Mathematical Modelling of the Inhibitory Role of Regulatory T Cells in Tumor Immune Response

Zhongtao Yang,Yasuhiro Takeuchi,Yueping Dong,Cuihong Yang

doi:10.1155/2020/4834165

Abstract

The immune system against tumors acts through a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells (TCs), such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this paper, we propose a tumor immune interaction model based on Tregs-mediated tumor immune escape mechanism. When helper T cells’ (HTCs) stimulation rate by the presence of identified tumor antigens is below critical value, the coexistence (tumor and immune) equilibrium is always stable in its existence region. When HTCs stimulation rate is higher than the critical value, the inhibition rate of effector cells (ECs) by Tregs can destabilize the coexistence equilibrium and cause Hopf bifurcations and produce a limit cycle. This model shows that Tregs might play a crucial role in triggering the tumor immune escape. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal antibody immunotherapy (MAI) as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control TCs more, while MAI can delay the inhibitory effect of Tregs on ECs. The result also shows that the combination of both immunotherapies can control TCs and reduce the inhibitory effect of Tregs better than a single immunotherapy can control.

Highlights

Tumors can be benignant, premalignant, and malignant
It is important to understand tumor’s mechanisms of establishment and destruction, cell-mediate immunity with cytotoxic T lymphocytes (CTLs), and natural killer cells (NKs), generally called effector cells (ECs) that are cytotoxic to tumor cells (TCs), and play a basic role in immune response against tumors [2, 3]
Efficient antitumor immunity requires the action of helper T cells (HTCs), which can directly activate naive CD8+ T cells to differentiate into CTLs [4,5,6]

Summary

Introduction

Tumors can be benignant (not cancerous), premalignant (precancerous), and malignant (cancerous). In 2014, Dong et al constructed a three-dimensional ODEs model focusing on the effects of HTCs on the tumor immune system [4]. In 2003, in order to study the role of cytokine therapy in the activation of the immune system, Stolongo-Costa et al introduced cycle therapy term Fcos2ωt and established a cycle immunotherapy model. HTCs can recognize TCs and promote the growth of ECs. And ECs can provide direct protective immunity by attacking TCs. When there are more HTCs and ECs, in order to maintain immune homeostasis, the body will produce corresponding Tregs to suppress ECs, and Tregs originating from both HTCs and ECs. en, we establish a four-dimensional ODEs model described as below:. E fourth equation gives the rate change of the Tregs population, r1 and r2 are the activation rates of Tregs by ECs and HTCs, respectively. X, y, z, and u denote the dimensionless densities of TCs, ECs, HTCs, and Tregs populations, respectively

Model Analysis

Treatment Model

Numerical Simulations

H H H θ5

Discussion and Conclusion