Several Problems In Biological Magnetic Resonance Data Analysis

Nuclear magnetic resonance (NMR) is widely used in physics, chemistry, biology, medicine, and other scientific fields. Biological NMR provides methodological support for life science re-search in molecular level, cellular level and overall level, especially in protein structure&dynam-ics and metabonomics. We concentrate on the interdisciplinary field:bio-NMR data analysis and mathematical modeling. The experimental data and phenomenon are provided by our collabora-tors in Wuhan Magnetic Resonance Center.The thesis consists of six parts. The first chapter introduces backgrounds on data analysis and bio-NMR related to our work.In the second chapter, we prove a central-limit theorem of order a(0<α<1) Renyi condi-tional entropy and obtain sharp rate of convergence. By carefully analyzing the Renyi conditional entropy between the distribution of the normalized sum of iid random variables and Gaussian dis-tribution, we show the central-limit theorem related to α(0<α<1) order Renyi conditional entropy, and obtain sharp convergence rate. Such a rate of convergence is used to model selection and model diagnosis.In the third chapter, we propose a new method for the normalization of metabolomics in one-dimensional spectral data-CPIN(clustering partial integral normalization). The key idea of normalization is to select a group of bins as a reference to show the variations of metabolites. We uses the hierarchical clustering to obtain candidate groups, balance the trade off between similarity and diversity, and improve the consistency by OPLS. The procedure and the rationality of CPIN are described in detail. The validity of CPIN is demonstrated by two groups of samples of1H spectrum.Chapter four discusses the dimension reduction and visualization of the NMR spectrum of metabolites. We generalize conventional linear dimensionality reduction method to the appropri-ate nonlinear dimension reduction method by using kernel methods. We give the rigorous mathe-matical derivation of NMR data dimensionality reduction methods widely used in metabonomics (such as PCA, LDA, PLS, OPLS), then extend PLS and OPLS by using kernel methods to ker-nel space. We use real NMR data of metabolites to show the validity of the proposed nonlinear dimension reduction method.The fifth chapter depicts the mathematical modeling work in dynamics of biological macro-molecules with magnetic resonance experiments. For E. coli sugar phosphotransferase system. We establish a dynamic model of the protein using ordinary differential equations, elaborate the weak interaction of proteins. The model grasps the underlying biological mechanisms from new NMR experiments. Specifically, it explains the relationship between Phosphate group transfer efficiency and Dissociation constant through a simple reaction model. It also shows the meaning among proteins weak interaction; further transfer of binary systems containing a mathematical path model, then establishing mathematical model including binary channel to the transporting system, it could predict the Phosphate group transfer efficiency of2-pathway and3-pathway.We summarize current works and some problems for further research in chapter six.