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Rosen ME, Grant CP, Dallon JC. Mean square displacement for a discrete centroid model of cell motion. PLoS One. 2021;16(12):e0261021doi: 10.1371/journal.pone.0261021.
Rosen, M. E., Grant, C. P., & Dallon, J. C. (2021). Mean square displacement for a discrete centroid model of cell motion. PloS one, 16(12), e0261021. https://doi.org/10.1371/journal.pone.0261021
Rosen, Mary Ellen, et al. "Mean square displacement for a discrete centroid model of cell motion." PloS one vol. 16,12 (2021): e0261021. doi: https://doi.org/10.1371/journal.pone.0261021
Rosen ME, Grant CP, Dallon JC. Mean square displacement for a discrete centroid model of cell motion. PLoS One. 2021 Dec 20;16(12):e0261021. doi: 10.1371/journal.pone.0261021. eCollection 2021. PMID: 34928985; PMCID: PMC8687545.
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PLoS One. 2021 Dec 20;16(12):e0261021. doi: 10.1371/journal.pone.0261021. eCollection 2021.

Mean square displacement for a discrete centroid model of cell motion.

PloS one

Mary Ellen Rosen, Christopher P Grant, J C Dallon

Affiliations

  1. Department of Mathematics, Brigham Young University, Provo, Utah, United States of America.

PMID: 34928985 PMCID: PMC8687545 DOI: 10.1371/journal.pone.0261021

Abstract

The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.

Conflict of interest statement

The authors have declared that no competing interests exist.

References

  1. Annu Rev Biophys Biomol Struct. 1997;26:373-99 - PubMed
  2. Math Biosci. 2013 Nov;246(1):1-7 - PubMed
  3. Phys Rev Lett. 2007 Nov 23;99(21):210601 - PubMed
  4. J R Soc Interface. 2008 Aug 6;5(25):813-34 - PubMed
  5. Proc Natl Acad Sci U S A. 2006 Jul 5;103(27):10259-10264 - PubMed
  6. Biophys J. 1991 Oct;60(4):910-21 - PubMed
  7. Phys Chem Chem Phys. 2011 Feb 7;13(5):1800-12 - PubMed
  8. Sci Am. 1987 Dec;257(6):72-6, 89-90 - PubMed
  9. Phys Rev E. 2017 Aug;96(2-1):022132 - PubMed
  10. Biophys J. 2006 Dec 1;91(11):4296-305 - PubMed
  11. J Biomech Eng. 2013 Jul 1;135(7):71008 - PubMed
  12. Sci Rep. 2015 Jun 30;5:11690 - PubMed
  13. Cell Biochem Biophys. 2012 Jul;63(3):199-209 - PubMed
  14. Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 1):051505 - PubMed

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