Several Mutual Information-based Models For Measuring Co-evolution Between Protein Residues

Evolution is the change in the inherited characteristics of biological populations over suc-cessive generations. In the evolutionary process, the change of a biological object triggered by the change of a related object is called as "co-evolution". When there is a mutation of function-ally or structurally important residues, compensatory mutations may occur to preserve or restore the function or structure of the protein. Thus the knowledge of residues co-evolution helps to predict protein function and guide experimental analysis. In the dissertation, mutual informa-tion is modified to measure protein residues co-evolution using various biological constraints and mathematical methods. First MIB, MIP and MIBP models are proposed using different bi-ological constraints. It characterizes the pairwise sites co-evolution from a new way. Second nDMI is supplied to measure multiple residues co-evolution. At last, Pearson’s Correlation Co-efficient provides the correlation of subsequence-pair based on co-evolution relationship. The main results can be summarized as follows:1、In chapter2, Mutual Information with amino acid background distribution(MIB) is presented. To eliminate the evolutionary pressure effect to amino acid distribution in the MSA, amino acid background distribution is incorporated to modify the observed amino acid distribution in MI-based co-evolution measurement. It figures out that MIB is more effective in measuring amino acid co-evolution.2、In chapter3, mutual information of residues physicochemical properties (MIP) is pro-vided. MIBP is also proposed by applying residues physicochemical properties into the MIB model. To some extent, protein’s function and structure is based on residues’ physicochemical properties. The classification often overlapping groups of20types of amino acids is chosen. Using mutual information model, MIP is developed to estimate the variation of physicochemical properties of two given sites. Results indicates that physicochemical properties of residues around catalytic sites are strongly co-evolved.3、In chapter4, n-dimensional Mutual Information (nDMI) method is introduced to i-dentify co-evolution of multiple residues. It has been proven that multiple residues are co-evolved. Using mutual information matrix and its eigenvalues, mutual information based co-evolution measurement for two residues is extended to multiple residues. Comparing existing pairwise residues co-evolution measurement, nDMI method is ef-fective in identification of multiple co-evolved residues, especially in G protein and GPCRs.4、In chapter5, a measurement using Pearson’s Correlation Coefficient is proposed to measure the correlation of two subsequences based on co-evolution relationship. It has been proven that multiple residues take part in co-evolution, and these residues are gathered in several subsequences in protein chain. The co-evolution among the adjacent residues,and the correlation between the distinct regions offer insights into function and evolution of the protein and residues. These subsequences possess some flexibility in the composition of side chains, such as the catalyzed environment.