Abstract
Mitotic checkpoints orchestrate cell division through intricate molecular networks that ensure genomic stability. While experimental research has uncovered key aspects of checkpoint function, the complexity of protein interactions and spatial dynamics necessitates computational modeling for a deeper, system-level understanding. This review explores mathematical frameworks-from ordinary differential equations to stochastic simulations, which reveal checkpoint dynamics across multiple scales, encompassing models ranging from simple protein interactions to whole-system simulations with thousands of parameters. These approaches have elucidated fundamental properties, including bistable switches driving spindle assembly checkpoint (SAC) activation, spatial organization principles underlying spindle position checkpoint (SPOC) signaling, and critical system-level features ensuring checkpoint robustness. This study evaluates diverse modeling approaches, from rule-based models to chemical organization theory, highlighting their successful application in predicting protein localization patterns and checkpoint response dynamics validated through live-cell imaging. Contemporary challenges persist in integrating spatial and temporal scales, refining parameter estimation, and enhancing spatial modeling fidelity. However, recent advances in single-molecule imaging, data-driven algorithms, and machine learning techniques, particularly deep learning for parameter optimization, present transformative opportunities for improving model accuracy and predictive power. By bridging molecular mechanisms with system-level behaviors through validated computational frameworks, this review offers a comprehensive perspective on the mathematical modeling of cell cycle control, with practical implications for cancer research and therapeutic development.