  Among the unsolved problems in computational biology, protein folding is one
of the most interesting challenges. To study this folding, tools like neural
networks and genetic algorithms have received a lot of attention, mainly due to
the NP-completeness of the folding process. The background idea that has given
rise to the use of these algorithms is obviously that the folding process is
predictable. However, this important assumption is disputable as chaotic
properties of such a process have been recently highlighted. In this paper,
which is an extension of a former work accepted to the 2011 International Joint
Conference on Neural Networks (IJCNN11), the topological behavior of a
well-known dynamical system used for protein folding prediction is evaluated.
It is mathematically established that the folding dynamics in the 2D
hydrophobic-hydrophilic (HP) square lattice model, simply called "the 2D model"
in this document, is indeed a chaotic dynamical system as defined by Devaney.
Furthermore, the chaotic behavior of this model is qualitatively and
quantitatively deepened, by studying other mathematical properties of disorder,
namely: the indecomposability, instability, strong transitivity, and constants
of expansivity and sensitivity. Some consequences for both biological paradigms
and structure prediction using this model are then discussed. In particular, it
is shown that some neural networks seems to be unable to predict the evolution
of this model with accuracy, due to its complex behavior.
