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By using various issues such as stress response, drag resistance, and bone metabolism as research subjects, we established a method of mathematical oncology that can solve those issues by combining systems biological modeling, cell biological experiments, and dynamical systems theory.

We unraveled a mathematical structure of the classical Hoffman model for the classical paths in the stress response, and found out that the damped oscillation results from an unstable periodic orbit. Furthermore, we conducted numerical simulations by newly introducing a phosphorylation model, and confirmed that the damped oscillation occurs similar to the previous models.

We then proved that the damped oscillation results from a stable periodic solution that transitionally appears based on the dynamical system theory. In addition, we clarified that the phosphorylation of NF-κB contributes to reproducibility of a period and amplitude of vibration. Next, we conducted additional vitro experiments and obtained a cell biological proof of the above-mentioned assumption.

We established a mathematical model for a drug-resistance acquisition mechanism of lung cancer nostrum Gefitinib resulted from cell membrane molecule MET, and conducted real-time numerical simulations through parameter identification by using measurement values and dimensional analysis.

We further conducted cell biological experiments, and acquired novel knowledge that disproves the existing assumption about malignant progression signal generation. Through those activities, we newly established a method of the dimensional analysis for estimating orders of parameters that are difficult to measure through experiments, from the mathematical model and other information actually measured, such as a size of a cell, the number of molecules, and a reaction time.

We constructed the mathematical model of cytodifferentiation by using bone metabolism as a research subject, and found a solution by using the catastrophe theory and the mode dynamical system in which dynamic equilibrium is collapsed due to parameter variation. In addition, we theoretically clarified a mechanism leading to osteoporosis due to parameter variation in a control factor path.

We conducted theoretical analysis and numerical simulations by newly introducing the phosphorylated model for stress response, thereby clarifying that damped oscillation of an expression amount of NF-κB results from the stable periodic solution that transitionally appears through the dynamical systems theory and the cell biological experiments. By using the drug-resistance acquisition mechanism of lung cancer nostrum Gefitinib resulted from cell membrane molecule MET as a research subject, we established the method of the dimensional analysis for parameter identification using measurement values and the dimensional analysis. In addition, we theoretically disproved the existing assumption that the drug resistance is obtained by way of MET. This was proved through experiments.

mathematical oncology, NF-κB path, phosphorylation, dynamical systems theory, drug resistance, Gefitinib, MET, dimensional analysis

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