Protein Modelling and Surface Folding by Limiting the Degrees of Freedom - Computational Modeling in Tissue Engineering - page 18

created near-identical models with minimal computational load. This model can be
expanded to large, multi-molecular network structures.
1 Introduction
Tissue Engineering is an interdisciplinary field in the cross-section of biology,
medicine, chemistry, physics, material sciences, engineering sciences and infor-
matics. One aspect of tissue engineering represents modelling of extracellular
matrix of connective tissue. The mechanical properties of the extracellular matrix
are defined by its structure and composition. Collagen, for example, is the most
abundant extracellular matrix protein in connective tissue, and is composed of
three polypeptide strands each with 1,000 amino acids that are assembled to form a
fibril [ 31 ]. The fiber network arrangement of the collagen matrix determines its
tensile strength. In order to define the correct position of the collagen in a struc-
ture, an optimized tertiary structure must be characterized.
With the purpose of modelling a protein such as collagen, energy calculations
must consider six degrees of freedom for each single atom. The calculations
include hydrogen bonding and van der Walls forces, and moreover, because the
interactions of the amino acids are both hydrophobic and hydrophilic forces in an
aqueous environment, these calculations must also be considered in time [ 27 ]. The
time for protein folding takes place in milliseconds to minutes [ 68 ]. In the case of
collagen or other large proteins, there are assistance proteins, the so-called
chaperones such as P52, which support protein folding and tertiary structure by
holding initial amino acids for assembly of the total protein [ 61 ].
Protein modelling is considered to be a nondeterministic polynomial (NP) time
problem that is regarded as inherently difficult if its solution requires significant
resources, regardless of the algorithm that is used to solve the problem [ 45 ]. In
order to solve a NP problem, we need to consider a program that makes 2 n
operations before halting, since exponential-time algorithms might be unusable
from the practical point of view. Collagen is an exceptionally large protein, but
even for a small number of molecules (e.g. n = 100) and 10 12 computer operations
per second, a program would run for about 4 9 10 10 years to solve a problem
([ 70 ] and Appendix 1) and therein lies the challenge for protein modelling.
Protein modelling is generally based on the fact that a structure is striving for
the lowest state of energy based on the Lennard-Jones potential that defines energy
as a function of the distances of the minimizations. Protein modelling uses free
Gibbs energy to obtain the lowest state of energy. Currently, there are eight major
methods used to denote protein conformation spaces or lowest state of energy:
1.1 Molecular Dynamics in which every coordinate position of the atoms con-
tained within the amino acids in the sequence is taken into consideration. This