In Chapter 3, we investigate the folding dynamics of the plant-seed protein Crambin
in a liquid environment, that usually happens to be water with some certain viscosity. To take
into account the viscosity, necessitates a stochastic approach. This can be summarized by a 2D-Langevin equation, even though the simulation is still carried out in 3D. Solution of the
Langevin equation will be the basic task in order to proceed with a Molecular Dynamics
simulation, which will accompany a delicate Monte Carlo technique. The potential wells, used
to engineer the energy space assuming the interaction of monomers constituting the protein-chain, are simply modeled by a combination of two parabola. This combination will
approximate the real physical interactions, that are given by the well known Lennard-Jones
potential. Contributions to the total potential from torsion, bending and distance dependent
potentials are good to the fourth nearest neighbor. The final image is in very good geometric
agreement with the real shape of the protein chain, which can be obtained from the protein data
bank. The quantitative measure of this agreement is the similarity parameter with the native
structure, which is found to be 0.91 < 1 for the best sample. The folding time can be
determined from Debye-relaxation process. We apply two regimes and calculate the folding
time, corresponding to the elastic domain mode, which yields 5.2ps for the same sample.
Keywords: Computer simulation, Diffusion, Theory and modeling
