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Background: Frequently occurring in cancer are the aberrant alterations of regulatory onco-metabolites, various oncogenes/epigenetic stochasticity, and suppressor genes, as well as the deficient mismatch repair mechanism, chronic inflammation, or those deviations belonging to the other cancer characteristics. How these aberrations that evolve overtime determine the global phenotype of malignant tumors remains to be completely understood. Dynamic analysis may have potential to reveal the mechanism of carcinogenesis and can offer new therapeutic intervention. Aims: We introduce simplified mathematical tools to model serial quantitative data of cancer biomarkers. We also highlight an introductory overview of mathematical tools and models as they apply from the viewpoint of known cancer features. Methods: Mathematical modeling of potentially actionable genomic products and how they proceed overtime during tumorigenesis are explored. This report is intended to be instinctive without being overly technical. Results: To date, many mathematical models of the common features of cancer have been developed. However, the dynamic of integrated heterogeneous processes and their cross talks related to carcinogenesis remains to be resolved. Conclusions: In cancer research, outlining mathematical modeling of experimentally obtained data snapshots of molecular species may provide insights into a better understanding of the multiple biochemical circuits. Recent discoveries have provided support for the existence of complex cancer progression in dynamics that span from a simple 1-dimensional deterministic system to a stochastic (ie, probabilistic) or to an oscillatory and multistable networks. Further research in mathematical modeling of cancer progression, based on the evolving molecular kinetics (time series), could inform a specific and a predictive behavior about the global systems biology of vulnerable tumor cells in their earlier stages of oncogenesis. On this footing, new preventive measures and anticancer therapy could then be constructed.

An Introduction to the Mathematical Modeling in the Study of Cancer Systems Biology