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Bulletin of Mathematical Biology

, Volume 76, Issue 7, pp 1590–1606 | Cite as

Stochastic Modelling of Chromosomal Segregation: Errors Can Introduce Correction

  • Anastasios MatzavinosEmail author
  • Blerta Shtylla
  • Zachary Voller
  • Sijia Liu
  • Mark A. J. Chaplain
Original Article

Abstract

Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.

Keywords

Stochastic noise Cell division Chromosome segregation Coefficient of variation Markov jump process Absorption time Stochastic chemical kinetics  

Notes

Acknowledgments

This research has been supported in part by the Mathematical Biosciences Institute and the National Science Foundation under Grant DMS 0931642. The research of Sijia Liu has been supported in part by an Alberta Wolfe Research Fellowship from the Iowa State University Mathematics department. The research of Blerta Shtylla has been supported in part by the National Science Foundation under Grant NSF DMS 1358932. MAJC gratefully acknowledges the support of the ERC Advanced Investigator Grant 227619, “M5CGS - From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”.

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Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Anastasios Matzavinos
    • 1
    Email author
  • Blerta Shtylla
    • 3
  • Zachary Voller
    • 2
  • Sijia Liu
    • 2
  • Mark A. J. Chaplain
    • 4
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsPomona CollegeClaremontUSA
  3. 3.Department of MathematicsIowa State UniversityAmesUSA
  4. 4.Division of MathematicsUniversity of DundeeDundeeUK

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