Mathematical Models of Immune Regulation and Cancer Vaccines

Abstract

An array of powerful mathematical tools can be used to identify the key underlying components and interactions that determine the mechanics of biological systems such as the immune system and its interaction with cancer. In this dissertation, we develop mathematical models to study the dynamics of immune regulation in the context of the primary immune response and tumor growth. Regulatory T cells play a key role in the contraction of the immune response, a phase that follows the peak response to bring cell levels back to normal. To understand how the immune response is regulated, it is imperative to study the dynamics of regulatory cells, and in particular, the conditions under which they are functionally stable. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and possibly turn into immune promoting cells. We develop dynamical models to investigate the effects of an unstable regulatory T cell population on the immune response. These models display the usual characteristics of an immune response with the added capabilities of being able to correct for initial imbalances in T cell populations. We also observe an increased robustness of the immune response with respect to key parameters. Similar conclusions are demonstrated with regards to the effects of regulatory T cell switching on immunodominance. TGF-beta is an immunoregulatory protein that contributes to inadequate anti-tumor immune responses in cancer patients. Recent experimental data suggests that TGF-beta inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model to gain insight into the cooperative interaction between anti-TGF-beta and vaccine treatments. Using numerical simulations and stability analysis we study the following scenarios: a control case of no treatment, anti-TGF-beta treatment, vaccine treatment, and combined anti-TGF-beta vaccine treatments. Consistent with experimental data, we show that monotherapy alone cannot successfully eradicate a tumor. Tumor eradication requires the combination of these therapeutic approaches. We also demonstrate that our model captures the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy.