Significance of Knotted Structures for Function of Proteins and Nucleic Acids - September 17-21, 2014

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. 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). [2] S.Y. Shaw and J.C. Wang, Science Vol. 260, 533 (1993). [3] V. V. Rybenkoov et al., PNAS Vol. 90, 5307 (1993).

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