new, personalized, and targeted therapeutic options for many severe and highly prevalent diseases, from aggressive cancers to infectious and autoimmune diseases. To this end, immunology should surpass its current descriptive and phenomenological nature, and become quantitative, and thereby predictive.Immunology is an ideal field for deploying the tools, methodologies, and philosophy of systems biology, an approach that combines quantitative experimental data, computational biology, and mathematical modeling. This is because, from an organism-wide perspective, the immunity is a biological system of systems, a paradigmatic instance of a multi-scale system. At the molecular scale, the critical phenotypic responses of immune cells are governed by large biochemical networks, enriched in nested regulatory motifs such as feedback and feedforward loops. This network complexity confers them the ability of highly nonlinear behavior, including remarkable examples of homeostasis, ultra-sensitivity, hysteresis, and bistability. Moving from the cellular level, different immune cell populations communicate with each other by direct physical contact or receiving and secreting signaling molecules such as cytokines. Moreover, the interaction of the immune system with its potential targets (e.g., pathogens or tumor cells) is far from simple, as it involves a number of attack and counterattack mechanisms that ultimately constitute a tightly regulated multi-feedback loop system. From a more practical perspective, this leads to the consequence that today's immunologists are facing an ever-increasing challenge of integrating massive quantities from multi-platforms.In this chapter, we support the idea that the analysis of the immune system demands the use of systems-level approaches to ensure the success in the search for more effective and personalized immune-based therapies.

Improving Bacillus Calmette-Guérin (BCG) immunotherapy for bladder cancer by adding interleukin 2 (IL-2): a mathematical model

One of the treatments offered to non-invasive bladder cancer patients is BCG instillations, using a well-established, time-honoured protocol. Some of the patients, however, do not respond to this protocol. To examine possible changes in the protocol, we provide a platform for in silico testing of alternative protocols for BCG instillations and combinations with IL-2, to be used by urologists in planning new treatment strategies for subpopulations of bladder cancer patients who may benefit from a personalized protocol. We use a systems biology approach to describe the BCG-tumour-immune interplay and translate it into a set of mathematical differential equations. The variables of the equation set are the number of tumour cells, bacteria cells, immune cells, and cytokines participating in the tumour-immune response. Relevant parameters that describe the system's dynamics are taken from a variety of independent literature, unrelated to the clinical trial results assessed by the model predictions. Model simulations use a clinically relevant range of initial tumour sizes (tumour volume) and tumour growth rates (tumour grade), representative of a virtual population of fifty patients. Our model successfully retrieved previous clinical results for BCG induction treatment and BCG maintenance therapy with a complete response (CR) rate of 82%. Furthermore, we designed alternative maintenance protocols, using IL-2 combinations with BCG, which improved success rates up to 86% and 100% of the patients, albeit without considering possible side effects. We have shown our simulation platform to be reliable by demonstrating its ability to retrieve published clinical trial results. We used this platform to predict the outcome of treatment combinations. Our results suggest that the subpopulation of non-responsive patients may benefit from an intensified combined BCG IL-2 maintenance treatment.

Variability in tuberculosis granuloma T cell responses exists, but a balance of pro- and anti-inflammatory cytokines is associated with sterilization

Lung granulomas are the pathologic hallmark of tuberculosis (TB). T cells are a major cellular component of TB lung granulomas and are known to play an important role in containment of Mycobacterium tuberculosis (Mtb) infection. We used cynomolgus macaques, a non-human primate model that recapitulates human TB with clinically active disease, latent infection or early infection, to understand functional characteristics and dynamics of T cells in individual granulomas. We sought to correlate T cell cytokine response and bacterial burden of each granuloma, as well as granuloma and systemic responses in individual animals. Our results support that each granuloma within an individual host is independent with respect to total cell numbers, proportion of T cells, pattern of cytokine response, and bacterial burden. The spectrum of these components overlaps greatly amongst animals with different clinical status, indicating that a diversity of granulomas exists within an individual host. On average only about 8% of T cells from granulomas respond with cytokine production after stimulation with Mtb specific antigens, and few “multi-functional” T cells were observed. However, granulomas were found to be “multi-functional” with respect to the combinations of functional T cells that were identified among lesions from individual animals. Although the responses generally overlapped, sterile granulomas had modestly higher frequencies of T cells making IL-17, TNF and any of T-1 (IFN-γ, IL-2, or TNF) and/or T-17 (IL-17) cytokines than non-sterile granulomas. An inverse correlation was observed between bacterial burden with TNF and T-1/T-17 responses in individual granulomas, and a combinatorial analysis of pair-wise cytokine responses indicated that granulomas with T cells producing both pro- and anti-inflammatory cytokines (e.g. IL-10 and IL-17) were associated with clearance of Mtb. Preliminary evaluation suggests that systemic responses in the blood do not accurately reflect local T cell responses within granulomas.

The characteristic feature of Mycobacterium tuberculosis (Mtb) infection is the formation of lesions, which are organized structures of immune cells in the lungs called granulomas, which contain the bacteria. When the granuloma functions effectively, it can kill the bacteria. T cells (a type of immune cell, also present in granulomas) are known to play an important role in control of tuberculosis. However, functions of T cells at individual granuloma levels are unknown. Here, we studied the functional characteristics of T cells, which are defined by the production of chemical messengers (cytokines) at the granuloma level in a non-human primate model. We compared the relationship between cytokine response and the number of bacteria (Mtb) in each granuloma. Each granuloma was found to be unique, suggesting different types exist within an animal. Only a small proportion of T cells produced any cytokine, but different types of cytokines were observed within each granuloma. A balance between different types of cytokine was associated with more killing of bacteria in granulomas. Understanding how to improve the T cell responses to obtain killing of bacteria in the granuloma will be important for vaccine development.

Modeling early events in Francisella tularensis pathogenesis

Computational models can provide valuable insights into the mechanisms of infection and be used as investigative tools to support development of medical treatments. We develop a stochastic, within-host, computational model of the infection process in the BALB/c mouse, following inhalational exposure to Francisella tularensis SCHU S4. The model is mechanistic and governed by a small number of experimentally verifiable parameters. Given an initial dose, the model generates bacterial load profiles corresponding to those produced experimentally, with a doubling time of approximately 5 h during the first 48 h of infection. Analytical approximations for the mean number of bacteria in phagosomes and cytosols for the first 24 h post-infection are derived and used to verify the stochastic model. In our description of the dynamics of macrophage infection, the number of bacteria released per rupturing macrophage is a geometrically-distributed random variable. When combined with doubling time, this provides a distribution for the time taken for infected macrophages to rupture and release their intracellular bacteria. The mean and variance of these distributions are determined by model parameters with a precise biological interpretation, providing new mechanistic insights into the determinants of immune and bacterial kinetics. Insights into the dynamics of macrophage suppression and activation gained by the model can be used to explore the potential benefits of interventions that stimulate macrophage activation.

Tuberculosis in Canada: Detection, Intervention and Compliance

This paper provides an overview of the current state of TB in Canada by referencing information presented at the workshop, "Tuberculosis: Detection, Prevention, and Compliance." The workshop took place on November 14 and 15, 2012 in Ottawa. The workshop was organized by the Centre for Disease Modeling and the Public Health Agency of Canada as a two-day knowledge translation event that was comprised of scientific and policy focused presentations designed to address four key objectives: (1) Evaluate the success of current tuberculosis (TB) health policies and control strategies in Canada and for specific Canadian sub-populations; (2) Determine the impact of detection, intervention, compliance, and education strategies in terms of TB incidence and prevalence; (3) Develop targets for future interventions by identifying key characteristics of TB epidemics that impact the success of TB health policies and control strategies; (4) Leverage our existing ties with public health decision makers, aboriginal health organizations, and organizations serving the homeless to develop a research community that is based on close collaboration, and will foster national TB control efforts. The workshop elicited robust discussions between experts from a variety of academic disciplines and government officials. A summary of the information presented, comments shared, and questions posed, will provide a comprehensive understanding of the status of TB in Canada and future directions to be taken for improved control of the disease.

Mathematical modeling of Interleukin-35 promoting tumor growth and angiogenesis

Interleukin-35 (IL-35), a cytokine from the Interleukin-12 cytokine family, has been considered as an anti-inflammatory cytokine which promotes tumor progression and tumor immune evasion. It has also been demonstrated that IL-35 is secreted by regulatory T cells. Recent mouse experiments have shown that IL-35 produced by cancer cells promotes tumor growth via enhancing myeloid cell accumulation and angiogenesis, and reducing the infiltration of activated CD8[Formula: see text] T cells into tumor microenvironment. In the present paper we develop a mathematical model based on these experimental results. We include in the model an anti-IL-35 drug as treatment. The extended model (with drug) is used to design protocols of anti-IL-35 injections for treatment of cancer. We find that with a fixed total amount of drug, continuous injection has better efficacy than intermittent injections in reducing the tumor load while the treatment is ongoing. We also find that the percentage of tumor reduction under anti-IL-35 treatment improves when the production of IL-35 by cancer is increased.

Integrative model of the immune response to a pulmonary macrophage infection: what determines the infection duration?

The immune mechanisms which determine the infection duration induced by pathogens targeting pulmonary macrophages are poorly known. To explore the impact of such pathogens, it is indispensable to integrate the various immune mechanisms and to take into account the variability in pathogen virulence and host susceptibility. In this context, mathematical models complement experimentation and are powerful tools to represent and explore the complex mechanisms involved in the infection and immune dynamics. We developed an original mathematical model in which we detailed the interactions between the macrophages and the pathogen, the orientation of the adaptive response and the cytokine regulations. We applied our model to the Porcine Respiratory and Reproductive Syndrome virus (PRRSv), a major concern for the swine industry. We extracted value ranges for the model parameters from modelling and experimental studies on respiratory pathogens. We identified the most influential parameters through a sensitivity analysis. We defined a parameter set, the reference scenario, resulting in a realistic and representative immune response to PRRSv infection. We then defined scenarios corresponding to graduated levels of strain virulence and host susceptibility around the reference scenario. We observed that high levels of antiviral cytokines and a dominant cellular response were associated with either short, the usual assumption, or long infection durations, depending on the immune mechanisms involved. To identify these mechanisms, we need to combine the levels of antiviral cytokines, including , and . The latter is a good indicator of the infected macrophage level, both combined provide the adaptive response orientation. Available PRRSv vaccines lack efficiency. By integrating the main interactions between the complex immune mechanisms, this modelling framework could be used to help designing more efficient vaccination strategies.

Global sensitivity analysis used to interpret biological experimental results

Modeling host/pathogen interactions provides insight into immune defects that allow bacteria to overwhelm the host, mechanisms that allow vaccine strategies to be successful, and illusive interactions between immune components that govern the immune response to a challenge. However, even simplified models require a fairly high dimensional parameter space to be explored. Here we use global sensitivity analysis for parameters in a simple model for biofilm infections in mice. The results indicate which parameters are insignificant and are 'frozen' to yield a reduced model. The reduced model replicates the full model with high accuracy, using approximately half of the parameter space. We used the sensitivity to investigate the results of the combined biological and mathematical experiments for osteomyelitis. We are able to identify parts of the compartmentalized immune system that were responsible for each of the experimental outcomes. This model is one example for a technique that can be used generally.

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.

Modelling the interaction between the host immune response, bacterial dynamics and inflammatory damage in comparison with immunomodulation and vaccination experiments

The immune system is a complex system of chemical and cellular interactions that responds quickly to queues that signal infection and then reverts to a basal level once the challenge is eliminated. Here, we present a general, four-component model of the immune system's response to a Staphylococcal aureus (S. aureus) infection, using ordinary differential equations. To incorporate both the infection and the immune system, we adopt the style of compartmenting the system to include bacterial dynamics, damage and inflammation to the host, and the host response. We incorporate interactions not previously represented including cross-talk between inflammation/damage and the infection and the suppression of the anti-inflammatory pathway in response to inflammation/damage. As a result, the most relevant equilibrium of the system, representing the health state, is an all-positive basal level. The model is able to capture eight different experimental outcomes for mice challenged with intratibial osteomyelitis due to S. aureus, primarily involving immunomodulation and vaccine therapies. For further validation and parameter exploration, we perform a parameter sensitivity analysis which suggests that the model is very stable with respect to variations in parameters, indicates potential immunomodulation strategies and provides a possible explanation for the difference in immune potential for different mouse strains.

A mathematical model of the initial interaction between Mycobacterium tuberculosis and macrophages

There is a large body of literature describing molecular level interactions between Mycobacterium tuberculosis (Mtb) and macrophages. Macrophages initiate a range of anti-bacterial mechanisms in response to infection, and Mtb is capable of surviving and circumventing many of these responses. We apply a computational approach to ask: what are the effects on the cellular level of these opposing interactions? The model considers the interplay between bacterial killing and the pathogen's interference with macrophage function. The results reveal an oscillating balance between host and pathogen, but the balance is transient and varies in length, indicating that stochasticity in the bacterial population or host response could contribute to the diverse incubation periods observed in exposed individuals. The model captures host and strain variation and gives new insight into host-pathogen compatibility and co-evolution.

The development of a fully-integrated immune response model (FIRM) simulator of the immune response through integration of multiple subset models

Background

The complexity and multiscale nature of the mammalian immune response provides an excellent test bed for the potential of mathematical modeling and simulation to facilitate mechanistic understanding. Historically, mathematical models of the immune response focused on subsets of the immune system and/or specific aspects of the response. Mathematical models have been developed for the humoral side of the immune response, or for the cellular side, or for cytokine kinetics, but rarely have they been proposed to encompass the overall system complexity. We propose here a framework for integration of subset models, based on a system biology approach.

Results

A dynamic simulator, the Fully-integrated Immune Response Model (FIRM), was built in a stepwise fashion by integrating published subset models and adding novel features. The approach used to build the model includes the formulation of the network of interacting species and the subsequent introduction of rate laws to describe each biological process. The resulting model represents a multi-organ structure, comprised of the target organ where the immune response takes place, circulating blood, lymphoid T, and lymphoid B tissue. The cell types accounted for include macrophages, a few T-cell lineages (cytotoxic, regulatory, helper 1, and helper 2), and B-cell activation to plasma cells. Four different cytokines were accounted for: IFN-γ, IL-4, IL-10 and IL-12. In addition, generic inflammatory signals are used to represent the kinetics of IL-1, IL-2, and TGF-β. Cell recruitment, differentiation, replication, apoptosis and migration are described as appropriate for the different cell types. The model is a hybrid structure containing information from several mammalian species. The structure of the network was built to be physiologically and biochemically consistent. Rate laws for all the cellular fate processes, growth factor production rates and half-lives, together with antibody production rates and half-lives, are provided. The results demonstrate how this framework can be used to integrate mathematical models of the immune response from several published sources and describe qualitative predictions of global immune system response arising from the integrated, hybrid model. In addition, we show how the model can be expanded to include novel biological findings. Case studies were carried out to simulate TB infection, tumor rejection, response to a blood borne pathogen and the consequences of accounting for regulatory T-cells.

Conclusions

The final result of this work is a postulated and increasingly comprehensive representation of the mammalian immune system, based on physiological knowledge and susceptible to further experimental testing and validation. We believe that the integrated nature of FIRM has the potential to simulate a range of responses under a variety of conditions, from modeling of immune responses after tuberculosis (TB) infection to tumor formation in tissues. FIRM also has the flexibility to be expanded to include both complex and novel immunological response features as our knowledge of the immune system advances.

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.

On the interactions of sensitive and resistant Mycobacterium tuberculosis to antibiotics

In this work we propose a system of non linear ordinary differential equations for the dynamics of Mycobacterium tuberculosis (Mtb) within the host, in order to study the role of macrophages, T cells and antibiotics in the control of sensitive and resistant Mtb. Conditions for the persistence of sensitive and resistant bacteria are given in terms of the secondary infections produced by bacteria and macrophages, the immune response, and the antibiotic treatment. Model analysis predicts backward bifurcations for certain values of the parameters. In this case, the dynamics is characterized by the coexistence of two infection states with low and high bacteria load, respectively.