A minimal deterministic model reveals integration of spindle assembly and position checkpoints in mitosis

The spindle assembly checkpoint (SAC) and spindle position checkpoint (SPOC) are essential surveillance systems that ensure accurate chromosome segregation and proper spindle orientation during mitosis. While their individual mechanisms have been extensively studied, their functional integration remains poorly understood. Here, I present a minimal deterministic mathematical model that captures key interactions between SAC and SPOC, incorporating central components such as Mad2, Cdc20, APC/C, Bfa1, Bub2, Tem1, Kin4, and the mitotic kinase Cdc5. The analysis identifies four distinct operational regimes-checkpoint silence, SAC-dominant arrest, SPOC-dominant arrest, and dual-checkpoint arrest-providing a conceptual framework for how cells respond to various spindle defects. This work represents the first comprehensive mathematical framework that integrates these two critical checkpoint systems. The model includes tension-sensitive feedback and demonstrates that deterministic dynamics alone can generate ultrasensitive, switch-like checkpoint responses-without requiring stochastic fluctuations or spatial complexity. Simulations reproduce key experimental observations, including the effects of in vitro mutations in core components and the rheostat-like degradation dynamics of Securin and Cyclin B. Notably, the model exhibits dual regulatory behavior: a bistable toggle switch within the SAC core driven by autocatalytic feedback, and a graded, rheostat-like output at the level of checkpoint satisfaction. This reconciles seemingly contradictory observations of discrete molecular switches with continuous cellular responses. Together, these findings offer a simplified yet predictive framework for dissecting mitotic checkpoint integration and lay the groundwork for future experimental and theoretical studies of SAC-SPOC coordination.