Mathematical Models of the Role of the Immune System in FOLFOX Therapy for Colorectal Adenocarcinoma

Abstract

Colorectal cancer is one of the most prevalent cancers, leading to 1.36 million diagnoses and 0.7 million deaths annually worldwide (Jemal et al., 2011). The current standard-of-care for this cancer is FOLFOX, a chemotherapeutic combination of three drugs, 5-fluoruracil (5-FU), oxaliplatin and folinic acid. Although originally developed as a standard chemotherapy, this combination was found to have significant immune effects, and understanding the role of the immune system in the success of this therapy has potential to help in development of new therapies and in optimizing the best combinations of chemotherapy and immunotherapy would most benefit which patients. The goal of this work was to answer the question: What is the role of the immune system in the success of FOLFOX chemotherapy against colorectal carcinoma? To answer this question, several compartmental ordinary differential equation models were developed that capture the complex interplay between the immune system, tumors, and treatment with chemo-and-immunotherapy. These models included, among other species, T cells, natural killer (NK) cells, myeloid derived suppressor cells (MDSCs), and interferon-gamma (IFN-γ). Parameters for these mathematical models were estimated individually from independent literature sources, and further calibrated by comparison to clinically and experimentally observed cell counts and molecular concentrations in tumor-bearing mice. Two parameters were allowed to vary, to account for subject-to-subject differences: tumor growth rate and antigenicity, an aggregate measure that corresponds to the tumor’s ability to stimulate an antigen-specific adaptive immune response. The model without treatment was used to predict that T cells have a much greater role in tumor control than NK cells, across changes in growth rate and antigenicity, stemming from low NK counts in the tumor, both due to low recruitment to the tumor and high depletion from tumor kill. The model with treatment found that the most significant effects of FOLFOX treatment were direct cytotoxicity to tumor cells and 5-FU kill of MDSCs, and that oxaliplatin immune effects on IFN-gamma production contributed much less to the success of FOLFOX, across the entire range of antigenicity and growth rates. Increasing the growth rate lead to a significant effect of immunogenic cell death and a reduced, but still important, effect of MDSC killing, whereas for lower growth rates, the immunogenic cell death effects were negligible. The success of FOLFOX was also found to depend on a multitude of other factors, including the schedule of treatment and the tumor size at the time of treatment. Slow growing, highly antigenic, and early-treated tumors fared best with treatment with FOLFOX. Predictions of combinations of chemo-and-immunotherapies showed the potential to fully cure subject by supplementing FOLFOX therapy with dendritic cell therapy, but tumor eradication was only possible for highly antigenic tumors. Using mathematical modeling, it was possible to quantify the role of the immune system in treatment of colorectal cancer with FOLFOX and not only explain the results of experiments, but also make predictions about treatment outcomes.