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

Abstract

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.

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“…Immune cell proliferation does not follow linear rules and it is controlled by different factors such as the concentration, the expression of the receptors, and finally, but not less importantly, the interaction with other cytokines, which can act synergistically, or not, towards a specific behavior or effect. For example, there are cytokines that can have inhibitory effects on IL-2 induction, such as IL-4 [63]. If we consider that the treatment has induced the upregulation of IL-4, under both tested basal and stimulated conditions, we might have an explanation that can partially elucidate the interpretation of our results.…”

A Quantum Neural Network for Modeling of T Helper Cell Dynamics

“…Their mathematical model of MAP infection highlights the roles of initial bacterial dose, T cell response efficiency, and immune kinetics in influencing the timing of the Th1/Th2 shift, offering insights for managing JD through vaccination or early treatment strategies. Atitey and Anchang (2022) focus on the dynamic interactions of cytokines and immune cells during pathogen invasion [2]. They propose a hybrid computational model, MMQE, integrating ordinary differential equations and stochastic elements to predict immune system responses influenced by cytokines like IL-2 and IL-4.…”

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