Mathematical modeling and application of IL-1β/TNF signaling pathway in regulating chondrocyte apoptosis

Introduction: Mathematical model can be used to model complex biological processes, and have shown potential in describing apoptosis in chondrocytes. Method: In order to investigate the regulatory mechanisms of TNF signaling pathway in regulating chondrocyte apoptosis, a fractional-order differential equation model is proposed to describe the dynamic behavior and mutual interaction of apoptosis-related genes under the activation of TNF signaling pathway. Compared with the traditional molecular biology techniques, the proposed mathematical modeling has advantages to providing a more comprehensive understanding of the regulatory mechanisms of TNF signaling pathway in chondrocyte apoptosis. Result: In this paper, differentially expressed genes induced by IL-1β in human chondrocyte apoptosis are screened using high-throughput sequencing. It is found that they were significantly enriched in the TNF signaling pathway. Therefore, a mathematical model of the TNF signaling pathway is built. Using real-time PCR experiments, mRNA data is measured and used to identify the model parameters, as well as the correlation coefficient. Finally, the sensitivity of the model parameters is discussed by using numerical simulation methods, which can be used to predict the effects of different interventions and explore the optimal intervention strategies for regulating chondrocyte apoptosis. Discussion: Therefore, fractional-order differential equation modeling plays an important role in understanding the regulatory mechanisms of TNF signaling pathway in chondrocyte apoptosis and its potential clinical applications.