Providing a Stochastic Petri Net Model for Interactions of the Immune System and B16-F10 Tumor Cells in order to Investigate the Effect of Myeloid-Derived Suppressor Cells (MDSC) on Behavioral States of Tumor

Purpose: Using mathematical models for cancer treatment had excellent outcomes in recent years. Modeling of the tumor-immune interactions is possible by several mathematical models. Stochastic models such as Stochastic Petri Net (SPN) consider the random effects and uncertainty in the biological environments. Therefore, they are a good choice for simulation of biological systems, specially the complex dynamical network of tumor-immune interactions. Methods: In this paper we have modeled the interactions of the B16-F10 tumor cells, Cytotoxic T cells (CTL) and Myeloid Derived Suppressor cell (MDSC) by SPN. By systematic search on immunology resources, we identified the behaviors, characteristics, and effective interactions between these cells. We used SPN to construct the dynamics of these cells, therefore a dynamical network of tumor-immune interactions (DNTII) has been made. By considering these cells as places and all interactions as transitions of SPN, we can simulate this complex biological network. The model has control parameters that their regulation causes DNTII to mimic different behaviors of tumor-immune system. Results: The model can properly simulate dynamical complex network of tumor-immune interactions compared to biological reality. This model is capable to represent different behavior of tumor-immune system such as tumor escape from immune response, overcoming the immune system on the tumor cells and equilibrium of the tumor and immune system. Conclusion: By using this model, we can test different immunology hypothesis in a simulation environment without spending any time and cost.