Minimum Energy Conformations of Self-Interacting Polymer Chains via Multipopulation Genetic Algorithms (MpGA) (Communications in Computational Physics, 2018)
Identification of stable three-dimensional conformations in proteins and peptidesthat correspond to minima in potential and free energy hypersurfaces has beenunder intense scrutiny over the past decades since the paradigm structure-functionwas proposed [1]. This classical paradigm states that most of biologically active conformationsin proteins and peptides can be associated with global minima energy stateson the energy hypersurface of the polypeptide chain [2, 3]. In this work we discuss theonset of macroscopic minimum-energy conformations on small interacting peptidescomposed by only two types of residues: hydrophobic (A) or polar (B). Based on aprevious 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 adjacentresidues whereas $V_2$ is a Lennard-Jones (LJ) type intermolecular potential withboth an attractive and repulsive part. In addition, the $V_2$ term can switch to repulsiveor attractive depending on the type of pair interaction AA, AB or BB considered. As anovel approach to the standard geometric-based minimization methods [5–7], we proposea Multipopulation Genetic Algorithm (MpGA) as a minimization algorithm [8].The central advantage of this approach is a wider search on the energy hypersurface. Inorder to test the validity of our method, we reproduced in excellent agreement the resultspreviously obtained in 2D by [4]. Our results show that in three dimensions ourmethod enlarges the number of stable macroscopic conformations found for a givenpolypeptide. 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 compactnessexpected in the three dimensional structure as function of the composition ofthe chain.
Keywords: Protein folding; genetic algorithms; energy minimization; interacting heteropolymers; coarse-grained models.