Multiscale Modeling of the Early CD8 T-Cell Immune Response in Lymph Nodes: An Integrative Study

Modeling immune cell behavior across scales in cancer

Detailed, mechanistic models of immune cell behavior across multiple scales in the context of cancer provide clinically relevant insights needed to understand existing immunotherapies and develop more optimal treatment strategies. We highlight mechanistic models of immune cells and their ability to become activated and promote tumor cell killing. These models capture various aspects of immune cells: (a) single‐cell behavior by predicting the dynamics of intracellular signaling networks in individual immune cells, (b) multicellular interactions between tumor and immune cells, and (c) multiscale dynamics across space and different levels of biological organization. Computational modeling is shown to provide detailed quantitative insight into immune cell behavior and immunotherapeutic strategies. However, there are gaps in the literature, and we suggest areas where additional modeling efforts should be focused to more prominently impact our understanding of the complexities of the immune system in the context of cancer.

This article is categorized under:

Biological Mechanisms > Cell Signaling

Models of Systems Properties and Processes > Mechanistic Models

Models of Systems Properties and Processes > Cellular Models

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling

MOTIVATION

Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell).

RESULTS

PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen.

AVAILABILITY AND IMPLEMENTATION

PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Towards multiscale modeling of the CD8+ T cell response to viral infections

The CD8⁺ T cell response is critical to the control of viral infections. Yet, defining the CD8⁺ T cell response to viral infections quantitatively has been a challenge. Following antigen recognition, which triggers an intracellular signaling cascade, CD8⁺ T cells can differentiate into effector cells, which proliferate rapidly and destroy infected cells. When the infection is cleared, they leave behind memory cells for quick recall following a second challenge. If the infection persists, the cells may become exhausted, retaining minimal control of the infection while preventing severe immunopathology. These activation, proliferation and differentiation processes as well as the mounting of the effector response are intrinsically multiscale and collective phenomena. Remarkable experimental advances in the recent years, especially at the single cell level, have enabled a quantitative characterization of several underlying processes. Simultaneously, sophisticated mathematical models have begun to be constructed that describe these multiscale phenomena, bringing us closer to a comprehensive description of the CD8⁺ T cell response to viral infections. Here, we review the advances made and summarize the challenges and opportunities ahead. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Fates Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models.

Model-Based Assessment of the Role of Uneven Partitioning of Molecular Content on Heterogeneity and Regulation of Differentiation in CD8 T-Cell Immune Responses

Activation of naive CD8 T-cells can lead to the generation of multiple effector and memory subsets. Multiple parameters associated with activation conditions are involved in generating this diversity that is associated with heterogeneous molecular contents of activated cells. Although naive cell polarisation upon antigenic stimulation and the resulting asymmetric division are known to be a major source of heterogeneity and cell fate regulation, the consequences of stochastic uneven partitioning of molecular content upon subsequent divisions remain unclear yet. Here we aim at studying the impact of uneven partitioning on molecular-content heterogeneity and then on the immune response dynamics at the cellular level. To do so, we introduce a multiscale mathematical model of the CD8 T-cell immune response in the lymph node. In the model, cells are described as agents evolving and interacting in a 2D environment while a set of differential equations, embedded in each cell, models the regulation of intra and extracellular proteins involved in cell differentiation. Based on the analysis of in silico data at the single cell level, we show that immune response dynamics can be explained by the molecular-content heterogeneity generated by uneven partitioning at cell division. In particular, uneven partitioning acts as a regulator of cell differentiation and induces the emergence of two coexisting sub-populations of cells exhibiting antagonistic fates. We show that the degree of unevenness of molecular partitioning, along all cell divisions, affects the outcome of the immune response and can promote the generation of memory cells.

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved.

Cell studio: A platform for interactive, 3D graphical simulation of immunological processes

The field of computer modeling and simulation of biological systems is rapidly advancing, backed by significant progress in the fields of experimentation techniques, computer hardware, and programming software. The result of a simulation may be delivered in several ways, from numerical results, through graphs of the simulated run, to a visualization of the simulation. The vision of an in-silico experiment mimicking an in-vitro or in-vivo experiment as it is viewed under a microscope is appealing but technically demanding and computationally intensive. Here, we report “Cell Studio,” a generic, hybrid platform to simulate an immune microenvironment with biological and biophysical rules. We use game engines—generic programs for game creation which offer ready-made assets and tools—to create a visualized, interactive 3D simulation. We also utilize a scalable architecture that delegates the computational load to a server. The user may view the simulation, move the “camera” around, stop, fast-forward, and rewind it and inject soluble molecules into the extracellular medium at any point in time. During simulation, graphs are created in real time for a broad view of system-wide processes. The model is parametrized using a user-friendly Graphical User Interface (GUI). We show a simple validation simulation and compare its results with those from a “classical” simulation, validated against a “wet” experiment. We believe that interactive, real-time 3D visualization may aid in generating insights from the model and encourage intuition about the immunological scenario.

Existence and stability of periodic solutions of an impulsive differential equation and application to CD8 T-cell differentiation

Unequal partitioning of the molecular content at cell division has been shown to be a source of heterogeneity in a cell population. We propose to model this phenomenon with the help of a scalar, nonlinear impulsive differential equation (IDE). To study the effect of molecular partitioning at cell division on the effector/memory cell-fate decision in a CD8 T-cell lineage, we study an IDE describing the concentration of the protein Tbet in a CD8 T-cell, where impulses are associated to cell division. We discuss how the degree of asymmetry of molecular partitioning can affect the process of cell differentiation and the phenotypical heterogeneity of a cell population. We show that a moderate degree of asymmetry is necessary and sufficient to observe irreversible differentiation. We consider, in a second part, a general autonomous IDE with fixed times of impulse and a specific form of impulse function. We establish properties of the solutions of that equation, most of them obtained under the hypothesis that impulses occur periodically. In particular, we show how to investigate the existence of periodic solutions and their stability by studying the flow of an autonomous differential equation. Then we apply those properties to prove the results presented in the first part.

A multiscale modelling approach for the regulation of the cell cycle by the circadian clock

We present a multiscale mathematical model for the regulation of the cell cycle by the circadian clock. Biologically, the model describes the proliferation of a population of heterogeneous cells connected to each other. The model consists of a high dimensional transport equation structured by molecular contents of the cell cycle-circadian clock coupled oscillator. We propose a computational method for resolution adapted from the concept of particle methods. We study the impact of molecular dynamics on cell proliferation and show an example where discordance of division rhythms between population and single cell levels is observed. This highlights the importance of multiscale modeling where such results cannot be inferred from considering solely one biological level.

The Role of Multiscale Protein Dynamics in Antigen Presentation and T Lymphocyte Recognition

T lymphocytes are stimulated when they recognize short peptides bound to class I proteins of the major histocompatibility complex (MHC) protein, as peptide-MHC complexes. Due to the diversity in T-cell receptor (TCR) molecules together with both the peptides and MHC proteins they bind to, it has been difficult to design vaccines and treatments based on these interactions. Machine learning has made some progress in trying to predict the immunogenicity of peptide sequences in the context of specific MHC class I alleles but, as such approaches cannot integrate temporal information and lack explanatory power, their scope will always be limited. Here, we advocate a mechanistic description of antigen presentation and TCR activation which is explanatory, predictive, and quantitative, drawing on modeling approaches that collectively span several length and time scales, being capable of furnishing reliable biological descriptions that are difficult for experimentalists to provide. It is a form of multiscale systems biology. We propose the use of chemical rate equations to describe the time evolution of the foreign and host proteins to explain how the original proteins end up being presented on the cell surface as peptide fragments, while we invoke molecular dynamics to describe the key binding processes on the molecular level, including those of peptide-MHC complexes with TCRs which lie at the heart of the immune response. On each level, complementary methods based on machine learning are available, and we discuss the relationship between these divergent approaches. The pursuit of predictive mechanistic modeling approaches requires experimentalists to adapt their work so as to acquire, store, and expose data that can be used to verify and validate such models.

Spatiotemporal Dynamics of Virus Infection Spreading in Tissues

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

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.

A Neutrophil Phenotype Model for Extracorporeal Treatment of Sepsis

Neutrophils play a central role in eliminating bacterial pathogens, but may also contribute to end-organ damage in sepsis. Interleukin-8 (IL-8), a key modulator of neutrophil function, signals through neutrophil specific surface receptors CXCR-1 and CXCR-2. In this study a mechanistic computational model was used to evaluate and deploy an extracorporeal sepsis treatment which modulates CXCR-1/2 levels. First, a simplified mechanistic computational model of IL-8 mediated activation of CXCR-1/2 receptors was developed, containing 16 ODEs and 43 parameters. Receptor level dynamics and systemic parameters were coupled with multiple neutrophil phenotypes to generate dynamic populations of activated neutrophils which reduce pathogen load, and/or primed neutrophils which cause adverse tissue damage when misdirected. The mathematical model was calibrated using experimental data from baboons administered a two-hour infusion of E coli and followed for a maximum of 28 days. Ensembles of parameters were generated using a Bayesian parallel tempering approach to produce model fits that could recreate experimental outcomes. Stepwise logistic regression identified seven model parameters as key determinants of mortality. Sensitivity analysis showed that parameters controlling the level of killer cell neutrophils affected the overall systemic damage of individuals. To evaluate rescue strategies and provide probabilistic predictions of their impact on mortality, time of onset, duration, and capture efficacy of an extracorporeal device that modulated neutrophil phenotype were explored. Our findings suggest that interventions aiming to modulate phenotypic composition are time sensitive. When introduced between 3–6 hours of infection for a 72 hour duration, the survivor population increased from 31% to 40–80%. Treatment efficacy quickly diminishes if not introduced within 15 hours of infection. Significant harm is possible with treatment durations ranging from 5–24 hours, which may reduce survival to 13%. In severe sepsis, an extracorporeal treatment which modulates CXCR-1/2 levels has therapeutic potential, but also potential for harm. Further development of the computational model will help guide optimal device development and determine which patient populations should be targeted by treatment.

Sepsis occurs when a patient develops a whole body immune response due to infection. In this condition, white blood cells called neutrophils circulate in an active state, seeking and eliminating invading bacteria. However, when neutrophils are activated, healthy tissue is inadvertently targeted, leading to organ damage and potentially death. Even though sepsis kills millions worldwide, there are still no specific treatments approved in the United States. This may be due to the complexity and diversity of the body’s immune response, which can be managed well using computational modeling. We have developed a computational model to predict how different levels of neutrophil activation impact survival in an overactive inflammatory conditions. The model was utilized to assess the effectiveness of a simulated experimental sepsis treatment which modulates neutrophil populations and activity. This evaluation determined that treatment timing plays a critical role in therapeutic effectiveness. When utilized properly the treatment drastically improves survival, but there is also risk of causing patient harm when introduced at the wrong time. We intend for this computational model to support and guide further development of sepsis treatments and help translate these preliminary results from bench to bedside.