A theoretical model of anaphase. (English) Zbl 07902942
Summary: This paper develops a theory for anaphase in cells. After a brief description of microtubules, the mitotic spindle and the centrosome, a mathematical model for anaphase is introduced and developed in the context of the cell cytoplasm and liquid crystalline structures. Prophase, prometaphase and metaphase are then briefly described in order to focus on anaphase, which is the main study of this paper. The entities involved are modelled in terms of liquid crystal defects and microtubules are represented as defect flux lines. The mathematical techniques employed make extensive use of energy considerations based on the work that was developed by
C. M. Dafermos [Q. J. Mech. Appl. Math. 23, No. 2, 49–64 (1970; doi:10.1093/qjmam/23.2.49)]
from the classical Frank-Oseen nematic liquid crystal energy
[F. C. Frank, “Liquid crystals. On the theory of liquid crystals”, Discuss. Faraday Soc. 25, 19–28 (1958);
C. W. Oseen, Trans. Faraday Soc. 29, 883–899 (1933; Zbl 0008.04203)].
With regard to liquid crystal theory we introduce the concept of regions of influence for defects which it is believed have important implications beyond the subject of this paper. The results of this paper align with observed biochemical phenomena and are explored in application to HeLa cells and Caenorhabditis elegans. This unified approach offers the possibility of gaining insight into various consequences of mitotic abnormalities which may result in Down syndrome, Hodgkin lymphoma, breast, prostate and various other types of cancer.
Keywords:
anaphase; nematic liquid crystal; defects; Dafermos energy; cytoplasm; microtubules; regions of influence; HeLa cell; Caenorhabditis elegansCitations:
Zbl 0008.04203References:
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