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The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous work (Huang and Yong, 2013) for simplifying the Fas signaling-induced apoptotic pathway identified by Hua et al. (2005) for human tumor T cells. The previous paper studied the downstream intracelluar-signaling subsystem, while the present one is concerned with the upstream death-inducing signaling complex (DISC) subsystem. Under the assumption that the bind of Fas-associated death domains and FLICE-inhibitory proteins to the DISC is much faster than that of the initiator procaspases, we greatly simplify the upstream subsystem from 35 reactions with 26 species to 6 reactions with 9 species by adopting the classical and recently justified partial equilibrium approximation method. Numerical simulations show that the simplified model is in an excellent agreement with the original model. Most importantly, the simplified model clearly reveals the key reactants and dominated pathways in the Fas signaling process, and thus provides new insights into the apoptosis. [ABSTRACT FROM AUTHOR]