# A Mathematical Framework for Kinetochore-Driven Activation Feedback in the Mitotic Checkpoint

## TL;DR

This paper introduces a minimal mathematical model of the spindle assembly checkpoint that incorporates feedback mechanisms, spatial properties, and biochemical details to better understand kinetochore-driven mitotic regulation.

## Contribution

It presents a novel nonlinear differential equation framework that captures SAC activation and silencing, emphasizing the importance of feedback and spatial effects in mitotic control.

## Key findings

- The model reproduces bifurcation signaling switches with all kinetochores attached.
- Diffusion effects influence system stability and SAC silencing.
- Experimental diffusion coefficients are insufficient for rapid APC/C inhibition.

## Abstract

Proliferating cells properly divide into their daughter cells through a process that is mediated by kinetochores, protein-complexes that assemble at the centromere of each sister chromatid. Each kinetochore has to establish a tight bipolar attachment to the spindle apparatus before sister-chromatid separation is initiated. The Spindle Assembly Checkpoint (SAC) links the biophysical attachment status of the kinetochores to mitotic progression, and ensures that even a single misaligned kinetochore keeps the checkpoint active. The mechanism by which this is achieved is still elusive. Current computational models of the human SAC disregard important biochemical properties by omitting any kind of feedback loop, proper kinetochore signals, and other spatial properties such as the stability of the system and diffusion effects. To allow for more realistic in silico study of the dynamics of the SAC model, a minimal mathematical framework for SAC activation and silencing is introduced. A nonlinear ordinary differential equation model successfully reproduces bifurcation signaling switches with attachment of all 92 kinetochores and activation of APC/C by kinetochore-driven feedback. A partial differential equation model and mathematical linear stability analyses indicate the influence of diffusion and system stability. The conclusion is that quantitative models of the human SAC should account for the positive feedback on APC/C activation driven by the kinetochores which is essential for SAC silencing. Experimental diffusion coefficients for MCC sub-complexes are found to be insufficient for rapid APC/C inhibition. The presented analysis allows for systems-level understanding of mitotic control and the minimal new model can function as a basis for developing further quantitative-integrative models of the cell division cycle