Phenomenological Approach to Cancer Cell Persistence

Modeling the Role of Immune Cell Conversion in the Tumor-Immune Microenvironment

Tumors develop in a complex physical, biochemical, and cellular milieu, referred to as the tumor microenvironment. Of special interest is the set of immune cells that reciprocally interact with the tumor, the tumor-immune microenvironment (TIME). The diversity of cell types and cell-cell interactions in the TIME has led researchers to apply concepts from ecology to describe the dynamics. However, while tumor cells are known to induce immune cells to switch from anti-tumor to pro-tumor phenotypes, this type of ecological interaction has been largely overlooked. To address this gap in cancer modeling, we develop a minimal, ecological model of the TIME with immune cell conversion, to highlight this important interaction and explore its consequences. A key finding is that immune conversion increases the range of parameters supporting a co-existence phase in which the immune system and the tumor reach a stalemate. Our results suggest that further investigation of the consequences of immune cell conversion, using detailed, data-driven models, will be critical for greater understanding of TIME dynamics.

Phenotypic evolution as an Ornstein-Uhlenbeck process: The effect of environmental variation and phenotypic plasticity

Here we investigate phenotypic evolution from the perspective of the Ornstein-Uhlenbeck (OU) process. Evolutionarily speaking, the model assumes the existence of stabilizing selection toward a phenotypic optimum. The standard (OU) model is modified to include environmental variation by taking a moving phenotypic optimum and endowing organisms with phenotypic plasticity. These two processes lead to an effective fitness landscape, which deforms the original. We observe that the simultaneous occurrence of environmental variation and phenotypic plasticity leads to skewed phenotypic distributions. The skewness of the resulting phenotypic distributions strongly depends on the rate of environmental variation and strength of selection. When generalized to more than one trait, the phenotypic distributions are not only affected by the magnitude of the rate of environmental variation but also by its direction. A remarkable feature of our predictions is the existence of an upper bound for the critical rate of environmental variation to allow population persistence, even if there is no cost associated with phenotypic plasticity.