Abstract
Understanding the dynamic behavior of kinetochores is crucial for understanding the mechanisms of accurate chromosome segregation during cell division. In this study, we introduced non-linear exponents p and q into two new systems to capture the complex movements that govern the intersister movement of kinetochores during chromosome segregation. Our analysis revealed a power-law relationship between these exponents and the maximum amplitude A of sister kinetochore 2, indicating that even small adjustments in p and q lead to significant changes in kinetochore movement. This sensitivity suggests that kinetochore dynamics are governed by scale-invariant principles, potentially reflecting intrinsic properties of the kinetochore-microtubule interface such as motor protein activity. We observed that the Type II model with perturbation functions, demonstrated stability with rapidly dampening oscillations across various forms of noise and sudden shocks. This highlights the effectiveness of adaptable regulatory mechanisms in maintaining stability during mitosis. In contrast, the Type I model without such regulatory parameters exhibited sustained, bounded oscillations that did not dampen over time and showed significant fragility under stochastic noise, potentially compromising chromosome segregation fidelity. Our findings highlight the role of the exponents p and q in modulating kinetochore behavior and suggest that enhancing or mimicking these regulatory mechanisms could be a potential strategy for improving cell division fidelity as shown in our theoretical work.