Differential Evolution for Protein Structure Prediction Using the HP Model - Foundations on Natural and Artificial Computation - page 327

3.1 Encoding and Fitness

Individuals in DE are real-valued vectors which, in turn, are decoded into a
specific fold of an amino acid chain in the square lattice. We used the same real-
valued encoding proposed by Lopes and Bitello [13] with relative coordinates.
In the bi-dimensional lattices there are only three possible moves: (F)orward,
(R)ight and (L)eft. Therefore, the phenotypical representation of a solution is
defined over the alphabet F, R, L. The genotype that represents such phenotyp-
ical protein conformation is a real-valued vector X. Considering X ij th

element of vector X i ,and P the string representing the sequence of moves of the
folding, and α<β<δ<γ arbitrary constants in R , the genotype-phenotype
mapping is defined as follows:
If α < X ij ≤

the j −

βthenP j = L
If β < X ij <δ thenP j = F
If δ

(1)

≤ X ij <γ thenP j = R

We used α = 1, δ =1and γ = 3, as in [13]. If a component of

a mutant vector (candidate solution) goes off its limits, as consequence of the
DE formula for each candidate solution (line 9 in the pseudo-code), we set the
component to a random value in the corresponding interval of the bound limit.
Note that the mapping allows several genotypes to represent a single phenotype.
We used initial “stretched” individuals (all elements of the string are F )when
creating the initial population. The procedure ensures initial individuals with
diversity in the genotypic level, as for the Fs are used random values in the
corresponding interval.
Finally, we used the simple fitness function that considers only the maximiza-
tion of H-H contacts. The infeasible solutions are given a fitness of 0.

−

3, β =

−

(a) (b) (c) (d) (e)

Fig. 1. Repair processes. (a) Original illegal conformation; (b-c) and (d) Intermediate
steps and final conformation with the absolute moves procedure; (e) Final conformation
with the procedure which uses the Cartesian coordinates.

3.2 Repair Process

This process takes as input an infeasible protein folding (more than one amino
acid in the same lattice location) and tries to repair it to a feasible one, trying
to maintain most of the original illegal conformation. We implemented two dif-
ferent strategies. The first one works in the Cartesian coordinate space: From an
illegal folding, it processes the chain across its amino acids and, if a conflict is