Abstract
Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these interactions are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.
Highlights
Mathematical modeling of cancer-immune system interactions (CISI) can reveal the fundamental mechanisms that govern the dynamics of tumor growth (Altrock et al, 2015; Eftimie et al, 2010), and represent and important tool to devise and test new forms of immunotherapy in silico (Talkington et al, 2018)
We develop a base model of cancer-immune cell interaction
We have shown that the base model can only reproduce biologically plausible behavior if the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects
Summary
Mathematical modeling of cancer-immune system interactions (CISI) can reveal the fundamental mechanisms that govern the dynamics of tumor growth (Altrock et al, 2015; Eftimie et al, 2010), and represent and important tool to devise and test new forms of immunotherapy in silico (Talkington et al, 2018). A summary of these interactions shows that all combinations of stimulation and suppression on growth between cancer and immune cells may act simultaneously (see Fig. 1A). These interactions direct the interplay between the cancer and the immune system. Their integration into mathematical models can reveal how immunotherapeutic approaches may be employed with maximum efficiency. The main immunotherapy approaches today work by impairing mechanisms that allow cancers to suppress immune action or by the administration of effector cells to the host (Dougan and Dranoff, 2009; Mellman et al, 2011) (see Fig. 1B)
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