Some things to look at: (including two books in the Canisius Library)
0. On EASEL:

Meera Sitharam:
she gave a talk at Canisius several years ago on modular assembly of biological structures.

  • An October 2014 workshop: Configuration spaces of linkages, organized by Brigitte Servatius and Meera Sitharam.

Report from the workshop   has slides from talks at the workshop
Report from another workshop, july 2017  
Goal: understand the topological structure of conformation spaces for cycloalkanes, which are molecules of the form CnH2n – a ring of n carbon atoms, each of which bonds to 2 hydrogen atoms. Currently the only well understood example is the conformation space for cyclooctane, C8H16, which has the structure of a 2-sphere with a Klein bottle attached along 2 circles. Approach trying to understand a simpler example, C6H12 – cyclohexane, by estimating the number of degrees of freedom, using known conformations (e.g., chair, boat, etc), their energy levels, and the chemically feasible switches between them.
  • 3-Trees

3-trees are glued together tetrahedra, as a first approximation of a molecule.  The 3-tree is viewed as a rigid graph or framework. A partial 3-tree has edges removed so that it is flexible. The EASEL program keeps track of allowable lengths of the edges which can added back in to make it rigid. This is the idea behind Convex Cayley Configuration Space.

I also saw a reference to work by Richard Pollack, with some title like “convexifying a polygon” 1999?  His website is at, but I didn’t see a link to this work.

  • Other references that might discuss topology and geometry of biological molecules:

Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure, by William R. Taylor, Andras Aszodi   (I have a pdf of this book).

Monastyrsky, M.I. Topology in Molecular Biology. Springer (2007). Is it available at canisius as an ebook?

Roald Hoffmann on the philosophy, art, and science of chemistry      QD6 .H64 2012

Solids and surfaces : a chemist’s view of bonding in extended structures   Hoffmann, Roald.    QD471 .H83 1988

  • A nice undergraduate thesis on Linkages
 Kevin Walker, Configuration spaces of linkages, Princeton 1985  saved by me as WalkerLinkages.pdf
  • Some photocopied articles that I have (listed in my bibliographies):
 adams,c et al: stick numbers and compositions of knots and links \preprint
conway, gordon: knots and links in spatial graphs ’83 jour. of graph theory 7
hausmann: sur la topologie des bras articules ’89 \slnm 1474  Alg.Top.-Pozkak (linkages)
  • a link to youtube video of recent lecture on knotted graphs (by Topology and Chemistry author);