Cell aging has always been an important topic in biological research, and telomere shortening is one of the key issues in cell aging studies. Telomeres are special DNA sequences located at the ends of chromosomes that gradually shorten as cells divide, triggering cell senescence, death, or cancer when shortened to critical levels. In the present study, the data of telomere length change were collected by experiment and the shortening process was described by statistical model. However, the existing results mainly focus on the probability distribution fitting of experimental data, and lack the systematic support of non-equilibrium statistical physics theory, leading to a series of key problems that have not been solved. For example, in the complex intracellular environment, the real-time dynamics of telomere shortening are difficult to observe directly, and the underlying microscopic mechanisms remain insufficiently understood. The lack of theoretical prediction tools for the relevant statistics of telomere shortening restricts the application of this study in the quantification of aging and clinical diagnosis. Therefore, it is urgent to introduce new methods to explore the changes in telomere shortening length and its association with aging and build interdisciplinary models to solve the problems.
Recently, a collaborative team from the Deng Weihua lab at Lanzhou University, China, published an article titled " Modeling telomere shortening process " in Quantitative Biology. Based on the perspective of nonequilibrium statistical physics, the team established the microscopic model of the telomere shortening process and derived the macroscopic equation by the continuous time random walk (CTRW) model, which provided a new method for the quantitative study of the telomere shortening process.

Figure 1 illustrates the telomere shortening process based on the CTRW model. Assuming that the cell division cycle follows a power-law distribution, the Fokker-Planck equation describing the evolution of telomere length was derived by combining the jump lengths of incomplete chromosome end duplication (normal distribution) and telomerase action (Poisson distribution). The results show that the kinetic behavior is between normal diffusion and anomalous diffusion. Following this, the specific parameters (such as exonuclease strength ) from non-specific parameters (such as power-law index that can be expressed), which reveal heterogeneity in the rate of telomere shortening between infants and adults are further distinguished. The Feynman-Kac equation is derived to quantify the first passage time (the initiation time of cellular senescence) and occupancy time (the cumulative time in the critical interval) of telomere shortening to the critical length, which provided a theoretical prediction tool for the aging time scale.
DOI: 10.1002/qub2.74