A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus

Abstract

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.

A Fast Second-Order Explicit Predictor-Corrector Numerical Technique To Investigating And Predicting The Dynamic Of Cytokine Levels And Human Immune Cells Activation In Response To Gram-Positive Bacteria: Staphylococcus Aureus

“…Since the proposed technique is an explicit predictor-corrector approach and second-order accuracy, it is faster and more efficient than a wide set of statistical and numerical methods discussed in the literature for solving general systems of mixed ODEs/PDEs modeling real-world problems [26,28,65] and references therein. Some data used in the simulations are taken from [71]. Both tables and graphs (Tables 3-4 and Figures 2-3) suggest that the approximate solutions (macrophages and cytokine expressions) increase until a maximum concentration, so called "peaks", after approximately t hours, and become constant when the antigens are eliminated by the immune response.…”

“…The graphs (Figures 2-3) also indicate that the body response varies based on the damage inflicted by the bacteria S. aureus. Because of the activation of cytokines in the human immune response, the numerical experiments are performed assuming low initial concentration of gram-positive bacteria S. aureus as discussed in [71]. However, high expressions of the pathogen S. aureus due to the tissue damage associated with endotoxicity of gram-positive bacteria provoke a fast increase in cellular and cytokine responses (see Figure 4).…”

“…This case is not analyzed in this work and should be considered as the topic of our future investigations. Furthermore, high concentrations of the antigens are not sufficiently discussed in the literature because of the lack of data to validate the increased expressions [71].…”

“…This work considers the dynamic of mixed cellular-cytokine model given in [71] and described by a system of ordinary and partial differential equations. Assuming that the average tissue concentration obtained from the cellular model is the initial condition, the expected concentrations of TNFα, IL6, IL8 and IL10 are functions of resting macrophages y 2 (x, t) and the activated ones y 3 (x, t).…”

Effects of Sepsis on Immune Response, Microbiome and Oxidative Metabolism in Preterm Infants

“…In this scenario, numerous studies in recent years have aimed to describe the mechanisms of the immune response, and predictive models have been proposed [ 44 ]. Moreover, transcriptomic studies have found different responses in sepsis caused by Gram-positive compared to those caused by Gram-negative bacteria not only in adults but also in children and preterm infants [ 45 ].…”