The structure of protein is essentially important for life activities. Proteins can perform their functions only by specific structures. In this thesis, the kink and multi-kink model for protein description are reviewed. It is shown that most of the loop parts in Protein Databank (PDB) can be described by very limited number of kinks within the experimental precision. Furthermore, by applying the model into two well studied real proteins (myoglobin and villin headpiece HP35), it is shown that the multi-kink model gives correct folding pathway and thermal dynamical properties compared with the experimental results for both proteins. In particular, the kink model is computationally inexpensive compared with other existing models. In the last chapter, a new visualization method for the heavy atoms in the side-chain is presented.

In order to investigate the formation of different types of pit shapes on the crystalline surfaces, a mathematical model has been considered, which does not take into account surface diffusion and which defines the removal or transformation of different characteristic sites on the surface according to a set of frequencies. The characteristic sites are defined according to Terrace-Ledge-Kink model for the simple cubic crystal. With the help of the geometry of the step systems, specific conditions have been obtained under which the step systems considered could be obtained for a pit of monoatomic thickness. The dissolution of a simple cubic crystal has been simulated according to a set of probabilities. / Thesis / Master of Engineering (ME)