  A geometric analysis of protein folding, which complements many of the models
in the literature, is presented. We examine the process from unfolded strand to
the point where the strand becomes self-interacting. A central question is how
it is possible that so many initial configurations proceed to fold to a unique
final configuration. We put energy and dynamical considerations temporarily
aside and focus upon the geometry alone. We parameterize the structure of an
idealized protein using the concept of a ribbon from differential geometry. The
deformation of the ribbon is described by introducing a generic twisting
Ansatz. The folding process in this picture entails a change in shape guided by
the local amino acid geometry. The theory is reparamaterization invariant from
the start, so the final shape is independent of folding time. We develop
differential equations for the changing shape. For some parameter ranges, a
sine-Gordon torsion soliton is found. This purely geometric waveform has
properties similar to dynamical solitons. Namely: A threshold distortion of the
molecule is required to initiate the soliton, after which, small additional
distortions do not change the waveform. In this analysis, the soliton twists
the molecule until bonds form. The analysis reveals a quantitative relationship
between the geometry of the amino acids and the folded form.
