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Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions.

ABSTRACT: Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4+T cells, CD8+T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge-Kutta method failed to solve it. Consequently, the "Adams predictor-corrector" method is used. The results reveal that the patient's immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4+T cells can be an alternative to both CD8+T cell therapy and cytokines in some cases. Moreover, CD4+T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4+T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8+T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients' treatment intervention strategies.

SUBMITTER: Makhlouf AM

PROVIDER: S-EPMC7049850 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions.

Makhlouf Ahmed M AM El-Shennawy Lamiaa L Elkaranshawy Hesham A HA

Computational and mathematical methods in medicine 20200219

Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equation ...[more]

PMID: 32148558

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Project description:BackgroundMonoclonal antibodies blocking the Cytotoxic T-lymphocyte antigen 4 (CTLA-4) receptor have revolutionized the field of anti-cancer therapy for the last few years. The human T-cell-based immune responses are modulated by two contradicting signals. CTLA-4 provides a T cell inhibitory signal through its interaction with B7 ligands (B7-1 and B7-2), while CD28 provides a stimulatory signal when interacting with the same ligands. A previous theoretical model has focused on understanding the processes of costimulatory and inhibitory complex formations at the synapse. Nevertheless, the effects of monoclonal antibody (mAb)-mediation on these complexes are relatively unexplored. In this work, we expand on the previous model to develop a new mathematical framework for studying the effects of anti-CTLA-4 mAbs on the co-stimulatory (CD28/B7 ligands) and the co-inhibitory (CTLA-4/B7 ligands) complex formation at the immunological synapse. In particular, we focus on two promising anti-CTLA-4 mAbs, tremelimumab (from AstraZeneca) and ipilimumab (from Bristol-Myers Squibb), which are currently in clinical trials and the market, respectively, for targeting multiple tumors.MethodsThe mathematical model in this work has been constructed based on ordinary differential equations and available experimental binding kinetics data for the anti-CTLA-4 antibodies from literature.ResultsThe numerical simulations from the current model are in agreement with a number of experimental data. Especially, the dose-curves for blocking the B7 ligand binding to CTLA-4 by ipilimumab are comparable with the results from a previous competitive binding assay by flow cytometry and ELISA. Our simulations predict the dose response and the relative efficacies of the two mAbs in blocking the inhibitory CTLA-4/B7 complexes.ConclusionsThe results show that different factors, such as multivalent interactions, mobility of molecules and competition effects, could impact the effects of antibody-mediation. The results, in particular, describe that the competitive effects could impact the dose-dependent inhibition by the mAbs very significantly. We present this model as a useful tool that can easily be translated to study the effects of any anti-CTLA-4 antibodies on immunological synaptic complex formation, provided reliable biophysical data for mAbs are available.

Dataset Information

Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions.

Publications

Mathematical Modelling for the Role of CD4<sup>+</sup>T Cells in Tumor-Immune Interactions.

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