Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Poster Session II
53 – POS
Board 25
Thermal Properties of Polymer Knots in the Presence of Short-range Interactions
Yani Zhao
.
Institute of Physics, University of Szczecin, Szczecin, Poland.
Polymer rings forming complex topological configurations are studied in connection with several
applications ranging from biochemistry to mechanical engineering. A brief account on the latest
experimental results in the subject will be reviewed. The most difficult problem in dealing with
the statistical mechanics of polymer knots is to distinguish their topological configurations. In
this talk the results of extensive simulations of single polymer knots on a simple cubic lattice and
with lengths up to thousand segments will be presented. To equilibrate the knots and for the
Monte Carlo sampling, which is based on the Wang-Landau algorithm, a set of pivot moves is
used. To preserve the topology of the knots after each move, two recently developed techniques
have been employed. One is the so-called PAEA method. It is able to detect the changes of
topology exactly and is very fast. The other method uses the Vassiliev knot invariant of degree 2
represented in the form of contour integrals. This invariant has the great advantage of allowing
large pivot moves, which are able to accelerate the Monte Carlo sampling procedure. As an
application of these methods, the calculation of the specific energy, the radius of gyration and the
heat capacity of several types of polymer knots in a solution with poor or good solvents will be
presented. Some consequences on the thermodynamics of polymer knots will be drawn. The
problem of sampling certain rare knot conformations and of detecting pseudo phase transitions
associated with these conformations will be discussed. A comparison with the previously known
result will be made.
54 – POS
Board 26
Unknotting the Gordian Knot: Single Molecule Force Spectroscopy on UCH-L1
Fabian Ziegler
1
, Nicole Lim
2
, Benjamin Pelz
1
, Mathias Arens
1
, Soumit Mandal
1
, Wei-Ping Ng
2
,
Sophie E. Jackson
2
.Matthias Rief
1
.
1
Technische Universität München, Garching, Germany,
2
University of Cambridge, Cambridge,
United Kingdom.
We perform Single Molecule Force Spectroscopy with Optical Tweezers to single molecules of
the knotted protein UCH-L1, a protein knot with a 5
2
(so called "Gordian") topology.
Force offers ideal possibilities to control the conformation of the knotted chain. Here we apply
force in the range of several piconewton to single molecules of UCH-L1.
With mutations of single amino acids in the sequence of UCH-L1 we can pull with different
geometries. Pulling at the n- and c-terminus of the sequence leads to unfolding and tightening the
knot, while other pulling positions can reduce the knot from a 5
2
to a 3
1
structure or even
completely unknot the polypeptide chain. With these mutants, we study the folding kinetics in
dependence of the knot formation of UCH-L1.
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