Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Sunday Abstracts
Molecular Simulations of Knotted Proteins and DNA
Benjamin Trefz
1
, Thomas Wüst
2
, Florian Rieger
1
,
Peter Virnau
1
.
1
Uni Mainz, Mainz, Germany,
2
WSL, Birmensdorf, Switzerland.
After providing a short introduction to knotted proteins, I will present simulations of a coarse-
grained heteropolymer model and argue that the addition of sequence may facilitate evolution
towards unknotted proteins. I will also discuss implications of knots in technological applications
such as nanopore sequencing, and present a mechanism which allows two knots on a polymer
chain to pass through each other and swap positions along the strand. Associated "topological"
free energy barriers only amount to a few kT, which may enable the interchange of knots on a
single DNA molecule.
Probability of DNA Knots and the Effective Diameter of DNA Double Helix
Tetsuo Deguchi
, Erica Uehara.
Ochanomizu University, Tokyo, Japan.
We evaluate the probability for self-avoiding polygons (SAP) being equivalent to a given knot
type, which we call the knot probability of the given knot, through simulation making use of knot
invariants. We consider SAP consisting of cylindrical segments whose radius parametrizes the
excluded volume. We show that a scaling formula of the knot probability as a function of the
number of segments and the radius of cylindrical segments give good fitting curves to the
numerical data of the knot probability for various knots not only prime knots but also a wide
variety of composite knots [1]. Extending the cylindrical SAP to the worm-like ring-chain model
we produce theoretical estimates of the knot probability which can be compared with
experimental results of DNA knots, where the diameter of cylindrical segments of the worm-like
chain corresponds to the effective diameter of DNA double helix. Here we recall that the
distribution of knot types produced by random cyclization of phage P4 DNA via its long
cohesive ends was investigated experimentally in solution with different concentrations of
counter ions [2,3].
[1] E. Uehara and T. Deguchi, in preparation.
[2] S.Y. Shaw and J.C. Wang, Science Vol. 260, 533 (1993).
[3] V. V. Rybenkoov et al., PNAS Vol. 90, 5307 (1993).
Coarse-grain Models of DNA Free Energy and Sequence-dependent Minicircle Shapes
John H. Maddocks.
Section of Mathematics, Swiss Federal Institute of Technology, Lausanne (EPFL)
cgDNA is a sequence-dependent coarse grain model of the free energy of DNA at the level of
rigid bases (http:lcvmwww.epfl.ch/cgDNA). I will briefly describe this model, and then show
how it can be combined with the theory of birods to compute shapes of equilibria (and in
particular associated values of the free energy) of DNA minicircles, ie closed loops of DNA of
arbitrary length and sequence (including for this conference some knotted cases).
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