Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Poster Session I
19 – POS
Board 19
Persistence Length Dependence of Knot Probability in Compact Off-lattice Random
Polymers
Marek Kochanczyk
.
Institute of Fundamental Technological Research, Warsaw, Poland.
The existence and spectrum of knots in proteins depends on the interplay of physics and
evolution. In attempts to disentangle these two factors, an estimate of background propensity of
knotting in a generic protein-like polymer of given length, devoid of evolutionary selection
pressure, is highly desirable.
In this work, to obtain model polymers, a backbone trace was generated by filling a sphere
uniformly at random with C
α
atoms. Volume of the sphere was proportional to the protein chain
length and realistic atomic density was assumed with minimal C
α
--C
α
distance of 0.38 nm.
Virtual bonds were assigned by finding the minimal Hamiltonian path between positions of all
C
α
atoms (solved as a global optimization problem equivalent to the traveling salesman
problem).
It turned out that generated structures, although matching well to global folds of real protein
structures [Brylinski et al.
Phys. Chem. Chem. Phys.
13, 17044 (2011)], have persistence length
on average twice shorter than that of real protein chains. The spread of persistence lengths of
generated structures allowed to observe that chains of shorter persistence lengths have their
dependence of unknot probability on the (overall) chain length close to that of random self-
avoiding polygons [Baiesi et al.
Phys. Rev. Lett.
99, 058301 (2007)]. At the same time, chains of
the same number of residues (and compactness) but larger persistence length have higher
knotting probability.
This result suggests that prevalent self-avoiding walk-based approaches could underestimate the
background propensity of knotting in proteins which, due to the usually non-negligible
secondary structure content, have higher persistence lengths.
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