Chapter 10 - Evolutionary Game Strategy of an Evolutionary Biological Network of Somatic Cells in the Organ Carcinogenesis and Aging Process

Abstract

In this chapter, the natural selection scheme of an evolutionary biological network of carcinogenesis was derived from a robust negative feedback scheme based on the nonlinear stochastic Nash game strategy. The evolvability and phenotypic robustness criterion of the evolutionary cancer network were also estimated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. The cancer is caused by the declining process of the cellular protection mechanism of the robust negative feedback scheme in the carcinogenesis process. Based on the global linearization technique, the evolvability and phenotypic robustness could be efficiently estimated by solving a set of linear matrix inequalities (LMI)-constrained optimization problems. The simulation revealed that the phenotypic shift of the lung cancer-associated cell network takes 54.5years from a normal state to stage I cancer, 1.5years from stage I to stage II cancer, and 2.5years from stage II to stage III cancer, with a reasonable match for the statistical result of the average age of lung cancer. These results suggest that a robust negative feedback scheme, based on a stochastic evolutionary game strategy, plays a critical role in an evolutionary biological network of carcinogenesis under a natural selection scheme.