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2017 ; 7
(ä): 42300
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Proteins analysed as virtual knots
#MMPMID28205562
Alexander K
; Taylor AJ
; Dennis MR
Sci Rep
2017[Feb]; 7
(ä): 42300
PMID28205562
show ga
Long, flexible physical filaments are naturally tangled and knotted, from
macroscopic string down to long-chain molecules. The existence of knotting in a
filament naturally affects its configuration and properties, and may be very
stable or disappear rapidly under manipulation and interaction. Knotting has been
previously identified in protein backbone chains, for which these mechanical
constraints are of fundamental importance to their molecular functionality,
despite their being open curves in which the knots are not mathematically well
defined; knotting can only be identified by closing the termini of the chain
somehow. We introduce a new method for resolving knotting in open curves using
virtual knots, which are a wider class of topological objects that do not require
a classical closure and so naturally capture the topological ambiguity inherent
in open curves. We describe the results of analysing proteins in the Protein Data
Bank by this new scheme, recovering and extending previous knotting results, and
identifying topological interest in some new cases. The statistics of virtual
knots in protein chains are compared with those of open random walks and
Hamiltonian subchains on cubic lattices, identifying a regime of open curves in
which the virtual knotting description is likely to be important.