  We adopt the point of view that analysis of the stability of the protein
folding process is central to understanding the underlying physics of folding.
Stability of the folding process means that many perturbations do not disrupt
the progress from the random coil to the native state. In this paper we explore
the stability of folding using established methods from physics and
mathematics. Our result is a preliminary theory of the physics of folding. We
suggest some tests of these ideas using folding simulations.
  We begin by supposing that folding events are related in some way to
mechanical waves on the molecule. We adopt an analytical approach to the
physics which was pioneered by M.V. Berry, (in another context), based upon
mathematics developed mainly by R. Thom and V.I. Arnold. We find that the
stability of the folding process can be understood in terms of structures known
as caustics, which occur in many kinds of wave phenomena.
  The picture that emerges is that natural selection has given us a set of
protein molecules which have mechanical waves that propagate according to
several mathematically specific restrictions. Successful simulations of folding
can be used to test and constrain these wave motions. With some additional
assumptions the theory explains or is consistent with a number of experimental
facts about folding. We emphasize that this wave-based approach is
fundamentally different from energy-based approaches.
