Toward a multiscale model of antigen presentation in immunity

Modelling of the Innate and Adaptive Immune Response to SARS Viral Infection, Cytokine Storm and Vaccination

In this work, we develop mathematical models of the immune response to respiratory viral infection, taking into account some particular properties of the SARS-CoV infections, cytokine storm and vaccination. Each model consists of a system of ordinary differential equations that describe the interactions of the virus, epithelial cells, immune cells, cytokines, and antibodies. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study the dynamics of solutions. The behavior of the solutions is characterized by large peaks of virus concentration specific to acute respiratory viral infections. At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. Viral infection down-regulates interferon production. This competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. After that, we introduce the adaptive immune response with antigen-specific T- and B-lymphocytes. The resulting model shows how the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, an increase in the initial viral load leads to a shorter incubation period and higher maximal viral load. The model shows that a deficient production of antibodies leads to an increase in the incubation period and even higher maximum viral loads. In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on the parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by the excessive production of proinflammatory cytokines. Finally, we study the production of antibodies due to vaccination. We determine the dose-response dependence and the optimal interval of vaccine dose. Assumptions of the model and obtained results correspond to the experimental and clinical data.

Modelling cell surface dynamics and cell-cell interactions using Cell Studio: a three-dimensional visualization tool based on gaming technology

Predictive modelling of complex biological systems and biophysical interactions requires the inclusion of multiple nano- and micro-scale events. In many scenarios, however, numerical solutions alone do not necessarily enhance the understanding of the system. Instead, this work explores the use of an agent-based model with visualization capabilities to elucidate interactions between single cells. We present a model of juxtacrine signalling, using Cell Studio, an agent-based modelling system, based on gaming and three-dimensional visualization tools. The main advantages of the system are its ability to apply any cell geometry and to dynamically visualize the diffusion and interactions of the molecules within the cells in real time. These provide an excellent tool for obtaining insight about different biological scenarios, as the user may view the dynamics of a system and observe its emergent behaviour as it unfolds. The agent-based model was validated against the results of a mean-field model of Notch receptors and ligands in two neighbouring cells. The conversion to an agent-based model is described in detail. To demonstrate the advantages of the model, we further created a filopodium-mediated signalling model. Our model revealed that diffusion and endocytosis alone are insufficient to produce significant signalling in a filopodia scenario. This is due to the bottleneck at the cell-filopodium contact region and the long distance to the end of the filopodium. However, allowing active transport of ligands into filopodia enhances the signalling significantly compared with a face-to-face scenario. We conclude that the agent-based approach can provide insights into mechanisms underlying cell signalling. The open-source model can be found in the Internet hosting service 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.

Mathematical modeling of tumor-induced immunosuppression by myeloid-derived suppressor cells: Implications for therapeutic targeting strategies

Myeloid-derived suppressor cells (MDSCs) belong to immature myeloid cells that are generated and accumulated during the tumor development. MDSCs strongly suppress the anti-tumor immunity and provide conditions for tumor progression and metastasis. In this study, we present a mathematical model based on ordinary differential equations (ODE) to describe tumor-induced immunosuppression caused by MDSCs. The model consists of four equations and incorporates tumor cells, cytotoxic T cells (CTLs), natural killer (NK) cells and MDSCs. We also provide simulation models that evaluate or predict the effects of anti-MDSC drugs (e.g., l-arginine and 5-Fluorouracil (5-FU)) on the tumor growth and the restoration of anti-tumor immunity. The simulated results obtained using our model were in good agreement with the corresponding experimental findings on the expansion of splenic MDSCs, immunosuppressive effects of these cells at the tumor site and effectiveness of l-arginine and 5-FU on the re-establishment of antitumor immunity. Regarding this latter issue, our predictive simulation results demonstrated that intermittent therapy with low-dose 5-FU alone could eradicate the tumors irrespective of their origins and types. Furthermore, at the time of tumor eradication, the number of CTLs prevailed over that of cancer cells and the number of splenic MDSCs returned to the normal levels. Finally, our predictive simulation results also showed that the addition of l-arginine supplementation to the intermittent 5-FU therapy reduced the time of the tumor eradication and the number of iterations for 5-FU treatment. Thus, the present mathematical model provides important implications for designing new therapeutic strategies that aim to restore antitumor immunity by targeting MDSCs.

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.

Combining Theoretical and Experimental Techniques to Study Murine Heart Transplant Rejection

The quality of life of organ transplant recipients is compromised by complications associated with life-long immunosuppression, such as hypertension, diabetes, opportunistic infections, and cancer. Moreover, the absence of established tolerance to the transplanted tissues causes limited long-term graft survival rates. Thus, there is a great medical need to understand the complex immune system interactions that lead to transplant rejection so that novel and effective strategies of intervention that redirect the system toward transplant acceptance (while preserving overall immune competence) can be identified. This study implements a systems biology approach in which an experimentally based mathematical model is used to predict how alterations in the immune response influence the rejection of mouse heart transplants. Five stages of conventional mouse heart transplantation are modeled using a system of 13 ordinary differential equations that tracks populations of both innate and adaptive immunity as well as proxies for pro- and anti-inflammatory factors within the graft and a representative draining lymph node. The model correctly reproduces known experimental outcomes, such as indefinite survival of the graft in the absence of CD4⁺ T cells and quick rejection in the absence of CD8⁺ T cells. The model predicts that decreasing the translocation rate of effector cells from the lymph node to the graft delays transplant rejection. Increasing the starting number of quiescent regulatory T cells in the model yields a significant but somewhat limited protective effect on graft survival. Surprisingly, the model shows that a delayed appearance of alloreactive T cells has an impact on graft survival that does not correlate linearly with the time delay. This computational model represents one of the first comprehensive approaches toward simulating the many interacting components of the immune system. Despite some limitations, the model provides important suggestions of experimental investigations that could improve the understanding of rejection. Overall, the systems biology approach used here is a first step in predicting treatments and interventions that can induce transplant tolerance while preserving the capacity of the immune system to protect against legitimate pathogens.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Computational immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.

Introduction of a Framework for Dynamic Knowledge Representation of the Control Structure of Transplant Immunology: Employing the Power of Abstraction with a Solid Organ Transplant Agent-Based Model

Agent-based modeling has been used to characterize the nested control loops and non-linear dynamics associated with inflammatory and immune responses, particularly as a means of visualizing putative mechanistic hypotheses. This process is termed dynamic knowledge representation and serves a critical role in facilitating the ability to test and potentially falsify hypotheses in the current data- and hypothesis-rich biomedical research environment. Importantly, dynamic computational modeling aids in identifying useful abstractions, a fundamental scientific principle that pervades the physical sciences. Recognizing the critical scientific role of abstraction provides an intellectual and methodological counterweight to the tendency in biology to emphasize comprehensive description as the primary manifestation of biological knowledge. Transplant immunology represents yet another example of the challenge of identifying sufficient understanding of the inflammatory/immune response in order to develop and refine clinically effective interventions. Advances in immunosuppressive therapies have greatly improved solid organ transplant (SOT) outcomes, most notably by reducing and treating acute rejection. The end goal of these transplant immune strategies is to facilitate effective control of the balance between regulatory T cells and the effector/cytotoxic T-cell populations in order to generate, and ideally maintain, a tolerant phenotype. Characterizing the dynamics of immune cell populations and the interactive feedback loops that lead to graft rejection or tolerance is extremely challenging, but is necessary if rational modulation to induce transplant tolerance is to be accomplished. Herein is presented the solid organ agent-based model (SOTABM) as an initial example of an agent-based model (ABM) that abstractly reproduces the cellular and molecular components of the immune response to SOT. Despite its abstract nature, the SOTABM is able to qualitatively reproduce acute rejection and the suppression of acute rejection by immunosuppression to generate transplant tolerance. The SOTABM is intended as an initial example of how ABMs can be used to dynamically represent mechanistic knowledge concerning transplant immunology in a scalable and expandable form and can thus potentially serve as useful adjuncts to the investigation and development of control strategies to induce transplant tolerance.

Multiscale modelling in immunology: a review

One of the greatest challenges in biomedicine is to get a unified view of observations made from the molecular up to the organism scale. Towards this goal, multiscale models have been highly instrumental in contexts such as the cardiovascular field, angiogenesis, neurosciences and tumour biology. More recently, such models are becoming an increasingly important resource to address immunological questions as well. Systematic mining of the literature in multiscale modelling led us to identify three main fields of immunological applications: host-virus interactions, inflammatory diseases and their treatment and development of multiscale simulation platforms for immunological research and for educational purposes. Here, we review the current developments in these directions, which illustrate that multiscale models can consistently integrate immunological data generated at several scales, and can be used to describe and optimize therapeutic treatments of complex immune diseases.

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

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

Modeling the T cell immune response: a fascinating challenge

The immune system is designed to protect the organism from infection and to repair damaged tissue. An effective response requires recognition of the threat, the appropriate effector mechanism to clear the pathogen and a return to homeostasis with minimal damage to self-tissues. T cells play a central role in orchestrating the immune response at all stages of the response and have been the subject of intense study by both experimental immunologists and modelers. This review examines some of the more critical questions in T cell biology and describes the latest attempts to address those questions using approaches that combine mathematical modeling and experiments.

Agent-based model of fecal microbial transplant effect on bile acid metabolism on suppressing Clostridium difficile infection: an example of agent-based modeling of intestinal bacterial infection

Agent-based modeling is a computational modeling method that represents system-level behavior as arising from multiple interactions between the multiple components that make up a system. Biological systems are thus readily described using agent-based models (ABMs), as multi-cellular organisms can be viewed as populations of interacting cells, and microbial systems manifest as colonies of individual microbes. Intersections between these two domains underlie an increasing number of pathophysiological processes, and the intestinal tract represents one of the most significant locations for these inter-domain interactions, so much so that it can be considered an internal ecology of varying robustness and function. Intestinal infections represent significant disturbances of this internal ecology, and one of the most clinically relevant intestinal infections is Clostridium difficile infection (CDI). CDI is precipitated by the use of broad-spectrum antibiotics, involves the depletion of commensal microbiota, and alterations in bile acid composition in the intestinal lumen. We present an example ABM of CDI (the C. difficile Infection ABM, or CDIABM) to examine fundamental dynamics of the pathogenesis of CDI and its response to treatment with anti-CDI antibiotics and a newer treatment therapy, fecal microbial transplant. The CDIABM focuses on one specific mechanism of potential CDI suppression: commensal modulation of bile acid composition. Even given its abstraction, the CDIABM reproduces essential dynamics of CDI and its response to therapy, and identifies a paradoxical zone of behavior that provides insight into the role of intestinal nutritional status and the efficacy of anti-CDI therapies. It is hoped that this use case example of the CDIABM can demonstrate the usefulness of both agent-based modeling and the application of abstract functional representation as the biomedical community seeks to address the challenges of increasingly complex diseases with the goal of personalized medicine.

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.

Modeling biology spanning different scales: an open challenge

It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.

Alloprimed CD8(+) T cells regulate alloantibody and eliminate alloprimed B cells through perforin- and FasL-dependent mechanisms

While it is well known that CD4(+) T cells and B cells collaborate for antibody production, our group previously reported that CD8(+) T cells down-regulate alloantibody responses following transplantation. However, the exact mechanism involved in CD8(+) T cell-mediated down-regulation of alloantibody remains unclear. We also reported that alloantibody production is enhanced when either perforin or FasL is deficient in transplant recipients. Here, we report that CD8(+) T cell-deficient transplant recipient mice (high alloantibody producers) exhibit an increased number of primed B cells compared to WT transplant recipients. Furthermore, CD8(+) T cells require FasL, perforin and allospecificity to down-regulate posttransplant alloantibody production. In vivo CD8-mediated clearance of alloprimed B cells was also FasL- and perforin-dependent. In vitro data demonstrated that recipient CD8(+) T cells directly induce apoptosis of alloprimed IgG1(+) B cells in co-culture in an allospecific and MHC class I-dependent fashion. Altogether these data are consistent with the interpretation that CD8(+) T cells down-regulate posttransplant alloantibody production by FasL- and perforin-dependent direct elimination of alloprimed IgG1(+) B cells.

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.

Systems biological approaches to measure and understand vaccine immunity in humans

Recent studies have demonstrated the utility of using systems approaches to identify molecular signatures that can be used to predict vaccine immunity in humans. Such approaches are now being used extensively in vaccinology, and are beginning to yield novel insights about the molecular networks driving vaccine immunity. In this review, we present a broad review of the methodologies involved in these studies, and discuss the promise and challenges involved in this emerging field of "systems vaccinology."

Functional complexity of the Leishmania granuloma and the potential of in silico modeling

In human and canine visceral leishmaniasis and in various experimental models of this disease, host resistance is strongly linked to efficient granuloma development. However, it is unknown exactly how the granuloma microenvironment executes an effective antileishmanial response. Recent studies, including using advanced imaging techniques, have improved our understanding of granuloma biology at the cellular level, highlighting heterogeneity in granuloma development and function, and hinting at complex cellular, temporal, and spatial dynamics. In this mini-review, we discuss the factors involved in the formation and function of Leishmania donovani-induced hepatic granulomas, as well as their importance in protecting against inflammation-associated tissue damage and the generation of immunity to rechallenge. Finally, we discuss the role that computational, agent-based models may play in answering outstanding questions within the field.

Understanding natural killer cell regulation by mathematical approaches

The activity of natural killer (NK) cells is regulated by various processes including education/licensing, priming, integration of positive and negative signals through an array of activating and inhibitory receptors, and the development of memory-like functionality. These processes are often very complex due to the large number of different receptors and signaling pathways involved. Understanding these complex mechanisms is therefore a challenge, but is critical for understanding NK cell regulation. Mathematical approaches can facilitate the analysis and understanding of complex systems. Therefore, they may be instrumental for studies in NK cell biology. Here we provide a review of the different mathematical approaches to the analysis of NK cell signal integration, activation, proliferation, and the acquisition of inhibitory receptors. These studies show how mathematical methods can aid the analysis of NK cell regulation.

A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,42,48,49]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,52,54]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.

Models and methods for analysis of lymphocyte repertoire generation, development, selection and evolution

T and B cell receptor repertoires are diversified by variable region gene rearrangement and selected based on functionality and lack of self-reactivity. Repertoires can also be defined based on phenotype and function rather than receptor specificity - such as the diversity of T helper cell subsets. Natural killer (NK) cell repertoires, in which each cell expresses a randomly chosen subset of its inhibitory receptor genes, and is educated based on self-MHC recognition by yet unknown mechanisms, are also phenotypic repertoires. Studying the generation, development and selection of lymphocyte repertoires, and their functions during immune responses, is essential for understanding the function of the immune system in healthy individuals and in immune deficient, autoimmune or cancer patients. The study of lymphocyte repertoires will enable clinical immunologists to develop better therapeutic monoclonal antibodies, vaccines, transplantation donor-recipient matching protocols, and other immune intervention strategies. The recent development of high-throughput methods for repertoire data collection - from multicolor flow cytometry through single-cell imaging to deep sequencing - presents us now, for the first time, with the ability to analyze and compare large samples of lymphocyte repertoires in health, aging and disease. The exponential growth of these datasets, however, challenges the theoretical immunology community to develop methods for data organization and analysis. Furthermore, the need to test hypotheses regarding immune function, and generate predictions regarding the outcomes of medical interventions, necessitates the development of complex mathematical and computational models, covering processes on multiple scales, from the genetic and molecular to the cellular and system scales.

A new model for the estimation of cell proliferation dynamics using CFSE data

CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.

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 hybrid multi-compartment model of granuloma formation and T cell priming in tuberculosis

Tuberculosis is a worldwide health problem with 2 billion people infected with Mycobacterium tuberculosis (Mtb, the bacteria causing TB). The hallmark of infection is the emergence of organized structures of immune cells forming primarily in the lung in response to infection. Granulomas physically contain and immunologically restrain bacteria that cannot be cleared. We have developed several models that spatially characterize the dynamics of the host-mycobacterial interaction, and identified mechanisms that control granuloma formation and development. In particular, we published several agent-based models (ABMs) of granuloma formation in TB that include many subtypes of T cell populations, macrophages as well as key cytokine and chemokine effector molecules. These ABM studies emphasize the important role of T-cell related mechanisms in infection progression, such as magnitude and timing of T cell recruitment, and macrophage activation. In these models, the priming and recruitment of T cells from the lung draining lymph node (LN) was captured phenomenologically. In addition to these ABM studies, we have also developed several multi-organ models using ODEs to examine trafficking of cells between, for example, the lung and LN. While we can predict temporal dynamic behaviors, those models are not coupled to the spatial aspects of granuloma. To this end, we have developed a multi-organ model that is hybrid: an ABM for the lung compartment and a non-linear system of ODE representing the lymph node compartment. This hybrid multi-organ approach to study TB granuloma formation in the lung and immune priming in the LN allows us to dissect protective mechanisms that cannot be achieved using the single compartment or multi-compartment ODE system. The main finding of this work is that trafficking of important cells known as antigen presenting cells from the lung to the lymph node is a key control mechanism for protective immunity: the entire spectrum of infection outcomes can be regulated by key immune cell migration rates. Our hybrid multi-organ implementation suggests that effector CD4+ T cells can rescue the system from a persistent infection and lead to clearance once a granuloma is fully formed. This could be effective as an immunotherapy strategy for latently infected individuals.

Emerging vaccine informatics

Vaccine informatics is an emerging research area that focuses on development and applications of bioinformatics methods that can be used to facilitate every aspect of the preclinical, clinical, and postlicensure vaccine enterprises. Many immunoinformatics algorithms and resources have been developed to predict T- and B-cell immune epitopes for epitope vaccine development and protective immunity analysis. Vaccine protein candidates are predictable in silico from genome sequences using reverse vaccinology. Systematic transcriptomics and proteomics gene expression analyses facilitate rational vaccine design and identification of gene responses that are correlates of protection in vivo. Mathematical simulations have been used to model host-pathogen interactions and improve vaccine production and vaccination protocols. Computational methods have also been used for development of immunization registries or immunization information systems, assessment of vaccine safety and efficacy, and immunization modeling. Computational literature mining and databases effectively process, mine, and store large amounts of vaccine literature and data. Vaccine Ontology (VO) has been initiated to integrate various vaccine data and support automated reasoning.

T cell state transition produces an emergent change detector

We model the stages of a T cell response from initial activation to T cell expansion and contraction using a system of ordinary differential equations. Results of this modeling suggest that state transitions enable the T cell population to detect change and respond effectively to changes in antigen stimulation levels, rather than simply the presence or absence of antigen. A key component of the system that gives rise to this emergent change detector is initial activation of naïve T cells. The activation step creates a barrier that separates the long-term, slow dynamics of naïve T cells from the short-term, fast dynamics of effector T cells. This separation allows the T cell population to compare current, up-to-date changes in antigen levels to long-term, steady state levels. As a result, the T cell population responds very effectively to sudden shifts in antigen levels, even if the antigen were already present prior to the change. This feature provides a mechanism for T cells to react to rapidly expanding sources of antigen stimulation, such as viruses, while maintaining tolerance to constant or slowly fluctuating sources of stimulation, such as healthy tissue during growth. In addition to modeling T cell activation, we also formulate a model of the proliferation of effector T cells in response to the consumption of positive growth signal, secreted throughout the T cell response. We discuss how the interaction between T cells and growth signal generates an emergent threshold detector that responds preferentially to large changes in antigen stimulation while ignoring small ones. As a final step, we discuss how the de novo generation of adaptive regulatory T cells during the latter phase of the T cell response creates a negative feedback loop that controls the duration and magnitude of the T cell response. Hence, the immune network continually adjusts to a shifting baseline of (self and non-self) antigens, and responds primarily to abrupt changes in these antigens rather than merely their presence or absence.

T cell responses in lymph nodes

Activation of T cells by antigen-presenting cells (APCs) in lymph nodes (LNs) is a key initiating event in many immune responses. Our understanding of this process has been both improved and complicated in recent years by evidence from techniques such as intravital microscopy that has revealed new levels of dynamism in the interaction of T cells and APCs. In particular, the complex motility of T cells within LNs, and their serial interactions with many APCs, imply that earlier static models of T cell activation need to be updated. Here we review the first attempts to model T cell interactions with APCs in LNs that incorporate simulations of T cell motility, based on experimental observations. We show that lattice-based modeling approaches are the dominant trend in these models, and then chart a possible course for development of these models toward spatially-resolved models of immune responses within LNs.

A multiscale systems perspective on cancer, immunotherapy, and Interleukin-12

Monoclonal antibodies represent some of the most promising molecular targeted immunotherapies. However, understanding mechanisms by which tumors evade elimination by the immune system of the host presents a significant challenge for developing effective cancer immunotherapies. The interaction of cancer cells with the host is a complex process that is distributed across a variety of time and length scales. The time scales range from the dynamics of protein refolding (i.e., microseconds) to the dynamics of disease progression (i.e., years). The length scales span the farthest reaches of the human body (i.e., meters) down to the range of molecular interactions (i.e., nanometers). Limited ranges of time and length scales are used experimentally to observe and quantify changes in physiology due to cancer. Translating knowledge obtained from the limited scales observed experimentally to predict patient response is an essential prerequisite for the rational design of cancer immunotherapies that improve clinical outcomes. In studying multiscale systems, engineers use systems analysis and design to identify important components in a complex system and to test conceptual understanding of the integrated system behavior using simulation. The objective of this review is to summarize interactions between the tumor and cell-mediated immunity from a multiscale perspective. Interleukin-12 and its role in coordinating antibody-dependent cell-mediated cytotoxicity is used illustrate the different time and length scale that underpin cancer immunoediting. An underlying theme in this review is the potential role that simulation can play in translating knowledge across scales.

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.

Identification of key processes that control tumor necrosis factor availability in a tuberculosis granuloma

Tuberculosis (TB) granulomas are organized collections of immune cells comprised of macrophages, lymphocytes and other cells that form in the lung as a result of immune response to Mycobacterium tuberculosis (Mtb) infection. Formation and maintenance of granulomas are essential for control of Mtb infection and are regulated in part by a pro-inflammatory cytokine, tumor necrosis factor-α (TNF). To characterize mechanisms that control TNF availability within a TB granuloma, we developed a multi-scale two compartment partial differential equation model that describes a granuloma as a collection of immune cells forming concentric layers and includes TNF/TNF receptor binding and trafficking processes. We used the results of sensitivity analysis as a tool to identify experiments to measure critical model parameters in an artificial experimental model of a TB granuloma induced in the lungs of mice following injection of mycobacterial antigen-coated beads. Using our model, we then demonstrated that the organization of immune cells within a TB granuloma as well as TNF/TNF receptor binding and intracellular trafficking are two important factors that control TNF availability and may spatially coordinate TNF-induced immunological functions within a granuloma. Further, we showed that the neutralization power of TNF-neutralizing drugs depends on their TNF binding characteristics, including TNF binding kinetics, ability to bind to membrane-bound TNF and TNF binding stoichiometry. To further elucidate the role of TNF in the process of granuloma development, our modeling and experimental findings on TNF-associated molecular scale aspects of the granuloma can be incorporated into larger scale models describing the immune response to TB infection. Ultimately, these modeling and experimental results can help identify new strategies for TB disease control/therapy.

Tuberculosis is a common and deadly infectious disease caused by a highly successful bacterium, Mycobacterium tuberculosis (Mtb). Multiple host immune factors control the formation of a self-organizing aggregate of immune cells termed a granuloma in the lungs after inhalation of Mtb. One such factor, tumor necrosis factor-α (TNF), is a protein that regulates inflammatory immune responses. Availability of TNF within a TB granuloma has been proposed to have a critical role in the protective immunity against TB. However, direct measurement of the level of TNF in a granuloma is not experimentally feasible. Therefore, we develop a mathematical model based on an experimental model of granuloma developed in mice to predict TNF availability in a granuloma. We measure values of critical model parameters and explore mechanisms that influence TNF availability in the granuloma. We find that cellular organization in a granuloma and intracellular trafficking of TNF control TNF availability in a granuloma. Further, our model analysis also highlights anti-TNF drug properties that determine their TNF neutralization power. Our findings complement and extend those of recent studies on the role of TNF in the immune response against TB.

Characterizing the dynamics of CD4+ T cell priming within a lymph node

Generating adaptive immunity postinfection or immunization requires physical interaction within a lymph node T zone between Ag-bearing dendritic cells (DCs) and rare cognate T cells. Many fundamental questions remain regarding the dynamics of DC-CD4+ T cell interactions leading to priming. For example, it is not known how the production of primed CD4+ T cells relates to the numbers of cognate T cells, Ag-bearing DCs, or peptide-MHCII level on the DC. To address these questions, we developed an agent-based model of a lymph node to examine the relationships among cognate T cell frequency, DC density, parameters characterizing DC-T cell interactions, and the output of primed T cells. We found that the output of primed CD4+ T cells is linearly related to cognate frequency, but nonlinearly related to the number of Ag-bearing DCs present during infection. This addresses the applicability of two photon microscopy studies to understanding actual infection dynamics, because these types of experiments increase the cognate frequency by orders of magnitude compared with physiologic levels. We found a trade-off between the quantity of peptide-major histocompatibility class II on the surface of individual DCs and number of Ag-bearing DCs present in the lymph node in contributing to the production of primed CD4+ T cells. Interestingly, peptide-major histocompatibility class II t(1/2) plays a minor, although still significant, role in determining CD4+ T cell priming, unlike the primary role that has been suggested for CD8+ T cell priming. Finally, we identify several pathogen-targeted mechanisms that, if altered in their efficiency, can significantly effect the generation of primed CD4+ T cells.

Virtual tissues in toxicology

New approaches are vital for efficiently evaluating human health risk of thousands of chemicals in commerce. In vitro models offer a high-throughput approach for assaying chemical-induced molecular and cellular changes; however, bridging these perturbations to in vivo effects across chemicals, dose, time, and species remains challenging. Technological advances in multiresolution imaging and multiscale simulation are making it feasible to reconstruct tissues in silico. In toxicology, these "virtual" tissues (VT) aim to predict histopathological outcomes from alterations of cellular phenotypes that are controlled by chemical-induced perturbations in molecular pathways. The behaviors of thousands of heterogeneous cells in tissues are simulated discretely using agent-based modeling (ABM), in which computational "agents" mimic cell interactions and cellular responses to the microenvironment. The behavior of agents is constrained by physical laws and biological rules derived from experimental evidence. VT extend compartmental physiologic models to simulate both acute insults as well as the chronic effects of low-dose exposure. Furthermore, agent behavior can encode the logic of signaling and genetic regulatory networks to evaluate the role of different pathways in chemical-induced injury. To extrapolate toxicity across species, chemicals, and doses, VT require four main components: (a) organization of prior knowledge on physiologic events to define the mechanistic rules for agent behavior, (b) knowledge on key chemical-induced molecular effects, including activation of stress sensors and changes in molecular pathways that alter the cellular phenotype, (c) multiresolution quantitative and qualitative analysis of histologic data to characterize and measure chemical-, dose-, and time-dependent physiologic events, and (d) multiscale, spatiotemporal simulation frameworks to effectively calibrate and evaluate VT using experimental data. This investigation presents the motivation, implementation, and application of VT with examples from hepatotoxicity and carcinogenesis.

Agent-based simulation of T-cell activation and proliferation within a lymph node

Recent intravital microscopy experiments have revealed the complex behavior of T cells within lymph nodes. Modeling T-cell responses in lymph nodes now requires integration of cell trafficking and motility with the molecular processes involved in T-cell activation. We describe an agent-based model that allows such integration, in which T cells undertake a random walk through a three-dimensional representation of the lymph node paracortex, integrating signals from dendritic cells (DCs), and proliferating in response. The model accommodates simulation of a large number of T cells packed at realistic densities, and includes dynamic cell trafficking that allows the lymph nodes to swell and shrink as the immune response progresses. The results from the model, including the kinetics of cognate T-cell proliferation and release, and the changes in their avidity profile, are similar to those observed in vivo. We therefore propose that this modeling framework is capable of successfully simulating T-cell activation while also accounting for new spatiotemporal knowledge of how T cells and DCs interact. Although some of the parameters used to drive the model are not yet experimentally validated, the model is capable of testing the effects of alternative values for any parameter on the T-cell response. We intend to refine each aspect of the model in collaboration with both theoreticians and experimentalists.

A systems biology network model for genetic association studies of nicotine addiction and treatment

OBJECTIVE

Interpreting genome-scale genetic association data, particularly for complex diseases and phenotypes, requires extensive use of prior knowledge across a broad range of potential biological and environmental influences, spanning many scientific subdisciplines. We suggest that known or hypothesized disease risk factors, and causal mechanisms, can be represented using an ontology, a computational specification of a set of concepts and the relations between them.

METHODS

We have integrated the expertise of multiple investigators in nicotine pharmacokinetics and pharmacodynamics, nicotine dependence, and clinical smoking cessation outcomes, and represented this knowledge in an ontology-based network model. Our model spans multiple scales, from molecules, genes and cellular pathways, to complex behavioral phenotypes and even environmental factors. To leverage previous and ongoing work in the field of ontology development, we adopt, expand upon and relate elements from existing ontologies whenever possible.

RESULTS

We discuss several applications of our ontology: to support interdisciplinary research by graphically representing a complex scientific theory, to facilitate meta-analysis across different studies, to highlight potential interactions, and to support statistical analysis and causal modeling. We demonstrate that our ontology can focus hypothesis testing on areas supported by current theory.

CONCLUSION

We describe how an ontology-based computational representation can be applied to disease risk factors and mechanisms, enabling the use of prior knowledge in large-scale genetic association studies in general. In specific, we have developed an initial Smoking Behavior Risk Ontology to support studies related to the pharmacogenetics of nicotine addiction and treatment.

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

In addition to traditional and novel experimental approaches to study host-pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host-pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or 'in silico' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host-pathogen interactions.

Agent-based modeling of host-pathogen systems: The successes and challenges

Agent-based models have been employed to describe numerous processes in immunology. Simulations based on these types of models have been used to enhance our understanding of immunology and disease pathology. We review various agent-based models relevant to host–pathogen systems and discuss their contributions to our understanding of biological processes. We then point out some limitations and challenges of agent-based models and encourage efforts towards reproducibility and model validation.

Dynamic knowledge representation using agent-based modeling: ontology instantiation and verification of conceptual models

The sheer volume of biomedical research threatens to overwhelm the capacity of individuals to effectively process this information. Adding to this challenge is the multiscale nature of both biological systems and the research community as a whole. Given this volume and rate of generation of biomedical information, the research community must develop methods for robust representation of knowledge in order for individuals, and the community as a whole, to "know what they know." Despite increasing emphasis on "data-driven" research, the fact remains that researchers guide their research using intuitively constructed conceptual models derived from knowledge extracted from publications, knowledge that is generally qualitatively expressed using natural language. Agent-based modeling (ABM) is a computational modeling method that is suited to translating the knowledge expressed in biomedical texts into dynamic representations of the conceptual models generated by researchers. The hierarchical object-class orientation of ABM maps well to biomedical ontological structures, facilitating the translation of ontologies into instantiated models. Furthermore, ABM is suited to producing the nonintuitive behaviors that often "break" conceptual models. Verification in this context is focused at determining the plausibility of a particular conceptual model, and qualitative knowledge representation is often sufficient for this goal. Thus, utilized in this fashion, ABM can provide a powerful adjunct to other computational methods within the research process, as well as providing a metamodeling framework to enhance the evolution of biomedical ontologies.

Introduction of an agent-based multi-scale modular architecture for dynamic knowledge representation of acute inflammation

Background

One of the greatest challenges facing biomedical research is the integration and sharing of vast amounts of information, not only for individual researchers, but also for the community at large. Agent Based Modeling (ABM) can provide a means of addressing this challenge via a unifying translational architecture for dynamic knowledge representation. This paper presents a series of linked ABMs representing multiple levels of biological organization. They are intended to translate the knowledge derived from in vitro models of acute inflammation to clinically relevant phenomenon such as multiple organ failure.

Results and Discussion

ABM development followed a sequence starting with relatively direct translation from in-vitro derived rules into a cell-as-agent level ABM, leading on to concatenated ABMs into multi-tissue models, eventually resulting in topologically linked aggregate multi-tissue ABMs modeling organ-organ crosstalk. As an underlying design principle organs were considered to be functionally composed of an epithelial surface, which determined organ integrity, and an endothelial/blood interface, representing the reaction surface for the initiation and propagation of inflammation. The development of the epithelial ABM derived from an in-vitro model of gut epithelial permeability is described. Next, the epithelial ABM was concatenated with the endothelial/inflammatory cell ABM to produce an organ model of the gut. This model was validated against in-vivo models of the inflammatory response of the gut to ischemia. Finally, the gut ABM was linked to a similarly constructed pulmonary ABM to simulate the gut-pulmonary axis in the pathogenesis of multiple organ failure. The behavior of this model was validated against in-vivo and clinical observations on the cross-talk between these two organ systems

Conclusion

A series of ABMs are presented extending from the level of intracellular mechanism to clinically observed behavior in the intensive care setting. The ABMs all utilize cell-level agents that encapsulate specific mechanistic knowledge extracted from in vitro experiments. The execution of the ABMs results in a dynamic representation of the multi-scale conceptual models derived from those experiments. These models represent a qualitative means of integrating basic scientific information on acute inflammation in a multi-scale, modular architecture as a means of conceptual model verification that can potentially be used to concatenate, communicate and advance community-wide knowledge.

Effect of multiple genetic polymorphisms on antigen presentation and susceptibility to Mycobacterium tuberculosis infection

Several molecules related to antigen presentation, including gamma interferon (IFN-gamma) and the major histocompatibility complex (MHC), are encoded by polymorphic genes. Some polymorphisms were found to affect susceptibility to tuberculosis (TB) when they were considered singly in epidemiological studies, but how multiple polymorphisms interact to determine susceptibility to TB in an individual remains an open question. We hypothesized that polymorphisms in some genes may counteract or intensify the effects of polymorphisms in other genes. For example, an increase in IFN-gamma expression may counteract the weak binding that a particular MHC variant displays for a peptide from Mycobacterium tuberculosis to establish the same T-cell response as another, more strongly binding MHC variant. To test this hypothesis, we developed a mathematical model of antigen presentation based on experimental data for the known effects of genetic polymorphisms and simulated time courses when multiple polymorphisms were present. We found that polymorphisms in different genes could affect antigen presentation to the same extent and therefore compensate for each other. Furthermore, we defined the conditions under which such relationships could exist. For example, increased IFN-gamma expression compensated for decreased peptide-MHC affinity in the model only above a certain threshold of expression. Below this threshold, changes in IFN-gamma expression were ineffectual compared to changes in peptide-MHC affinity. The finding that polymorphisms exhibit such relationships could explain discrepancies in the epidemiological literature, where some polymorphisms have been inconsistently associated with susceptibility to TB. Furthermore, the model allows polymorphisms to be ranked by effect, providing a new tool for designing association studies.