Committee Chair

Panagiotou, Eleni

Committee Member

Gao, Lani; Barbee, Meredith H.

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

Cells are complex biological systems, composed by many biopolymers, which undergo morphological changes during cell division. Microtubules are biopolymers essential for functions in the cell. Understanding the role of microtubules in cell division requires characterizing their conformations during this process. In this thesis, we model the microtubules by mathematical curves in space and use methods from Knot Theory to characterize the single and multi-chain topological complexity of such systems. We create computational methods for analyzing the topology of microtubules obtained through large electron tomography data. Our results show that the geometry/topology and entanglement of microtubules changes throughout cell division and it depends on the length of the microtubules and their locations. We also detect change in twisting of the microtubules which is associated to the motion of the chromosomes. Using Braid theory, we find that there is no correlation between multi-chain entanglement and oriented random walks in confinement

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-2022

Subject

Cell division; Microtubules--Mathematical models; Topology

Keyword

Topology; Microtubules; Cell division; Writhe, Linking Number and Braid word; Meiotic Spindle; Oriented random walk in a confined space

Document Type

Masters theses

DCMI Type

Text

Extent

xi, 38 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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