Eric Rawdon's Data Page

On this page, you will find links to software, other websites we have created for our data, and knot/link data. This page is essentially always under construction. Please visit my preprints and published papers page to find the papers and my collaborators.


Software to create disk image matrices

Follow this link to download the code to make pictures like the one on the left. The documentation for the program is there as well. This software is related to our work in the following publications.

  • Knotting fingerprints resolve knot complexity and knotting pathways in ideal knots
    David A. B. Hyde, Joshua Henrich, Eric J. Rawdon, and Kenneth C. Millett
    J. Phys.: Condens. Matter, 27: 354112, 2015.
    doi:10.1088/0953-8984/27/35/354112

  • Subknots in ideal knots, random knots, and knotted proteins
    Eric J. Rawdon, Kenneth C. Millett, and Andrzej Stasiak
    Sci. Rep., 5: 8928, 2015.
    doi:10.1038/srep08928



Software to create triangular/square image matrices

Follow this link to download the software to make pictures like the one on the left. The documentation for the program is there as well. This software is related to our work in the following publications.

  • KnotProt: a database of proteins with knots and slipknots
    Michal Jamroz, Wanda Niemyska, Eric J. Rawdon, Andrzej Stasiak, Kenneth C. Millett, Piotr Sulkowski, and Joanna I. Sulkowska
    Nucleic Acids Res., 43(D1):D306-D314, 2015.
    doi:10.1093/nar/gku1059

  • Knot localization in proteins
    Eric J. Rawdon, Kenneth C. Millett, Joanna I. Sulkowska, and Andrzej Stasiak
    Biochem. Soc. Trans., 41(2):538-541, 2013.
    doi:10.1042/BST20120329

  • Identifying knots in proteins
    Kenneth C. Millett, Eric J. Rawdon, Andrzej Stasiak, and Joanna I. Sulkowska
    Biochem. Soc. Trans., 41(2):533-537, 2013.
    doi:10.1042/BST20120339

  • Knotting pathways in proteins
    Joanna I. Sulkowska, Jeffrey K. Noel, Cesar A. Ramirez-Sarmiento, Eric J. Rawdon, Kenneth C. Millett, and Jose N. Onuchic
    Biochem. Soc. Trans., 41(2):523-527, 2013.
    doi:10.1042/BST20120342

  • Conservation of complex knotting and slipknotting patterns in proteins
    Joanna I. Sulkowska, Eric J. Rawdon, Kenneth C. Millett, Jose N. Onuchic, and Andrzej Stasiak
    Proc. Natl. Acad. Sci. USA, 109(26):E1715-E1723, 2012.
    doi:10.1088/1751-8113/45/22/225202





Tight knots at resolution one

Follow this link to see and download tight knots (i.e. minimized with respect to my definition of polygonal ropelength) at resolution one (i.e. the numbers of edges is about the same as their ropelengths). The polygons were ropelength-minimized using the freely available Ridgerunner package. This data is related to some ongoing projects, but is not a part of any published papers.



Some related papers include:

  • Shapes of tight composite knots
    Jason Cantarella, Al LaPointe, and Eric J. Rawdon
    J. Phys. A, 45(22): 225202, 2012.
    doi:10.1088/1751-8113/45/22/225202

  • Knot tightening by constrained gradient descent
    Ted Ashton, Jason Cantarella, Michael Piatek, and Eric J. Rawdon
    Experiment. Math., 20(1): 57-90, 2011.
    doi:10.1080/10586458.2011.544581





LinkProt

The database LinkProt catalogs all linking in the RCSB Protein Data Bank. The database updates weekly so that it includes to most recently deposited proteins. Users can upload their own protein chains for automated analysis. This work is in collaboration with a number of people. See this page for the current list of authors. The following article summarizes the capabilities of LinkProt.

  • LinkProt: a database collecting information about biological links
    Pawel Dabrowski-Tumanski, Aleksandra Jarmolinska, Wanda Niemyska, Eric Rawdon, Kenneth Millett, and Joanna Sulkowska
    Nucleic Acids Res., 45(D1):D243-D249, 2016.
    doi:10.1093/nar/gkw976



KnotProt

The database KnotProt catalogs all knotting in the RCSB Protein Data Bank. The database updates weekly so that it includes to most recently deposited proteins. Users can upload their own protein chains for automated analysis. This work is in collaboration with a number of people. See this page for the current list of authors. The following articles are related to our work with knotted proteins.

  • KnotProt: a database of proteins with knots and slipknots
    Michal Jamroz, Wanda Niemyska, Eric J. Rawdon, Andrzej Stasiak, Kenneth C. Millett, Piotr Sulkowski, and Joanna I. Sulkowska
    Nucleic Acids Res., 43(D1):D306-D314, 2015.
    doi:10.1093/nar/gku1059

  • Knot localization in proteins
    Eric J. Rawdon, Kenneth C. Millett, Joanna I. Sulkowska, and Andrzej Stasiak
    Biochem. Soc. Trans., 41(2):538-541, 2013.
    doi:10.1042/BST20120329

  • Identifying knots in proteins
    Kenneth C. Millett, Eric J. Rawdon, Andrzej Stasiak, and Joanna I. Sulkowska
    Biochem. Soc. Trans., 41(2):533-537, 2013.
    doi:10.1042/BST20120339

  • Knotting pathways in proteins
    Joanna I. Sulkowska, Jeffrey K. Noel, Cesar A. Ramirez-Sarmiento, Eric J. Rawdon, Kenneth C. Millett, and Jose N. Onuchic
    Biochem. Soc. Trans., 41(2):523-527, 2013.
    doi:10.1042/BST20120342

  • Conservation of complex knotting and slipknotting patterns in proteins
    Joanna I. Sulkowska, Eric J. Rawdon, Kenneth C. Millett, Jose N. Onuchic, and Andrzej Stasiak
    Proc. Natl. Acad. Sci. USA, 109(26):E1715-E1723, 2012.
    doi:10.1088/1751-8113/45/22/225202





Tight knots and links

We tighten our knots using the freely available package Ridgerunner package. We have visualizations of the tightening process for knots and links The tight knot files can be found here in the VECT format. This arxiv article describes some of our results as well as how to interpret these images.

Some related articles include:

  • The spectrum of tightly knotted flux tubes in QCD
    Roman V. Buniy, Jason Cantarella, Thomas W. Kephart, and Eric J. Rawdon
    Journal of Physics: Conference Series, 544(1): 012025, 2014.
    doi:10.1088/1742-6596/544/1/012025

  • The tight knot spectrum in QCD
    Roman V. Buniy, Jason Cantarella, Thomas W. Kephart, and Eric J. Rawdon
    Phys. Rev. D, 89: 054513, 2014.
    doi:10.1103/PhysRevD.89.054513

  • Shapes of tight composite knots
    Jason Cantarella, Al LaPointe, and Eric J. Rawdon
    J. Phys. A, 45(22): 225202, 2012.
    doi:10.1088/1751-8113/45/22/225202

  • Knot tightening by constrained gradient descent
    Ted Ashton, Jason Cantarella, Michael Piatek, and Eric J. Rawdon
    Experiment. Math., 20(1): 57-90, 2011.
    doi:10.1080/10586458.2011.544581



Upper bounds for equilateral stick numbers

We have produced candidates for the minimum equilateral stick number using KnotPlot. This work is in collaboration with Rob Scharein and appears in the paper:

  • Upper bounds for equilateral stick numbers
    Eric J. Rawdon and Robert G. Scharein
    In Physical knots: knotting, linking, and folding geometric
    volume 304 of Contemp. Math., pages 55-75, Providence, RI, 2002. Amer. Math. Soc..
    doi:10.1090/conm/304



Can computers discover ideal knots

Our original ropelength data used simulated annealing for ropelength minimization. The configurations, as well as a variety of spatial and topological measurements are available here. My former undergraduate researcher Michael Piatek did much of the work on the computations. The theoretical paper related to this work is:

Role of flexibility in entanglement

This work explores ropelength optimization with a hard bound on curvature. Our hope is to capture the shape of ropelength minimizers in physical materials with curvature constraints. Visualizations with associated spatial characters are available as is the paper published in Physical Review E, 70:011803, 2004. This work was in collaboration with Greg Buck and Michael Piatek did much of the work on the computations.

Knot type: 3.1 4.1 5.1 8.18 8.19 8.21 9.39 9.49
Convergence: [pdf] [pdf] [pdf] [pdf] [pdf] [pdf] [pdf] [pdf]


Energy, ropelength, and other physical aspects of equilateral knots

Energy optimized and ropelength optimized knots are available with spatial characteristics. The associated paper appears in Journal of Computational Physics, 186(2):426-456, 2003.
16 edge / 32 edge optimized for ropelength
16 edge / 32 edge optimized for energy
This work was done in collaboration with Ken Millett.




This work has been supported by NFS DMS grant numbers 0074315, 0296098, 0311010, 0621903, 0810415, 1115722, and 1418869. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.