  Local protein structure analysis is informative to protein structure analysis
and has been used successfully in protein structure prediction and others.
Proteins have recurring structural features, such as helix caps and beta turns,
which often have strong amino acid sequence preferences. And the challenges for
local structure analysis have been identification and assignment of such common
short structural motifs.
  This paper proposes a new mathematical framework that can be applied to
analysis of the local structure of proteins, where local conformations of
protein backbones are described using differential geometry of folded
tetrahedron sequences. Using the framework, we could capture the recurring
structural features without any structural templates, which makes local
structure analysis not only simpler, but also more objective.
  Programs and examples are available from http://www.genocript.com .
