Global mapping and multivariate analysis of protein and nucleic acid conformational spaces

In this thesis, multivariate analysis tools are used to analyze and intuitively understand the clustering behavior of the conformations of biological macromolecules, namely of nucleic acids and proteins. Each unit of these polymers, depending on the type of physical representation chosen to describe the molecular structure, (i.e. angles, Cartesian coordinates, etc.) must be described by many degrees of freedom (in multidimensional space). In order to study the conformations of all but the shortest segments of these linear polymers, techniques of multivariate analysis must be used to reduce the dimensions, to visualize, and to compare the features of available experimental structures.; We have developed a method for visualization and analysis which we describe as "global mapping" which employs multidimensional scaling (MDS). MDS has its origins in the field of psychology and belongs to a family of principal component analysis (PCA) methods which allow multivariate data to be represented by a reduced number of dimensions.; In the first portion of this thesis, the protein conformational space is mapped at the level of short peptides from high resolution protein structures. The initial goal was to create a Ramachandran-like map for short peptides, rather than single pairs of &phis;-psi angles. Hence we developed the concept of higher order (fragments several &phis;-psi pairs in length) the (&phis;-psi) n map. To accomplish this, angular distance information and MDS are used to cluster the peptide fragments in a three dimensional space.; In proteins the simplest conformational unit of structure is the single &phis;-psi pair represented by a tripeptide. A &phis;-psi plot can pictorially describe the conformation of an entire protein via the short tripeptide fragments. In nucleic acids the analogous unit is the dinucleoside monophosphate (DMP). As we will be describe later in further detail, the complete description of the DMP unit requires as many as ten torsion angles. To visualize the conformational space of DMP units, RNA and DNA (free and protein/drug bound) were mapped using high resolution crystal structures catalogued in the Nucleic Acid Database (NDB). The mapping of the conformational space reveals nine primary clusters which distinguish among the common A, B and Z forms and their various substates, plus seven secondary clusters for kinked or bent structures.