Some Studies On The Protein Folding And Reduction Of Complexity In Proteins

Proteins are of greatly importance in molecular biophysics. To understand the folding of protein molecules in proper environment and how the specific functions are formed is one of the hot topics in protein researches. Recently, there are some rapid progresses in grasping the picture of free energy landscapes of folding, extracting the speciality of structures of protein folds and exploring the possible composition simplicity of proteins. Meanwhile, many problems are still undiscovered. In this thesis, systematic studies are proceeded on 1) the simplification of protein composition and 2) the transitions (thermodynamic and kinetic) following the variation of temperature.Simplified models are the basis of the physical studies on proteins. The minimalist models may induce a clear picture of the complex system, and the success using the simple models affirms the possibility of simplification for protein systems. The question is, what kinds of models may be proper while comparing with real systems of proteins, which is important for theoretical understanding of proteins. We provide a systematic approach to the simplification problem. Based on the approximation with lattice models and contact-form potentials, a mismatch characteristic is proposed to depict the effectiveness of residue substitution. The physical meaning of "mismatch", as well as that of the best reduction of residue, is discussed. The simplification of proteins is realized by substituting residues with the representatives of their corresponding groups. The validity of our proposed grouping schemes is tested for well-designed model protein sequences. By mapping the sequences into a large space, we obtained some insights on the reduction for protein sequences rather than just residues. The mapping between reduced sequences and the 20-letter sequences is also investigated. Besides these, we also discussed the overlapping of levels and the similarity between sequences for the cases with different compositions. With these proof, we believe that the simplification of protein representation do exists, and that suitable compositional complexity is the fundamental requirement to re-build real protein systems. This part of works is arranged in the Chapter 2.To understanding folding thermodynamics and kinetics is the basic part to know proteins. The energetic and structural ingredients are essential for folding processes. With a simple statistical model, the thermodynamics and kinetics are outlined, which shows the effects of entropy and frustration to folding behavior. We also introduce a short-range correlation between residues to simulate the cooperativity. The dependence of the folding kinetics on the native bond maps provides some insights on the effects of native structures to folding rate. The folding transition is studied from the zeros of partition function on the complex temperature plane. It gives a more detailed description on the properties of the folding transition, with a better theoretical reliance. Some comparisons between different models are also discussed. Then, the kinetic transition of protein systems is analyzed in details. Not only the kinetic transition is clearly shown, but also the nature of this transition is also analyzed in-depth. As a result, the kinetic transition is attributed to a downhill kinetics, which is associated with the destablization of denatured states. Our predictions have their good consistence with the simulation results. Different realization of Monte Carlo method and off-lattice modeling are all shown the universality of the kinetic transition. These pictures offer us some interesting knowledge for folding mechanism and comparison between different models. This part of work is arranged in Chapter 3.At last, my main results and thought on the works in this thesis are concluded in the last chapter, Chapter 4.In Appendix, the details of lattice modeling and simulation methods are proposed.