Numerical simulation teaching plus other scholar citations? The mitotic spindle assembly checkpoint (MSAC) is an important regulatory mechanism of the cell cycle, ensuring proper chromosome segregation in mitosis. It delays the transition to anaphase until all chromosomes are properly attached to the mitotic spindle by emitting a diffusible “wait anaphase”-signal from unattached kinetochores. Current models of the checkpoint disregard important spatial properties like localization, diffusion and realistic numbers of kinetochores. To allow for in silico studies of the dynamics of these models in a more realistic environment, we introduce a mathematical framework for quasi-spatial simulation of localized biochemical processes that are typically observed during checkpoint activation and maintenance.
BackgroundThe Mitotic Spindle Assembly Checkpoint (MSAC) is an evolutionary conserved mechanism that ensures the correct segregation of chromosomes by restraining cell cycle progression from entering anaphase until all chromosomes have made proper bipolar attachments to the mitotic spindle. Its malfunction can lead to cancer.Principle FindingsWe have constructed and validated for the human MSAC mechanism an in silico dynamical model, integrating 11 proteins and complexes. The model incorporates the perspectives of three central control pathways, namely Mad1/Mad2 induced Cdc20 sequestering based on the Template Model, MCC formation, and APC inhibition. Originating from the biochemical reactions for the underlying molecular processes, non-linear ordinary differential equations for the concentrations of 11 proteins and complexes of the MSAC are derived.
Every cell division in budding yeast is inherently asymmetric and counts on the correct positioning of the mitotic spindle along the mother-daughter polarity axis for faithful chromosome segregation. A surveillance mechanism named the spindle position checkpoint (SPOC), monitors the orientation of the mitotic spindle and prevents cells from exiting mitosis when the spindle fails to align along the mother-daughter axis. SPOC is essential for maintenance of ploidy in budding yeast and similar mechanisms might exist in higher eukaryotes to ensure faithful asymmetric cell division. Here, we review the current model of SPOC activation and highlight the importance of protein localization and phosphorylation for SPOC function. Read even more details on Bifurcation analysis by Bashar Ibrahim.
Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations.