  These lectures will address two questions. Is there a simple variational
principle underlying the existence of secondary motifs in the native state of
proteins? Is there a general approach which can qualitatively capture the
salient features of the folding process and which may be useful for
interpreting and guiding experiments? Here, we present three different
approaches to the first question, which demonstrate the key role played by the
topology of the native state of proteins. The second question pertaining to the
folding dynamics of proteins remains a challenging problem -- a detailed
description capturing the interactions between amino acids among each other and
with the solvent is a daunting task. We address this issue building on the
lessons learned in tackling the first question and apply the resulting method
to the folding of various proteins including HIV protease and membrane
proteins. The results that will be presented open a fascinating perspective:
the two questions appear to be intimately related. The variety of results
reported here all provide evidence in favour of the special criteria adopted by
nature in the selection of viable protein folds, ranging from optimal
compactness to maximum dynamical and geometrical accessibility of the native
states.
