  We introduce a new model of proteins, which extends and enhances the
traditional graphical representation by associating a combinatorial object
called a fatgraph to any protein based upon its intrinsic geometry. Fatgraphs
can easily be stored and manipulated as triples of permutations, and these
methods are therefore amenable to fast computer implementation. Applications
include the refinement of structural protein classifications and the prediction
of geometric and other properties of proteins from their chemical structures.
