Protein Modelling and Surface Folding by Limiting the Degrees of Freedom - Computational Modeling in Tissue Engineering - page 20

[ 10 , 35 , 71 ]. Ab initio (from the beginning) refers to the beginning of an amino
acid sequence.
There are several major limitations with all of these models. In general, all of
the model simulations are restricted by computational time and cost. To minimize
a structure, there is a need to consider every change of position in the configuration
of a peptide or protein. In the case of establishing global minima, all possible
energies need to be tested which can become an exponentially large problem
[ 13 , 36 , 74 , 81 ]. Further, existing models do not consider the dynamic behavior of
proteins in an aqueous environment since they cannot consider water molecules
[ 28 , 38 , 57 , 76 ] primarily due to computer limitations [ 7 , 12 ]. Secondary structure
formation also depends on several other factors [ 90 ] including for example
accessibility of residues to a solvent [ 47 ], the protein structural class [ 22 ], and even
the organism from which the proteins are obtained [ 49 ]. These factors can further
confound modelling paradigms.
While X-ray crystallography is used to validate a protein structure, it only
shows an aspect of a structure in that it does not map the real aqueous environment
of the protein that affects protein interactions and structure. In addition, X-ray
crystallography does not describe the actual interactions that occur during the
folding process which is a further limitation [ 82 ]. In contrast, nuclear magnetic
resonance (NMR) can be used to show structure in real time in an aqueous
environment, but so far this method is limited to 70 amino acids [ 63 ].
Based on the limitations of existing protein modelling techniques, other
approaches need to be considered; for example, if the volume and area of the
protein can be optimized, this optimization can be used to calculate primary but
also tertiary structures. The method presented uses the optimal volumes to bring a
structure closest to the lowest energy state.
2 Model
The polypeptide chain of a protein can be represented by a low-dimensional
topology structure called a braid group [ 1 , 2 , 8 ]. It is defined as the union of arc
lengths forming a string, or braid that can readily model the fundamental prop-
erties of the peptide backbone [ 48 , 53 ]. Rather than considering a peptide as a
linear sequence of amino acid residues, the peptide bonds of the protein chain form
the arc lengths of our braid. A peptide chain thus consists of a series of rigid arc
lengths carrying various substitute groups. Each arc length runs from the oxygen to
carbon of the amide bond to, but not including the next peptide carbonyl carbon [ 9 ].
Folding the polypeptide chain into different conformations simply results in
changing the relative orientation of these arc lengths. Although this grouping does
not follow the biosynthetic pattern, it limits orientation changes to movements
about the rotating C-CO bond given by U and H as shown in Fig. 1 . Next, the
volume of the chain can be minimized [ 57 ]. The volume, given by a protein, can be