Inactivation of tumor suppressor genes and cancer therapy: An evolutionary game theory approach

Abstract

Inactivation of alleles in tumor suppressor genes (TSG) is one of the important issues resulting in evolution of cancerous cells. In this paper, the evolution of healthy, one and two missed allele cells is modeled using the concept of evolutionary game theory and replicator dynamics. The proposed model also takes into account the interaction rates of the cells as designing parameters of the system. Different combinations of the equilibrium points of the parameterized nonlinear system is studied and categorized into some cases. In each case, the interaction rates' values are suggested in a way that the equilibrium points of the replicator dynamics are located on an appropriate region of the state space. Based on the suggested interaction rates, it is proved that the system doesn't have any undesirable interior equilibrium point as well. Therefore, the system will converge to the desirable region, where there is a scanty level of cancerous cells. In addition, the proposed conditions for interaction rates guarantee that, when a trajectory of the system reaches the boundaries, then it will stay there forever which is a desirable property since the equilibrium points have been already located on the boundaries, appropriately. The simulation results show the effectiveness of the suggestions in the elimination of the cancerous cells in different scenarios.

Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective

“…[5] then, [6] where, [7] Both t1 and t2 are presented just to simplify the mathematical symbols in the paper and have no biological concepts. We categorized the system into different cases, as shown in the Fig.…”

“…Cancerous cells have interaction with non-cancerous ones (4), so they can spread their symptoms in different parts of the body (5,6). Innate and adaptive immune systems usually identify cancerous cells and kill them at the beginning of their emergence and prevent forming tumors (7). Besides, after forming a tumor, the cancer-immunity cycle can identify and attack it (8).…”

“…There are more studies regarding this method (11). Different aspects of cancer have been modeled using mathematical methods (13) including body response (14) and therapeutic techniques toward tumors; profits of radiation to improve the anticancer response (15,16); activation of oncogenes (7,17); and inactivation of tumor suppressor genes (18). The dynamics of targeted cancer therapy have been investigated using a mathematical model of somatic evolution (19).…”

“…Various mathematical approaches, such as game theory, replicator equations, and differential equations, have been applied in cancer investigation (29)(30)(31). The emergence of cancer was studied considering the interaction between healthy and cancerous cells as an evolutionary game (7,32). Models based on game theory were established that involve mutant cells, immune system cells, and medications as players of the game (32,33).…”

Evolutionary game of environmental investment under national environmental regulation in China

“…Nowadays, evolutionary game theory is applied to more and more fields. Some scholars used evolutionary game theory to explore medical problems, such as tumor (Malekian et al, 2016;Khadem et al, 2017) and medical applications (Chen et al, 2018a); Some scholars studied information technology problems with the utilization of evolutionary game theory, such as wireless sensor networks (Arora et al, 2016) and data warehouses (Sohrabi and Azgomi, 2019); Fields like migration (Leenheer et al, 2017) and intellectual property (Yang et al, 2018) have also been involved. And both economic and environmental issues have been widely researched by the theory of evolutionary game, such as carbon taxes (Chen and Hu, 2018), green building scheme design (Wang, 2018b), green supply chain (Babu and Mohan, 2018;Sun et al, 2019), electric vehicles (Fang et al, 2019b) and municipal solid waste source separation (Chen et al, 2018b).…”