| Like other biological macromolecules such as polysaccharides and nucleic acids, proteins are essential parts of organisms and participate in virtually every process within cells. Almost all vital activities and phenomena can be presented by proteins so that the researches of protein structure and function are extremely important. Fractal theory is a very active mathematic branch of modern nonlinear science, which has been used widely to describe irregular and non-differentiable geometric shapes existing in both natural world and scientific research. The theory and application of fractal has been permeated through every field of natural science. The research of protein structure based on fractal analysis has been found in a lot of literatures. In this thesis, we will use fractal method to study protein from two sides which are simulative computation and experimental measure. The main conclusions can be described as follows:1. Protein amino acid sequences can be analysed by using rescaled range analysis. In this paper, we convert the protein symbol sequence into a numerical serial with an appropriate coding rule. It is found that no matter what kinds of coding rule is selected, a better consequence can be got. The protein sequence is very simialr to the random sequence, and the relationship between structure and function of proteins can be explored by fractal theory.2. Based on the notion of local frcatal dimension, we present a new method named protein backbone local fractal dimension. It is more accurate and straightforward to study the hybrid orbital model of protein by using protein backbone local fractal dimension. Moreover, it is indicated when N≤15, protein can exhibit fractal properties, and the value of backbone local fractal dimension is higher than that of local fractal dimension but the correlation is better. The values of fractal dimension of four structural classes decreases in the order ofα,α/β,α+β,β.3. We calculated the fractal dimensions for four proteins, trypsin, chymotrypsin, elastaseand subtilisin which are belonged to the family of serine proteinase by using three methodologies and definitions of the fractal dimension. We analysed also the relationships between the fractal dimensions and space structure as well as the secondary structure contents. The results showed that the more similar structures, the more equal fractal dimensions, and if the fractal dimensions of proteins are different from each other, the three dimensional structure should not be similar. On the other hand, the fractal method can be applied to the elucidation of the proteins evolution. Moreover we notice that the multifractal theory should be used to explain the fractal dimensional relationship between the complete protein and the active site.4. Ten protein solutions were analyzed by using dynamic light scattering. It is indicated that the fractal dimension of protein solutions with anomalous diffusion model can be measured by dynamic light scattering technology. Simultaneously, the effects of temperature, protein concentration, pH and urea concentration on the fractal dimension, diffusion coefficient and hydrodynamic diameter of lysozyme and BSA were also studied by using dynamic light scattering. The results described the variation of protein structure under corresponding environmental conditions, which demonstrated that the fractal theory could be used to characterize the proetion structure.
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