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- W96280044 abstract "Proteins play a vital role in all organic life. The structure of a protein is directly related to its function. Hence, how they fold and what they fold into is of great interest. Given the spontaneous manner in which many proteins fold, one would not expect complicated structures like knots to occur in native states. Nevertheless, current research has shown that proteins do indeed contain local knots; some with as many as 6 crossings. In general, the role of knots in proteins and how they are formed is not completely understood. This thesis develops models of protein knotting by using knot theory and tangles. Mathematically, a knot is just a topological embedding of a circle in Euclidean 3-space, R, or the unit 3-sphere, S. A tangle is defined as a pair, (B, T ), where B is a 3-dimensional ball and T is a set of disjoint arcs properly embedded in B. We begin with 2-string tangles and use the tangle calculus developed by Ernst and Sumners to set up tangle equations. In this model the strings of the 2-tangles represent the protein chain. Solutions to these 2-string tangle equations are then found. Motivated by the hypothesized folding pathway of the knotted protein DehI, a more complicated 3-string tangle model is developed. It is hypothesized that a terminal end of the protein is threaded through two loops. In the proposed model, the threading of a terminal end of the protein through two loops is translated into a Γ-move on 3-string tangles. A Γ-move is a special type of 3-string tangle replacement. The 3-braids are utilized as a subset of 3-string tangles to find solutions in a limited case. Additionally, tangle models give insight into how to make specific knot types" @default.
- W96280044 created "2016-06-24" @default.
- W96280044 creator A5045407751 @default.
- W96280044 date "2018-11-29" @default.
- W96280044 modified "2023-10-11" @default.
- W96280044 title "Modeling knotted proteins with tangles" @default.
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- W96280044 doi "https://doi.org/10.17077/etd.7vrpktt2" @default.
- W96280044 hasPublicationYear "2018" @default.
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