Mathematical models of tumor-immune interactions in the context of chemotherapy
DateTuesday, April 2, 2019 - 4:00pm
AbstractIn recent years, advances in cancer research have shown that the body’s immune response to tumor cells plays a significant role in fighting cancer growth. Although the immune system is intrinsically capable of destroying tumor cells, tumors and their microenvironment have an ability to suppress the immune response. This talk develops a series of systems of deterministic and stochastic ordinary equations that capture the relationship between tumor cells, the immune system, and chemotherapy to determine the role of different immune cells and molecules in the tumor growth and treatment with the therapeutic cocktail FOLFOX. This model captures the complex interplay between CD4+ and CD8+ T cells, regulatory T cells, NK cells, dendritic cells, MDSCs, and both immunostimulatory (IL-2, IFN-gamma) and immunosuppressive (IL-10, TGF-beta) cytokines or factors, the primary tumor, circulating tumor cells, and tumor metastases. All parameters are estimated from experimental data. The model shows that for a single tumor nodule, NK cells play a negligleable role compared to cytolytic T cells, although this result depends heavily on the tumor antigen expression. For tumors with high antigen expression on their surface, T cells play the primary role in preventing metastasis formation, however circulating tumor cells with low antigen expression are eradicated mostly by NK cells. With this model, it is possible to replicate experimental data of tumor growth and treatment under depletion of NK cells and CD8+ T cells. The extension of this model to give individualized predictions to patients on combinations of chemotherapy and immunotherapy will be discussed.
The competitive exclusion principle in stochastic environments
DateTuesday, April 16, 2019 - 4:00pm
AbstractThe competitive exclusion principle states, in its most basic form, that a number of species competing for a smaller number of resources cannot coexist. Both experimental and theoretical studies have shown that in some instances environmental fluctuations can facilitate coexistence for competing species. Hutchinson conjectured that one can get coexistence because nonequilibrium conditions would make it possible for different species to be favored by the environment at different times. In this talk I will look at how random environmental fluctuations can facilitate coexistence. I will show that, contrary to Hutchinson's explanation, if one switches randomly between two environments in which species 1 persists and species 2 goes extinct, so that the same species is favored at all times, one can still get coexistence.
How biodiversity gradients are made: speciation, extinction, and colonization
DateTuesday, April 23, 2019 - 4:00pm
AbstractHow were hotspots of biodiversity formed? I take a macroevolutionary approach to understand which processes generated present-day biodiversity gradients and how long these processes have operated over deep time scales. In my talk I will focus on three global-scale biodiversity patterns: the peak in marine richness at the Central Indo-Pacific region, the latitudinal biodiversity gradient on land, and the difference between terrestrial and marine richness. Species can be added to a region through in-situ speciation or colonization from elsewhere, and removed through local or global extinction. To understand the relative roles of these processes, I reconstructed past biogeography on time-calibrated molecular phylogenies of vertebrates. A common link between these three biodiversity patterns is that species-rich regions have provided stable habitats for their occupants for much longer than species-poor regions.