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Abstract

Immunomodulatory approaches harnessing the patient’s T cell response against cancer have established themselves as a promising treatment option. Nevertheless, the poor predictability of a patient’s response shows our limited understanding of the factors that determine whether immunotherapy works. To gain an insight into the underlying mechanisms we develop a data-driven mathematical model of T cells responding to tumors under an immunotherapeutic intervention. To this end, we analyze data obtained from a murine model for melanoma, which is a responsive tumor with respect to immunotherapy and thus, a suitable testbed for new treatment options. In addition, we study the T cell response in a murine model of pancreatic ductal adenocarcinoma—in the clinical setting a tumor for which new therapeutic approaches are urgently needed. The treatment with an agonistic antibody against CD40, which is investigated in this thesis, shows promising results in preclinical studies with pancreatic cancer and is applied in clinical phase I studies for several tumor indications. Still, it is not well understood how this intervention shapes the T cell response and a data-driven modeling approach has not been attempted yet. First, we develop a method for the accurate analysis of dye dilution measurements of dividing cells in vivo, since our modeling approach strongly relies on proliferation data. For these measurements cells are initially stained with a fluorescent dye, such as CFSE, and their proliferative activity can be traced due to a halving of the dye intensity with every division. The resulting dye intensity peaks are usually clearly separated if the data are obtained from in vitro measurements and most analyzing approaches have been optimized for this case. In these methods it often suffices to use parametric distributions to describe the data. However, our data stems from in vivo experiments and has strongly overlapping peaks, such that its analysis is difficult with these approaches. For this reason, we develop a method where data-inherent information like the background intensity and the distribution of the dye intensities of undivided cells is used to account for the data specific shape of the peaks. It furthermore allows for the flexible combination of samples to obtain robust optimization results and is successfully tested with six data sets provided by collaboration partners. In this way, we can reliably discern the relative fractions of cells in different generations, even if the peaks are strongly overlapping. Secondly, we introduce and validate a data-driven mathematical model describing the anti-tumor T cell response. The model is devised with data obtained from two murine melanoma experiments performed by our collaboration partners, in which also the effect of anti-CD40 has been investigated. The measurements are conducted at various time points post naive T cell transfer and provide absolute cell counts, as well as complementary information on cell proliferation, which we analyze with our newly described method. Overall, these two data sets enable us to test various plausible mathematical model alternatives and to identify the most likely mechanism. In the draining lymph node our investigation reveals that the proliferation of T cells is attenuated over time and provides evidence of a division stop after four to six generations. In the tumor a cessation of proliferation is likely, but varies more between the experiments: We find a total of six or more divisions in one case and in the other case two further divisions after the cells enter the tumor. The proliferation in the tumor is faster than in the draining lymph node and stands in contrast to this abrupt division stop. Subsequently, we determine mechanisms which are changed by the treatment with anti-CD40. We find evidence for an enhanced activation of the naive T cells, which has been suggested previously. In addition, we identify a delayed egress from the draining lymph node due to the treatment. Thirdly, a similar mathematical model can explain the measured T cell dynamic in a murine pancreatic cancer model. In this model, we also confirm a division stop, both in the tumor and the draining lymph node. However, in contrast to the melanoma setting we find a faster proliferation before it ceases after six divisions. The difference of the proliferative activity is particularly pronounced in the draining lymph node, where it is not attenuated over time. Interestingly, for the pancreatic tumor both the model and the data point to an increased overall death of T cells, which in the melanoma setting was mainly confined to the tumor. Furthermore, we determine that the anti-CD40 treatment increases the proliferation rate and also find evidence for an enhanced activation. This raises the question whether the treatment is affecting the proliferation of already activated T cells, too. As the egress rate is not well constrained by the data, we cannot determine whether the drug slows egress also in this tumor model. Overall, in this work we introduce a method to analyze in vivo cell proliferation dye measurements. We also reveal properties of the naive T cell response to two different tumor types and the effects of anti-CD40 treatment on these dynamics. These mechanistic insights may help improve the way in which anti-CD40 is applied in the treatment of cancer.