Mathematical analysis and modeling of DNA segregation mechanisms

Bashar Ibrahim; Bashar Ibrahim

doi:10.3934/mbe.2018019

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 2: 429-440. doi: 10.3934/mbe.2018019

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Mathematical analysis and modeling of DNA segregation mechanisms

Bashar Ibrahim ^,

Department of Mathematics and Computer Science, University of Jena, Ernst-Abbe-Platz 2,07743 Jena, Germany

Received: 02 January 2017 Accepted: 04 May 2017 Published: 01 April 2018
MSC : Primary: 46N60, 34A09, 35K57, 32W50; Secondary: 46N20

The precise regulation of cell life division is indispensable to the reliable inheritance of genetic material, i.e. DNA, in successive generations of cells. This is governed by dedicated biochemical networks which ensure that all requirements are met before transition from one phase to the next. The Spindle Assembly Checkpoint (SAC) is an evolutionarily mechanism that delays mitotic progression until all chromosomes are properly linked to the mitotic spindle. During some asymmetric cell divisions, such as those observed in budding yeast, an additional mechanism, the Spindle Position Checkpoint (SPOC), is required to delay exit from mitosis until the mitotic spindle is correctly aligned. These checkpoints are complex and their elaborate spatiotemporal dynamics are challenging to understand intuitively. In this study, bistable mathematical models for both activation and silencing of mitotic checkpoints were constructed and analyzed. A one-parameter bifurcation was computed to show the realistic biochemical switches considering all signals. Numerical simulations involving systems of ODEs and PDEs were performed over various parameters, to investigate the effect of the diffusion coefficient. The results provide systems-level insights into mitotic transition and demonstrate that mathematical analysis constitutes a powerful tool for investigation of the dynamic properties of complex biomedical systems.
- Mathematical biology,
- modeling and simulation,
- mitotic control,
- spindle assembly checkpoint,
- spindle position checkpoint
Citation: Bashar Ibrahim. Mathematical analysis and modeling of DNA segregation mechanisms[J]. Mathematical Biosciences and Engineering, 2018, 15(2): 429-440. doi: 10.3934/mbe.2018019

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Abstract

The precise regulation of cell life division is indispensable to the reliable inheritance of genetic material, i.e. DNA, in successive generations of cells. This is governed by dedicated biochemical networks which ensure that all requirements are met before transition from one phase to the next. The Spindle Assembly Checkpoint (SAC) is an evolutionarily mechanism that delays mitotic progression until all chromosomes are properly linked to the mitotic spindle. During some asymmetric cell divisions, such as those observed in budding yeast, an additional mechanism, the Spindle Position Checkpoint (SPOC), is required to delay exit from mitosis until the mitotic spindle is correctly aligned. These checkpoints are complex and their elaborate spatiotemporal dynamics are challenging to understand intuitively. In this study, bistable mathematical models for both activation and silencing of mitotic checkpoints were constructed and analyzed. A one-parameter bifurcation was computed to show the realistic biochemical switches considering all signals. Numerical simulations involving systems of ODEs and PDEs were performed over various parameters, to investigate the effect of the diffusion coefficient. The results provide systems-level insights into mitotic transition and demonstrate that mathematical analysis constitutes a powerful tool for investigation of the dynamic properties of complex biomedical systems.

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