  To determine the 3D conformation of proteins is a necessity to understand
their functions or interactions with other molecules. It is commonly admitted
that, when proteins fold from their primary linear structures to their final 3D
conformations, they tend to choose the ones that minimize their free energy. To
find the 3D conformation of a protein knowing its amino acid sequence,
bioinformaticians use various models of different resolutions and artificial
intelligence tools, as the protein folding prediction problem is a NP complete
one. More precisely, to determine the backbone structure of the protein using
the low resolution models (2D HP square and 3D HP cubic), by finding the
conformation that minimize free energy, is intractable exactly. Both the proof
of NP-completeness and the 2D prediction consider that acceptable conformations
have to satisfy a self-avoiding walk (SAW) requirement, as two different amino
acids cannot occupy a same position in the lattice. It is shown in this
document that the SAW requirement considered when proving NP-completeness is
different from the SAW requirement used in various prediction programs, and
that they are different from the real biological requirement. Indeed, the proof
of NP completeness and the predictions in silico consider conformations that
are not possible in practice. Consequences of this fact are investigated in
this research work.

Biomolecules