Parallel Evolutionary Computations in Discerning Protein Structures - Parallel Computing for Bioinformatics and Computational Biology - page 461

Figure 19.1 This figure illustrates the φ angle in a small section of backbone atoms within
a protein. This angle representation is the same at each C-N-C α -C instance in any protein;
however, each angle is indexed according to how many φ angles appear in that particular
protein. This method ensures that each dihedral angle is uniquely specified.
protein's potential energy, the program requires the protein be specified by dihedral
angles. A dihedral angle is the angle formed by four atoms connected in a chain-like
manner. The dihedral angle itself is developed when the two planes (formed by the
first three and last three atoms in the chain) make an angle. Figure 19.1 illustrates a
dihedral angle. This particular dihedral angle is called φ angle within any protein.
The entire process for specifying a protein (polypeptide) is more involved than
just identifying dihedral angles of a protein. Assumptions and domain information
are also included in the specification process to make the size of the search space more
reasonable [11]. After each individual protein is specified with dihedral angles, each
atom becomes locatable in a three dimensional space allowing for a potential energy
program, like CHARMm, to calculate energy between each atom. The calculation
requires the binary angular values to be transferred to real-valued atom positions
and distances for the CHARMm variables. It takes approximately 6.8 ms to calculate
the potential energy for a single conformation on an Intel PIII 800 MHz machine.
It would take considerable computational time to find the absolute lowest energy
conformation for general proteins (by calculating the energy for each conformation
after discretizing all angles to 1024 bit degrees [11]). The order-of complexity is
O(n 6 ) , where n is the number of atoms. The polypeptides analyzed in this study
are Met-enkephalin (MET) and polyalanine 14 (POLY). Note that the fully specified
MET/POLY has 24/56 adjustable dihedral angles with 75 / 141 atoms each.
19.3 PROTEIN STRUCTURE DISCERNING METHODS
Approaches to finding the structure of a fully folded protein are numerous. They range
from software to hardware driven, theoretical to empirical, and fine to coarse grained.
The more generic methods are X-ray crystallography [12, 13], molecular dynamics,
nuclear magnetic resonance spectroscopy [14], Monte Carlo analysis [15], atomistic