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

ABCD of IA: A multi-scale agent-based model of T cell activation in inflammatory arthritis

Biomaterial-based agents have been demonstrated to regulate the function of immune cells in models of autoimmunity. However, the complexity of the kinetics of immune cell activation can present a challenge in optimizing the dose and frequency of administration. Here, we report a model of autoreactive T cell activation, which are key drivers in autoimmune inflammatory joint disease. The model is termed a multi-scale Agent-Based, Cell-Driven model of Inflammatory Arthritis (ABCD of IA). Using kinetic rate equations and statistical theory, ABCD of IA simulated the activation and presentation of autoantigens by dendritic cells, interactions with cognate T cells and subsequent T cell proliferation in the lymph node and IA-affected joints. The results, validated with in vivo data from the T cell driven SKG mouse model, showed that T cell proliferation strongly correlated with the T cell receptor (TCR) affinity distribution (TCR-ad), with a clear transition state from homeostasis to an inflammatory state. T cell proliferation was strongly dependent on the amount of antigen in antigenic stimulus event (ASE) at low concentrations. On the other hand, inflammation driven by Th17-inducing cytokine mediated T cell phenotype commitment was influenced by the initial level of Th17-inducing cytokines independent of the amount of arthritogenic antigen. The introduction of inhibitory artificial antigen presenting cells (iaAPCs), which locally suppress T cell activation, reduced T cell proliferation in a dose-dependent manner. The findings in this work set up a framework based on theory and modeling to simulate personalized therapeutic strategies in IA.

Transport Barriers Influence the Activation of Anti-Tumor Immunity: A Systems Biology Analysis

Effective anti-cancer immune responses require activation of one or more naïve T cells. If the correct naïve T cell encounters its cognate antigen presented by an antigen presenting cell, then the T cell can activate and proliferate. Here, mathematical modeling is used to explore the possibility that immune activation in lymph nodes is a rate-limiting step in anti-cancer immunity and can affect response rates to immune checkpoint therapy. The model provides a mechanistic framework for optimizing cancer immunotherapy and developing testable solutions to unleash anti-tumor immune responses for more patients with cancer. The results show that antigen production rate and trafficking of naïve T cells into the lymph nodes are key parameters and that treatments designed to enhance tumor antigen production can improve immune checkpoint therapies. The model underscores the potential of radiation therapy in augmenting tumor immunogenicity and neoantigen production for improved ICB therapy, while emphasizing the need for careful consideration in cases where antigen levels are already sufficient to avoid compromising the immune response.

New tools for immunologists: models of lymph node function from cells to tissues

The lymph node is a highly structured organ that mediates the body's adaptive immune response to antigens and other foreign particles. Central to its function is the distinct spatial assortment of lymphocytes and stromal cells, as well as chemokines that drive the signaling cascades which underpin immune responses. Investigations of lymph node biology were historically explored in vivo in animal models, using technologies that were breakthroughs in their time such as immunofluorescence with monoclonal antibodies, genetic reporters, in vivo two-photon imaging, and, more recently spatial biology techniques. However, new approaches are needed to enable tests of cell behavior and spatiotemporal dynamics under well controlled experimental perturbation, particularly for human immunity. This review presents a suite of technologies, comprising in vitro, ex vivo and in silico models, developed to study the lymph node or its components. We discuss the use of these tools to model cell behaviors in increasing order of complexity, from cell motility, to cell-cell interactions, to organ-level functions such as vaccination. Next, we identify current challenges regarding cell sourcing and culture, real time measurements of lymph node behavior in vivo and tool development for analysis and control of engineered cultures. Finally, we propose new research directions and offer our perspective on the future of this rapidly growing field. We anticipate that this review will be especially beneficial to immunologists looking to expand their toolkit for probing lymph node structure and function.

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

The lymph node (LN) is a vital organ of the lymphatic and immune system that enables timely detection, response, and clearance of harmful substances from the body. Each LN comprises of distinct substructures, which host a plethora of immune cell types working in tandem to coordinate complex innate and adaptive immune responses. An improved understanding of LN biology could facilitate treatment in LN-associated pathologies and immunotherapeutic interventions, yet at present, animal models, which often have poor physiological relevance, are the most popular experimental platforms. Emerging biomaterial engineering offers powerful alternatives, with the potential to circumvent limitations of animal models, for in-depth characterization and engineering of the lymphatic and adaptive immune system. In addition, mathematical and computational approaches, particularly in the current age of big data research, are reliable tools to verify and complement biomaterial works. In this review, we first discuss the importance of lymph node in immunity protection followed by recent advances using biomaterials to create in vitro/vivo LN-mimicking models to recreate the lymphoid tissue microstructure and microenvironment, as well as to describe the related immuno-functionality for biological investigation. We also explore the great potential of mathematical and computational models to serve as in silico supports. Furthermore, we suggest how both in vitro/vivo and in silico approaches can be integrated to strengthen basic patho-biological research, translational drug screening and clinical personalized therapies. We hope that this review will promote synergistic collaborations to accelerate progress of LN-mimicking systems to enhance understanding of immuno-complexity.

Predicting efficacy of 5-fluorouracil therapy via a mathematical model with fuzzy uncertain parameters

Background:

Due to imprecise/missing data used for parameterization of ordinary differential equations (ODEs), model parameters are uncertain. Uncertainty of parameters has hindered the application of ODEs that require accurate parameters.

Methods:

We extended an available ODE model of tumor-immune system interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. The fuzzy ODE (FODE) model assigns a fuzzy number to the parameters, to capture parametric uncertainty. We used the FODE model to predict tumor and immune cell dynamics and to assess the efficacy of 5-fluorouracil (5-FU) chemotherapy.

Result:

FODE model investigates how parametric uncertainty affects the uncertainty band of cell dynamics in the presence and absence of 5-FU treatment. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and natural killer cells, and decreasing that of myeloid-derived suppressor cells. The global sensitivity analysis was proved model robustness against random perturbation to parameters.

Conclusion:

ODE models with fuzzy uncertain kinetic parameters cope with insufficient/imprecise experimental data in the field of mathematical oncology and can predict cell dynamics uncertainty band.

Lymph node swelling combined with temporary effector T cell retention aids T cell response in a model of adaptive immunity

Swelling of lymph nodes (LNs) is commonly observed during the adaptive immune response, yet the impact on T cell (TC) trafficking and subsequent immune response is not well known. To better understand the effect of macro-scale alterations, we developed an agent-based model of the LN paracortex, describing the TC proliferative response to antigen-presenting dendritic cells alongside inflammation-driven and swelling-induced changes in TC recruitment and egress, while also incorporating regulation of the expression of egress-modulating TC receptor sphingosine-1-phosphate receptor-1. Analysis of the effector TC response under varying swelling conditions showed that swelling consistently aided TC activation. However, subsequent effector CD8+ TC production was reduced in scenarios where swelling occurred too early in the TC proliferative phase or when TC cognate frequency was low due to increased opportunity for TC exit. Temporarily extending retention of newly differentiated effector TCs, mediated by sphingosine-1-phosphate receptor-1 expression, mitigated any negative effects of swelling by allowing facilitation of activation to outweigh increased access to exit areas. These results suggest that targeting temporary effector TC retention and egress associated with swelling offers new ways to modulate effector TC responses in, for example, immuno-suppressed patients and to optimize of vaccine design.

Assessing the impact of HIV treatment interruptions using stochastic cellular Automata

Chronic HIV infection causes a progressive decrease in the ability to maintain homeostasis resulting, after some time, in eventual break down of immune functions. Recent clinical research has shed light on a significant contribution of the lymphatic tissues, where HIV causes accumulation of collagen, (fibrosis). Specifically, where tissue is populated by certain types of functional stromal cells designated Fibroblastic Reticular Cells (FRCs), these have been found to play a crucial role in balancing out apoptosis and regeneration of naïve T-cells through 2-way cellular signaling. Tissue fibrosis not only impedes this signaling, effectively reducing T-cell levels through increased apoptosis of cells of both T- and FRC type but has been found to be irreversible by current HIV standard treatment (cART). While the therapy aims to block the viral lifecycle, cART-associated increase of T-cell levels in blood appears to conceal existing FRC impairment through fibrosis. This hidden impairment can lead to adverse consequences if treatment is interrupted, e.g. due to poor adherence (missing doses) or through periods recovering from drug toxicities. Formal clinical studies on treatment interruption have indicated possible adverse effects, but quantification of those effects in relation to interruption protocol and patient predisposition remains unclear. Accordingly, the impact of treatment interruption on lymphatic tissue structure and T-cell levels is explored here by means of computer simulation. A novel Stochastic Cellular Automata model is proposed, which utilizes all sources of clinical detail available to us (though sparse in part) for model parametrization. Sources are explicitly referenced and conflicting evidence from previous studies explored. The main focus is on (i) spatial aspects of collagen build up, together with (ii) collagen increase after repeated treatment interruptions to explore the dynamics of HIV-induced fibrosis and T-cell loss.

The regulation of DOCK family proteins on T and B cells

The dedicator of cytokinesis (DOCK) family proteins consist of 11 members, each of which contains 2 domains, DOCK homology region (DHR)-1 and DHR-2, and as guanine nucleotide exchange factors, they mediate activation of small GTPases. Both DOCK2 and DOCK8 deficiencies in humans can cause severe combined immunodeficiency, but they have different characteristics. DOCK8 defect mainly causes high IgE, allergic disease, refractory skin virus infection, and increased incidence of malignant tumor, whereas DOCK2 defect mainly causes early-onset, invasive infection with less atopy and increased IgE. However, the underlying molecular mechanisms causing the disease remain unclear. This paper discusses the role of DOCK family proteins in regulating B and T cells, including development, survival, migration, activation, immune tolerance, and immune functions. Moreover, related signal pathways or molecule mechanisms are also described in this review. A greater understanding of DOCK family proteins and their regulation of lymphocyte functions may facilitate the development of new therapeutics for immunodeficient patients and improve their prognosis.

An in silico model of cytotoxic T-lymphocyte activation in the lymph node following short peptide vaccination

Tumour immunotherapy is dependent upon activation and expansion of tumour-targetting immune cells, known as cytotoxic T-lymphocytes (CTLs). Cancer vaccines developed in the past have had limited success and the mechanisms resulting in failure are not well characterized. To elucidate these mechanisms, we developed a human-parametrized, in silico, agent-based model of vaccination-driven CTL activation within a clinical short-peptide vaccination context. The simulations predict a sharp transition in the probability of CTL activation, which occurs with variation in the separation rate (or off-rate) of tumour-specific immune response-inducing peptides (cognate antigen) from the major histocompatibility class I (MHC-I) receptors of dendritic cells (DCs) originally at the vaccination site. For peptides with MHC-I off-rates beyond this transition, it is predicted that no vaccination strategy will lead to successful expansion of CTLs. For slower off-rates, below the transition, the probability of CTL activation becomes sensitive to the numbers of DCs and T cells that interact subsequent to DC migration to the draining lymph node of the vaccination site. Thus, the off-rate is a key determinant of vaccine design.

Role of T Cell-To-Dendritic Cell Chemoattraction in T Cell Priming Initiation in the Lymph Node: An Agent-Based Modeling Study

The adaptive immune response is initiated in lymph nodes by contact between antigen-bearing dendritic cells (DCs) and antigen-specific T cells. A selected number of naïve T cells that recognize a specific antigen may proliferate into expanded clones, differentiate, and acquire an effector phenotype. Despite growing experimental knowledge, certain mechanistic aspects of T cell behavior in lymph nodes remain poorly understood. Computational modeling approaches may help in addressing such gaps. Here we introduce an agent-based model describing T cell movements and their interactions with DCs, leading to activation and expansion of cognate T cell clones, in a two-dimensional representation of the lymph node paracortex. The primary objective was to test the putative role of T cell chemotaxis toward DCs, and quantitatively assess the impact of chemotaxis with respect to T cell priming efficacy. Firstly, we evaluated whether chemotaxis of naïve T cells toward a nearest DC may accelerate the scanning process, by quantifying, through simulations, the number of unique T cell—DC contact events. We demonstrate that, in the presence of naïve T cell-to-DC chemoattraction, a higher total number of contacts occurs, as compared to a T cell random walk scenario. However, the forming swarm of naïve T cells, as these cells get attracted to the neighborhood of a DC, may then physically restrict access of additional T cells to the DC, leading to an actual decrease in the cumulative number of unique contacts between naïve T cells and DCs. Secondly, we investigated the potential role of chemotaxis in maintaining cognate T cell clone expansion. The time course of cognate T cells number in the system was used as a quantitative characteristic of the expansion. Model-based simulations indicate that inclusion of chemotaxis, which is selective for already activated (but not naïve) antigen-specific T cells, may strongly accelerate the time of immune response occurrence, which subsequently increases the overall amplitude of the T cell clone expansion process.

Review of the systems biology of the immune system using agent-based models

The immune system is an inherent protection system in vertebrate animals including human beings that exhibit properties such as self-organisation, self-adaptation, learning, and recognition. It interacts with the other allied systems such as the gut and lymph nodes. There is a need for immune system modelling to know about its complex internal mechanism, to understand how it maintains the homoeostasis, and how it interacts with the other systems. There are two types of modelling techniques used for the simulation of features of the immune system: equation-based modelling (EBM) and agent-based modelling. Owing to certain shortcomings of the EBM, agent-based modelling techniques are being widely used. This technique provides various predictions for disease causes and treatments; it also helps in hypothesis verification. This study presents a review of agent-based modelling of the immune system and its interactions with the gut and lymph nodes. The authors also review the modelling of immune system interactions during tuberculosis and cancer. In addition, they also outline the future research directions for the immune system simulation through agent-based techniques such as the effects of stress on the immune system, evolution of the immune system, and identification of the parameters for a healthy immune system.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

Physiological factors leading to a successful vaccination: A computational approach

The immune system mounts a response to an infection by activating T cells. T cell activation occurs when dendritic cells, which have already interacted with the pathogen, scan a T cell that is cognate for (responsive to) the pathogen. This often occurs inside lymph nodes. The time it takes for this scanning event to occur, indeed the probability that it will occur at all, depends on many factors, including the rate that T cells and dendritic cells enter and leave the lymph node as well as the geometry of the lymph node and of course other cellular and molecular parameters. In this paper, we develop a hybrid stochastic-deterministic mathematical model at the tissue scale of the lymph node and simulate dendritic cells and cognate T cells to investigate the most important physiological factors leading to a successful and timely immune response after a vaccination. We use an agent-based model to describe the small population of cognate naive T cells and a partial differential equation description for the concentration of mature dendritic cells. We estimate the model parameters based on the known literature and measurements previously taken in our lab. We perform a parameter sensitivity analysis to quantify the sensitivity of the model results to the parameters. The results show that increasing T cell inflow through high endothelial venules, restricting cellular egress via the efferent lymph and increasing the total dendritic cell count by improving vaccinations are the among the most important physiological factors leading to an improved immune response. We also find that increasing the physical size of lymph nodes improves the overall likelihood that an immune response will take place but has a fairly weak effect on the response rate. The nature of dendritic cell trafficking through the LN (either passive or active transport) seems to have little effect on the overall immune response except if a change in overall egress time is observed.

Applications of mechanistic modelling to clinical and experimental immunology: an emerging technology to accelerate immunotherapeutic discovery and development

The application of in-silico modelling is beginning to emerge as a key methodology to advance our understanding of mechanisms of disease pathophysiology and related drug action, and in the design of experimental medicine and clinical studies. From this perspective, we will present a non-technical discussion of a small number of recent and historical applications of mathematical, statistical and computational modelling to clinical and experimental immunology. We focus specifically upon mechanistic questions relating to human viral infection, tumour growth and metastasis and T cell activation. These exemplar applications highlight the potential of this approach to impact upon human immunology informed by ever-expanding experimental, clinical and 'omics' data. Despite the capacity of mechanistic modelling to accelerate therapeutic discovery and development and to de-risk clinical trial design, it is not utilized widely across the field. We outline ongoing challenges facing the integration of mechanistic modelling with experimental and clinical immunology, and suggest how these may be overcome. Advances in key technologies, including multi-scale modelling, machine learning and the wealth of 'omics' data sets, coupled with advancements in computational capacity, are providing the basis for mechanistic modelling to impact on immunotherapeutic discovery and development during the next decade.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

Computational model of mesenchymal migration in 3D under chemotaxis

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell-matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices - collagen and fibrin - and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL-1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.

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.

IL-2 sensitivity and exogenous IL-2 concentration gradient tune the productive contact duration of CD8(+) T cell-APC: a multiscale modeling study

Background

The CD8⁺ T cell immune response fights acute infections by intracellular pathogens and, by generating an immune memory, enables immune responses against secondary infections. Activation of the CD8⁺ T cell immune response involves a succession of molecular events leading to modifications of CD8⁺ T cell population. To understand the endogenous and exogenous mechanisms controlling the activation of CD8⁺ T cells and to investigate the influence of early molecular events on the long-term cell population behavior, we developed a multiscale computational model. It integrates three levels of description: a Cellular Potts model describing the individual behavior of CD8⁺ T cells, a system of ordinary differential equations describing a decision-making molecular regulatory network at the intracellular level, and a partial differential equation describing the diffusion of IL-2 in the extracellular environment.

Results

We first calibrated the model parameters based on in vivo data and showed the model’s ability to reproduce early dynamics of CD8⁺ T cells in murine lymph nodes after influenza infection, both at the cell population and intracellular levels. We then showed the model’s ability to reproduce the proliferative responses of CD5^hi and CD5^lo CD8⁺ T cells to exogenous IL-2 under a weak TCR stimulation. This stressed the role of short-lasting molecular events and the relevance of explicitly describing both intracellular and cellular scale dynamics. Our results suggest that the productive contact duration of CD8⁺ T cell-APC is influenced by the sensitivity of individual CD8⁺ T cells to the activation signal and by the IL-2 concentration in the extracellular environment.

Conclusions

The multiscale nature of our model allows the reproduction and explanation of some acquired characteristics and functions of CD8⁺ T cells, and of their responses to multiple stimulation conditions, that would not be accessible in a classical description of cell population dynamics that would not consider intracellular dynamics.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0323-y) contains supplementary material, which is available to authorized users.

Topological Small-World Organization of the Fibroblastic Reticular Cell Network Determines Lymph Node Functionality

Fibroblastic reticular cells (FRCs) form the cellular scaffold of lymph nodes (LNs) and establish distinct microenvironmental niches to provide key molecules that drive innate and adaptive immune responses and control immune regulatory processes. Here, we have used a graph theory-based systems biology approach to determine topological properties and robustness of the LN FRC network in mice. We found that the FRC network exhibits an imprinted small-world topology that is fully regenerated within 4 wk after complete FRC ablation. Moreover, in silico perturbation analysis and in vivo validation revealed that LNs can tolerate a loss of approximately 50% of their FRCs without substantial impairment of immune cell recruitment, intranodal T cell migration, and dendritic cell-mediated activation of antiviral CD8+ T cells. Overall, our study reveals the high topological robustness of the FRC network and the critical role of the network integrity for the activation of adaptive immune responses.

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.

A virtual lymph node model to dissect the requirements for T-cell activation by synapses and kinapses

The initiation of T-cell responses in lymph nodes requires T cells to integrate signals delivered by dendritic cells (DCs) during long-lasting contacts (synapses) or more transient interactions (kinapses). However, it remains extremely challenging to understand how a specific sequence of contacts established by T cells ultimately dictates T-cell fate. Here, we have coupled a computational model of T-cell migration and interactions with DCs with a real-time, flow cytometry-like representation of T-cell activation. In this model, low-affinity peptides trigger T-cell proliferation through kinapses but we show that this process is only effective under conditions of high DC densities and prolonged antigen availability. By contrast, high-affinity peptides favor synapse formation and a vigorous proliferation under a wide range of antigen presentation conditions. In line with the predictions, decreasing the DC density in vivo selectively abolished proliferation induced by the low-affinity peptide. Finally, our results suggest that T cells possess a biochemical memory of previous stimulations of at least 1–2 days. We propose that the stability of T-cell–DC interactions, apart from their signaling potency, profoundly influences the robustness of T-cell activation. By offering the ability to control parameters that are difficult to manipulate experimentally, the virtual lymph node model provides new possibilities to tackle the fundamental mechanisms that regulate T-cell responses elicited by infections or vaccines.

Mathematics in modern immunology

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

An Image-Based Model of Fluid Flow Through Lymph Nodes

The lymphatic system returns fluid to the bloodstream from the tissues to maintain tissue fluid homeostasis. Lymph nodes distributed throughout the system filter the lymphatic fluid. The afferent and efferent lymph flow conditions of lymph nodes can be measured in experiments; however, it is difficult to measure the flow within the nodes. In this paper, we present an image-based modelling approach to investigating how the internal structure of the node affects the fluid flow pathways within the node. Selective plane illumination microscopy images of murine lymph nodes are used to identify the geometry and structure of the tissue within the node and to determine the permeability of the lymph node interstitium to lymphatic fluid. Experimental data are used to determine boundary conditions and optimise the parameters for the model. The numerical simulations conducted within the model are implemented in COMSOL Multiphysics, a commercial finite element analysis software. The parameter fitting resulted in the estimate that the average permeability for lymph node tissue is of the order of magnitude of [Formula: see text]. Our modelling shows that the flow predominantly takes a direct path between the afferent and efferent lymphatics and that fluid is both filtered and absorbed across the blood vessel boundaries. The amount that is absorbed or extravasated in the model is dependent on the efferent lymphatic lumen fluid pressure.

Organ-wide 3D-imaging and topological analysis of the continuous microvascular network in a murine lymph node

Understanding of the microvasculature has previously been limited by the lack of methods capable of capturing and modelling complete vascular networks. We used novel imaging and computational techniques to establish the topology of the entire blood vessel network of a murine lymph node, combining 63,706 confocal images at 2 μm pixel resolution to cover a volume of 3.88 mm(3). Detailed measurements including the distribution of vessel diameters, branch counts, and identification of voids were subsequently re-visualised in 3D revealing regional specialisation within the network. By focussing on critical immune microenvironments we quantified differences in their vascular topology. We further developed a morphology-based approach to identify High Endothelial Venules, key sites for lymphocyte extravasation. These data represent a comprehensive and continuous blood vessel network of an entire organ and provide benchmark measurements that will inform modelling of blood vessel networks as well as enable comparison of vascular topology in different organs.

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.

Predicting lymph node output efficiency using systems biology

Dendritic cells (DCs) capture pathogens and foreign antigen (Ag) in peripheral tissues and migrate to secondary lymphoid tissues, such as lymph nodes (LNs), where they present processed Ag as MHC-bound peptide (pMHC) to naïve T cells. Interactions between DCs and T cells result, over periods of hours, in activation, clonal expansion and differentiation of antigen-specific T cells, leading to primed cells that can now participate in immune responses. Two-photon microscopy (2PM) has been widely adopted to analyze lymphocyte dynamics and can serve as a powerful in vivo assay for cell trafficking and activation over short length and time scales. Linking biological phenomena between vastly different spatiotemporal scales can be achieved using a systems biology approach. We developed a 3D agent-based cellular model of a LN that allows for the simultaneous in silico simulation of T cell trafficking, activation and production of effector cells under different antigen (Ag) conditions. The model anatomy is based on in situ analysis of LN sections (from primates and mice) and cell dynamics based on quantitative measurements from 2PM imaging of mice. Our simulations make three important predictions. First, T cell encounters by DCs and T cell receptor (TCR) repertoire scanning are more efficient in a 3D model compared with 2D, suggesting that a 3D model is needed to analyze LN function. Second, LNs are able to produce primed CD4+T cells at the same efficiency over broad ranges of cognate frequencies (from 10(-5) to 10(-2)). Third, reducing the time that naïve T cells are required to bind DCs before becoming activated will increase the rate at which effector cells are produced. This 3D model provides a robust platform to study how T cell trafficking and activation dynamics relate to the efficiency of T cell priming and clonal expansion. We envision that this systems biology approach will provide novel insights for guiding vaccine development and understanding immune responses to infection.

Agent-based modeling: a systematic assessment of use cases and requirements for enhancing pharmaceutical research and development productivity

A crisis continues to brew within the pharmaceutical research and development (R&D) enterprise: productivity continues declining as costs rise, despite ongoing, often dramatic scientific and technical advances. To reverse this trend, we offer various suggestions for both the expansion and broader adoption of modeling and simulation (M&S) methods. We suggest strategies and scenarios intended to enable new M&S use cases that directly engage R&D knowledge generation and build actionable mechanistic insight, thereby opening the door to enhanced productivity. What M&S requirements must be satisfied to access and open the door, and begin reversing the productivity decline? Can current methods and tools fulfill the requirements, or are new methods necessary? We draw on the relevant, recent literature to provide and explore answers. In so doing, we identify essential, key roles for agent-based and other methods. We assemble a list of requirements necessary for M&S to meet the diverse needs distilled from a collection of research, review, and opinion articles. We argue that to realize its full potential, M&S should be actualized within a larger information technology framework—a dynamic knowledge repository—wherein models of various types execute, evolve, and increase in accuracy over time. We offer some details of the issues that must be addressed for such a repository to accrue the capabilities needed to reverse the productivity decline. © 2013 Wiley Periodicals, Inc.

The future of immunoimaging--deeper, bigger, more precise, and definitively more colorful

Immune cells are thoroughbreds, moving farther and faster and surveying more diverse tissue space than their nonhematopoietic brethren. Intravital 2-photon microscopy has provided insights into the movements and interactions of many immune cell types in diverse tissues, but more information is needed to link such analyses of dynamic cell behavior to function. Here, we describe additional methods whose application promises to extend our vision, allowing more complete, multiscale dissection of how immune cell positioning and movement are linked to system state, host defense, and disease.

A global "imaging'' view on systems approaches in immunology

The immune system exhibits an enormous complexity. High throughput methods such as the "-omic'' technologies generate vast amounts of data that facilitate dissection of immunological processes at ever finer resolution. Using high-resolution data-driven systems analysis, causal relationships between complex molecular processes and particular immunological phenotypes can be constructed. However, processes in tissues, organs, and the organism itself (so-called higher level processes) also control and regulate the molecular (lower level) processes. Reverse systems engineering approaches, which focus on the examination of the structure, dynamics and control of the immune system, can help to understand the construction principles of the immune system. Such integrative mechanistic models can properly describe, explain, and predict the behavior of the immune system in health and disease by combining both higher and lower level processes. Moving from molecular and cellular levels to a multiscale systems understanding requires the development of methodologies that integrate data from different biological levels into multiscale mechanistic models. In particular, 3D imaging techniques and 4D modeling of the spatiotemporal dynamics of immune processes within lymphoid tissues are central for such integrative approaches. Both dynamic and global organ imaging technologies will be instrumental in facilitating comprehensive multiscale systems immunology analyses as discussed in this review.

A model for migratory B cell oscillations from receptor down-regulation induced by external chemokine fields

A long-standing paradigm in B cell immunology is that effective somatic hypermutation and affinity maturation require cycling between the dark zone and light zone of the germinal center. The cyclic re-entry hypothesis was first proposed based on considerations of the efficiency of affinity maturation using an ordinary differential equations model for B cell population dynamics. More recently, two-photon microscopy studies of B cell motility within lymph nodes in situ have revealed the complex migration patterns of B lymphocytes both in the preactivation follicle and post-activation germinal center. There is strong evidence that chemokines secreted by stromal cells and the regulation of cognate G-protein coupled receptors by these chemokines are necessary for the observed spatial cell distributions. For example, the distribution of B cells within the light and dark zones of the germinal center appears to be determined by the reciprocal interaction between the level of the CXCR4 and CXCR5 receptors and the spatial distribution of their respective chemokines CXCL12 and CXCL13. Computer simulations of individual-based models have been used to study the complex biophysical and mechanistic processes at the individual cell level, but such simulations can be challenging to parameterize and analyze. In contrast, ordinary differential equations are more tractable, but traditional compartment model formalizations ignore the spatial chemokine distribution that drives B cell redistribution. Motivated by the desire to understand the motility patterns observed in an individual-based simulation of B cell migration in the lymph node, we propose and analyze the dynamics of an ordinary differential equation model incorporating explicit chemokine spatial distributions. While there is experimental evidence that B cell migration patterns in the germinal center are driven by extrinsically regulated differentiation programs, the model shows, perhaps surprisingly, that feedback from receptor down-regulation induced by external chemokine fields can give rise to spontaneous interzonal and intrazonal oscillations in the absence of any extrinsic regulation. While the extent to which such simple feedback mechanisms contributes to B cell migration patterns in the germinal center is unknown, the model provides an alternative hypothesis for how complex B cell migration patterns might arise from very simple mechanisms.

Modeling drug- and chemical-induced hepatotoxicity with systems biology approaches

We provide an overview of computational systems biology approaches as applied to the study of chemical- and drug-induced toxicity. The concept of “toxicity pathways” is described in the context of the 2007 US National Academies of Science report, “Toxicity testing in the 21st Century: A Vision and A Strategy.” Pathway mapping and modeling based on network biology concepts are a key component of the vision laid out in this report for a more biologically based analysis of dose-response behavior and the safety of chemicals and drugs. We focus on toxicity of the liver (hepatotoxicity) – a complex phenotypic response with contributions from a number of different cell types and biological processes. We describe three case studies of complementary multi-scale computational modeling approaches to understand perturbation of toxicity pathways in the human liver as a result of exposure to environmental contaminants and specific drugs. One approach involves development of a spatial, multicellular “virtual tissue” model of the liver lobule that combines molecular circuits in individual hepatocytes with cell–cell interactions and blood-mediated transport of toxicants through hepatic sinusoids, to enable quantitative, mechanistic prediction of hepatic dose-response for activation of the aryl hydrocarbon receptor toxicity pathway. Simultaneously, methods are being developing to extract quantitative maps of intracellular signaling and transcriptional regulatory networks perturbed by environmental contaminants, using a combination of gene expression and genome-wide protein-DNA interaction data. A predictive physiological model (DILIsym™) to understand drug-induced liver injury (DILI), the most common adverse event leading to termination of clinical development programs and regulatory actions on drugs, is also described. The model initially focuses on reactive metabolite-induced DILI in response to administration of acetaminophen, and spans multiple biological scales.

On-lattice simulation of T cell motility, chemotaxis, and trafficking in the lymph node paracortex

Agent-based simulation is a powerful method for investigating the complex interplay of the processes occurring in a lymph node during an adaptive immune response. We have previously established an agent-based modeling framework for the interactions between T cells and dendritic cells within the paracortex of lymph nodes. This model simulates in three dimensions the “random-walk” T cell motility observed in vivo, so that cells interact in space and time as they process signals and commit to action such as proliferation. On-lattice treatment of cell motility allows large numbers of densely packed cells to be simulated, so that the low frequency of T cells capable of responding to a single antigen can be dealt with realistically. In this paper we build on this model by incorporating new numerical methods to address the crucial processes of T cell ingress and egress, and chemotaxis, within the lymph node. These methods enable simulation of the dramatic expansion and contraction of the T cell population in the lymph node paracortex during an immune response. They also provide a novel probabilistic method to simulate chemotaxis that will be generally useful in simulating other biological processes in which chemotaxis is an important feature.

Understanding immunology via engineering design: the role of mathematical prototyping

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and "fitness for use," can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

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 multifaceted approach to modeling the immune response in tuberculosis

Tuberculosis (TB) is a deadly infectious disease caused by Mycobacterium tuberculosis (Mtb). No available vaccine is reliable and, although treatment exists, approximately 2 million people still die each year. The hallmark of TB infection is the granuloma, a self-organizing structure of immune cells forming in the lung and lymph nodes in response to bacterial invasion. Protective immune mechanisms play a role in granuloma formation and maintenance; these act over different time/length scales (e.g., molecular, cellular, and tissue scales). The significance of specific immune factors in determining disease outcome is still poorly understood, despite incredible efforts to establish several animal systems to track infection progression and granuloma formation. Mathematical and computational modeling approaches have recently been applied to address open questions regarding host-pathogen interaction dynamics, including the immune response to Mtb infection and TB granuloma formation. This provides a unique opportunity to identify factors that are crucial to a successful outcome of infection in humans. These modeling tools not only offer an additional avenue for exploring immune dynamics at multiple biological scales but also complement and extend knowledge gained via experimental tools. We review recent modeling efforts in capturing the immune response to Mtb, emphasizing the importance of a multiorgan and multiscale approach that has tuneable resolution. Together with experimentation, systems biology has begun to unravel key factors driving granuloma formation and protective immune response in TB. WIREs Syst Biol Med 2011 3 479-489 DOI: 10.1002/wsbm.131