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

Mathematical model for IL-2-based cancer immunotherapy

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD4+ T cells, the relative death rate of CD8+ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD4+ T cells die out. However, in cases where CD4+ and CD8+ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD4+ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD4+ T cells, while high doses for a short period of time over several days transiently increase the population of CD8+ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.

Computational Modeling to Determine the Effect of Phenotypic Heterogeneity in Tumors on the Collective Tumor-Immune Interactions

Tumor immunotherapy aims to maintain or enhance the killing capability of CD8+ T cells to clear tumor cells. The tumor-immune interactions affect the function of CD8+ T cells. However, the effect of phenotype heterogeneity of a tumor mass on the collective tumor-immune interactions is insufficiently investigated. We developed the cellular-level computational model based on the principle of cellular Potts model to solve the case mentioned above. We considered how asymmetric division and glucose distribution jointly regulated the transient changes in the proportion of proliferating/quiescent tumor cells in a solid tumor mass. The evolution of a tumor mass in contact with T cells was explored and validated by comparing it with previous studies. Our modeling exhibited that proliferating/quiescent tumor cells, exhibiting distinct anti-apoptotic and suppressive behaviors, redistributed within the domain accompanied by the evolution of a tumor mass. Collectively, a tumor mass prone to a quiescent state weakened the collective suppressive functions of a tumor mass on cytotoxic T cells and triggered a decline of apoptosis of tumor cells. Although quiescent tumor cells did not sufficiently do their inhibitory functions, the possibility of long-term survival was improved due to their interior location within a mass. Overall, the proposed model provides a useful framework to investigate collective-targeted strategies for improving the efficiency of immunotherapy.

Predictive Role of IL-2R and IL-10 in the Anti-inflammatory Response and Antiplatelet Therapy of Kawasaki Disease: A Retrospective Study

To date, Kawasaki disease (KD) has only been able to be diagnosed and evaluated using clinical characteristics. Additionally, the therapeutic effect and cardiovascular complications could not be verified until its occurrence. The present retrospective study analyzed the dynamic alterations of inflammatory cytokines, platelet (PLT) count, and subgroups of lymphocytes, such as cluster of differentiation (CD) 8+ T cells and CD19+ B cells, under different conditions in 64 children with KD. The percentage distribution of lymphocyte subgroups and the altered neutrophil lymphocyte ratio demonstrated that the inflammatory response was dominated by the B cell-mediated humoral immune response before intravenous immunoglobulin (IVIG) treatment, but mainly by T cells via cellular cytotoxic effects after IVIG treatment. Among the different types of inflammatory cytokines, the results of the present study revealed that the altered levels of interleukin-2 receptor (IL-2R) and interleukin-10 (IL-10) were closely associated with the percentage of CD8+ T cells and CD19+ B cells. Additionally, the two cytokines exhibited more sensitive fluctuations based on the status of the children with KD in various circumstances compared with other indexes, such as the percentages of CD8+ T cells and CD19+ B cells or the PLT count. These results suggested that children with KD who are ≥4 years old may benefit from IVIG but will not benefit from decreased platelet activation or suffer less cardiovascular complications. Additionally, starting clopidogrel usage earlier as an antiplatelet strategy should be considered based on the observed continuous rise in the PLT count in children with KD receiving IVIG. In conclusion, dynamically monitoring the levels of IL-2R and IL-10 has the potential to provide indications of the intensity and development of the inflammatory response in children with KD and may contribute to the early prediction and adjustment of pathological and pharmacological effects of therapy.

Mathematical Modeling of Proliferative Immune Response Initiated by Interactions Between Classical Antigen-Presenting Cells Under Joint Antagonistic IL-2 and IL-4 Signaling

During an adaptive immune response from pathogen invasion, multiple cytokines are produced by various immune cells interacting jointly at the cellular level to mediate several processes. For example, studies have shown that regulation of interleukin-4 (IL-4) correlates with interleukin-2 (IL-2) induced lymphocyte proliferation. This motivates the need to better understand and model the mechanisms driving the dynamic interplay of proliferation of lymphocytes with the complex interaction effects of cytokines during an immune response. To address this challenge, we adopt a hybrid computational approach comprising of continuous, discrete and stochastic non-linear model formulations to predict a system-level immune response as a function of multiple dependent signals and interacting agents including cytokines and targeted immune cells. We propose a hybrid ordinary differential equation-based (ODE) multicellular model system with a stochastic component of antigen microscopic states denoted as Multiscale Multicellular Quantitative Evaluator (MMQE) implemented using MATLAB. MMQE combines well-defined immune response network-based rules and ODE models to capture the complex dynamic interactions between the proliferation levels of different types of communicating lymphocyte agents mediated by joint regulation of IL-2 and IL-4 to predict the emergent global behavior of the system during an immune response. We model the activation of the immune system in terms of different activation protocols of helper T cells by the interplay of independent biological agents of classic antigen-presenting cells (APCs) and their joint activation which is confounded by the exposure time to external pathogens. MMQE quantifies the dynamics of lymphocyte proliferation during pathogen invasion as bivariate distributions of IL-2 and IL-4 concentration levels. Specifically, by varying activation agents such as dendritic cells (DC), B cells and their joint mechanism of activation, we quantify how lymphocyte activation and differentiation protocols boost the immune response against pathogen invasion mediated by a joint downregulation of IL-4 and upregulation of IL-2. We further compare our in-silico results to in-vivo and in-vitro experimental studies for validation. In general, MMQE combines intracellular and extracellular effects from multiple interacting systems into simpler dynamic behaviors for better interpretability. It can be used to aid engineering of anti-infection drugs or optimizing drug combination therapies against several diseases.

CD8+ TILs in NSCLC differentiate into TEMRA via a bifurcated trajectory: deciphering immunogenicity of tumor antigens

Background

CD8⁺ tumor-infiltrating lymphocytes (TILs) comprise phenotypically and functionally heterogeneous subpopulations. Of these, effector memory CD45RA re-expressing CD8⁺ T cells (Temra) have been discovered and characterized as the most terminally differentiated subset. However, their exact ontogeny and physiological importance in association with tumor progression remain poorly understood.

Methods

We analyzed primary tumors and peripheral blood samples from 26 patients with non-small cell lung cancer and analyzed their phenotypes and functional characteristics using flow cytometry, RNA-sequencing, and bioinformatics.

Results

We found that tumor-infiltrating Temra (tilTemra) cells largely differ from peripheral blood Temra (pTemra), with distinct transcriptomes and functional properties. Notably, although majority of the pTemra was CD27⁻CD28⁻ double-negative (DN), a large fraction of tilTemra population was CD27⁺CD28⁺ double-positive (DP), a characteristic of early-stage, less differentiated effector cells. Trajectory analysis revealed that CD8⁺ TILs undergo a divergent sequence of events for differentiation into either DP or DN tilTemra. Such a differentiation toward DP tilTemra relied on persistent expression of CD27 and CD28 and was associated with weak T cell receptor engagement. Thus, a higher proportion of DP Temra was correlated with lower immunogenicity of tumor antigens and consequently lower accumulation of CD8⁺ TILs.

Conclusions

These data suggest a complex interplay between CD8⁺ T cells and tumors and define DP Temra as a unique subset of tumor-specific CD8⁺ TILs that are produced in patients with relatively low immunogenic cancer types, predicting immunogenicity of tumor antigens and CD8⁺ TIL counts, a reliable biomarker for successful cancer immunotherapy.

Modeling Variability in Populations of Cells Using Approximated Multivariate Distributions

We are interested in studying the evolution of large homogeneous populations of cells, where each cell is assumed to be composed of a group of biological players (species) whose dynamics is governed by a complex biological pathway, identical for all cells. Modeling the inherent variability of the species concentrations in different cells is crucial to understand the dynamics of the population. In this work, we focus on handling this variability by modeling each species by a random variable that evolves over time. This appealing approach runs into the curse of dimensionality since exactly representing a joint probability distribution involving a large set of random variables quickly becomes intractable as the number of variables grows. To make this approach amenable to biopathways, we explore different techniques to (i) approximate the exact joint distribution at a given time point, and (ii) to track its evolution as time elapses. We start with the problem of approximating the probability distribution of biological species in a population of cells at some given time point. Data come from different fine-grained models of biological pathways of increasing complexities, such as (perturbed) Ordinary Differential Equations (ODEs). Classical approximations rely on the strong and unrealistic assumption that variables/species are independent, or that they can be grouped into small independent clusters. We propose instead to use the Chow-Liu tree representation, based on overlapping clusters of two variables, which better captures correlations between variables. Our experiments show that the proposed approximation scheme is more accurate than existing ones to model probability distributions deriving from biopathways. Then we address the problem of tracking the dynamics of a population of cells, that is computing from an initial distribution the evolution of the (approximate) joint distribution of species over time, called the inference problem. We evaluate several approximate inference algorithms (e.g., [14] , [17] ) for coarse-grained abstractions [12], [16] of biological pathways. Using the Chow-Liu tree approximation, we develop a new inference algorithm which is very accurate according to the experiments we report, for a minimal computation overhead. Our implementation is available at https://codeocean.com/capsule/6491669/tree.

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.

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.

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.