(untitled) (Communications in Computational Physics, 2018)
Identification of stable three-dimensional conformations in proteins and peptides that correspond to minima in potential and free energy hypersurfaces has been under intense scrutiny over the past decades since the paradigm structure-function was proposed [1]. This classical paradigm states that most of biologically active conformations in proteins and peptides can be associated with global minima energy states on the energy hypersurface of the polypeptide chain [2, 3]. In this work we discuss the onset of macroscopic minimum-energy conformations on small interacting peptides composed by only two types of residues: hydrophobic (A) or polar (B). Based on a previous work in 2D [4], we consider here an interacting three dimensional potential V =V_1+V_2 where V_1 corresponds to a intramolecular bending potential between adjacent residues whereas V_2 is a Lennard-Jones (LJ) type intermolecular potential with both an attractive and repulsive part. In addition, the V_2 term can switch to repulsive or attractive depending on the type of pair interaction AA, AB or BB considered. As a novel approach to the standard geometric-based minimization methods [5–7], we propose a Multipopulation Genetic Algorithm (MpGA) as a minimization algorithm [8]. The central advantage of this approach is a wider search on the energy hypersurface. In order to test the validity of our method, we reproduced in excellent agreement the results previously obtained in 2D by [4]. Our results show that in three dimensions our method enlarges the number of stable macroscopic conformations found for a given polypeptide. As an example of the role played by the interacting pairs AB, AA and BB, we discuss as well the case of small diblock polymers and quantify the degree of compactness expected in the three dimensional structure as function of the composition of the chain.