  This work examines the conformational ensemble involved in $\beta$-hairpin
folding by means of advanced molecular dynamics simulations and dimensionality
reduction. A fully atomistic description of the protein and the surrounding
solvent molecules is used and this complex energy landscape is sampled by means
of parallel tempering metadynamics simulations. The ensemble of configurations
explored is analysed using the recently proposed sketch-map algorithm. Further
simulations allow us to probe how mutations affect the structures adopted by
this protein. We find that many of the configurations adopted by a mutant are
the same as those adopted by the wild type protein. Furthermore, certain
mutations destabilize secondary structure containing configurations by
preventing the formation of hydrogen bonds or by promoting the formation of new
intramolecular contacts. Our analysis demonstrates that machine-learning
techniques can be used to study the energy landscapes of complex molecules and
that the visualizations that are generated in this way provide a natural basis
for examining how the stabilities of particular configurations of the molecule
are affected by factors such as temperature or structural mutations.
