  A comparative classification scheme provides a good basis for several
approaches to understand proteins, including prediction of relations between
their structure and biological function. But it remains a challenge to combine
a classification scheme that describes a protein starting from its well
organized secondary structures and often involves direct human involvement,
with an atomary level Physics based approach where a protein is fundamentally
nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen
and nitrogen atoms. In order to bridge these two complementary approaches to
proteins, conceptually novel tools need to be introduced. Here we explain how
the geometrical shape of entire folded proteins can be described analytically
in terms of a single explicit elementary function that is familiar from
nonlinear physical systems where it is known as the kink-soliton. Our approach
enables the conversion of hierarchical structural information into a
quantitative form that allows for a folded protein to be characterized in terms
of a small number of global parameters that are in principle computable from
atomary level considerations. As an example we describe in detail how the
native fold of the myoglobin 1M6C emerges from a combination of kink-solitons
with a very high atomary level accuracy. We also verify that our approach
describes longer loops and loops connecting $\alpha$-helices with
$\beta$-strands, with same overall accuracy.
