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Title: Projecting proteins and random walks : knotting in open curves via virtual knots
Author: Alexander, Keith
ISNI:       0000 0004 7432 8156
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2018
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In this thesis we develop a new method of knot recognition for open curves based on taking many projections and identifying them as virtual knots, an extended class of knotted objects which exist ‘in-between’ classical knot types. We call this method virtual closure. We explore how virtual closure differs from a method we call sphere closure which involves joining the ends of the curve to many far away points, finding that virtual closure is more sensitive to knotting and provides more complex and detailed conformational information. An important distinction we find is between curves which present a single dominant knot type across closures, which we call strongly knotted, and more ambiguous curves which are knotted but with many different knots depending on the closure chosen, which we call weakly knotted. We perform a knotting survey of all proteins in the Protein Data Bank using virtual closure. Compared to previous sphere closure surveys, we find 25% more knotted proteins. Of all the knotted proteins, 40% are found to be weakly knotted under virtual closure, many more than under sphere closure, hinting that the knotting in proteins is more ambiguous than was previously thought. We then investigate the knotting of random walks, finding that weak knotting is very rare in unconfined walks, but increasingly common in isotropically confined walks both on and off-lattice. We determine that weak knotting is essentially length independent, instead depending only on the degree of confinement - the ratio of average radius of gyration of unconfined walks to confined walks of the same length. The greater the degree of confinement, the more likely that knotting is weak. We reduce the number of confined dimensions, moving from walks in the sphere, to the tube and then to slits, finding that overall knotting and weak knotting become less common.
Supervisor: Hanna, Simon Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available