Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: A mathematical model

• Published in: PloS one 2017-05, Vol.12 (5), p.e0178479-e0178479
• Main Authors: Lai, Xiulan, Friedman, Avner
• Format: Article
• Language: English
• Subjects: Analysis; Animals; Antigens; Antineoplastic agents; Biology and Life Sciences; Breast cancer; Cancer; Cancer therapies; Cancer treatment; Cancer vaccines; Cancer Vaccines - immunology; Cancer Vaccines - pharmacology; CD4 antigen; CD4-Positive T-Lymphocytes - drug effects; CD4-Positive T-Lymphocytes - immunology; CD8 antigen; CD8-Positive T-Lymphocytes - drug effects; CD8-Positive T-Lymphocytes - immunology; Cell death; Cell division; Cell Line, Tumor; Chemotherapy; Clinical trials; Combination drug therapy; Combination therapy; Combined Modality Therapy - methods; Dendritic cells; Dendritic Cells - drug effects; Dendritic Cells - immunology; Differential equations; Dosage; Dosage and administration; Drugs; Gene expression; Granulocyte-macrophage colony-stimulating factor; Granulocyte-Macrophage Colony-Stimulating Factor - immunology; Humans; Immune checkpoint; Immunosuppressive agents; Immunotherapy; Inhibitors; Interleukin 12; Interleukin 2; Interleukin-12 - immunology; Interleukin-2 - immunology; Lung cancer; Lymphocytes; Lymphocytes T; Mathematical models; Medicine and Health Sciences; Mice; Models, Theoretical; Neoplasms - drug therapy; Neoplasms - immunology; Ordinary differential equations; Partial differential equations; PD-1 protein; Physical Sciences; Rodents; Treatment outcome; Tumor Burden - drug effects; Tumor Burden - immunology; Tumors; Vaccines
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0178479

In this paper we consider a combination therapy of cancer. One drug is a vaccine which activates dendritic cells so that they induce more T cells to infiltrate the tumor. The other drug is a checkpoint inhibitor, which enables the T cells to remain active against the cancer cells. The two drugs are positively correlated in the sense that an increase in the amount of each drug results in a reduction in the tumor volume. We consider the question whether a treatment with combination of the two drugs at certain levels is preferable to a treatment by one of the drugs alone at 'roughly' twice the dosage level; if that is the case, then we say that there is a positive 'synergy' for this combination of dosages. To address this question, we develop a mathematical model using a system of partial differential equations. The variables include dendritic and cancer cells, CD4+ and CD8+ T cells, IL-12 and IL-2, GM-CSF produced by the vaccine, and a T cell checkpoint inhibitor associated with PD-1. We use the model to explore the efficacy of the two drugs, separately and in combination, and compare the simulations with data from mouse experiments. We next introduce the concept of synergy between the drugs and develop a synergy map which suggests in what proportion to administer the drugs in order to achieve the maximum reduction of tumor volume under the constraint of maximum tolerated dose.