Theoretical Study Of Protein Folding And Protein Design Based On The Relative Entropy And Complex Network Methods

Proteins are the important biologic molecules which participate in constructing the biologic structure and controlling the biologic function. Protein folding is the key point of the relationship between genetic information and biologic function in the central dogma of molecular biology. The biologic molecular will be well understood if the protein folding problem will be solved. The protein folding problem has two components: the direct folding problem (i.e. folding) and the inverse problem (i.e. protein design). The main issue of the direct protein folding problem is to understand the basic principle how protein sequences determine their structure. The goal of these studies is to predict protein conformations from their sequence. The inverse folding problem concerns how to design an amino acid sequence which can fold to a given tertiary structure at a given temperature.Protein folding and protein design has become one of the most actively studied problems in modern molecular biology. An ab initio algorithm for protein folding were proposed, in which a minimization function called'relative entropy'was used instead of the system's Hamiltonian. In principle, the relative-entropy-based method is an improvement on the energy minimization approach and to be more consistent with the system minimization based on free energy. The method can be applied as a uniform frame for both folding and inverse folding of proteins. The relative entropy minimization algorithm has been developed by our group and applied to study protein folding and protein design successfully. The method is based entirely on physical principles and the essence of the method for the folding (reverse folding) problem is to search the conformation (sequence) with a maximum occupying probability for a given sequence (conformation).The complex network presents a new perspective for understanding protein folding. A protein molecule can be treated as a complex network with each residue simplified as a node and the interaction between them as a link. Network analysis of protein structures is one such attempt to understand possible relevance of various network parameters. By applying the static quantities, the results suggest that the character arises primarily from the topological properties.The main contents of this work consist of the following three aspects:the first part is about the application of protein design method based on the relative entropy and the HNP (H: hydrophobic, N: neutral, P: hydrophilic) model for different protein systems; the second part is the improvement of the relative entropy based protein folding method; and the third part is about the construction and application of the weighted amino acid network based on residue fluctuations.(1) The application of the protein design method based on the HNP model and the relative entropy theory is discussed for four structural classes of real proteins. The success rate for different types of amino acids and secondary structures is also analyzed, and the results are compared with that of the HP model. Testing on 190 proteins shows that this method is generally effective for the different structural classes of proteins. Additionally, we also analyze the reasons resulting in the difference of the success rate on different systems. Furthermore, the success rate of this method on the conserved residues is higher than the non-conserved residues. All analyses mentioned above make the foundation for the development and the application of this method in the future.(2) We have modified the relative-entropy-based method from two aspects as follows. An approximate value of the ensemble average of the contact potential was used in our previous work. In order to get a precise value and improve the theoretical integrity of the relative-entropy-based method, a new calculation method was proposed based on the thermodynamic perturbation theory in this paper. In addition, the Miyazawa-Jernigan (MJ) matrix instead of a predigested form of the MJ matrix is used as the contact potential function in this paper. Tests of the improved algorithm were performed on twelve small protein. The root mean square deviations of the predicted versus the native structures from Protein Data Bank range from 0.40 to 0.60 nm. Compared with the approximate calculation method, the results show that the average prediction accuracy of the method based on the thermodynamic theory can be improved by 0.044nm.(3) A new method is proposed to construct the weighted amino acid network. The weight of link is based on the mean-square fluctuations of the distance of the contact residue pairs. The mean-square fluctuations of the distance in all residue pairs are calculated based on the Gaussian network model (GNM). For the 180 proteins with low homology, the unweighted and the weighted amino acid networks are constructed and the analyses were carried out for the statistic characteristics of these network parameters separately. Additionally, we studied the influence of the weight on the network parameters and the network parameter difference of amino acids network. The"small–world"property and the hierarchical behavior were studied based on this method. Finally, the comparison of the betweenness value calculated from the weighted network with that of the unweighted network shows that the weighted amino acid network contains more information about amino acids than that of the unweighted network.