A topic of research that is frequently studied in Structural Biology is the problem of determining the degree of similarity between two protein structures. The most common solution is to perform a three dimensional structural alignment on the two structures. Rigid structural alignment algorithms have been developed in the past to accomplish this but treat the protein molecules as immutable structures. Since protein structures can bend and flex, rigid algorithms do not yield accurate results and as a result, flexible structural alignment algorithms have been developed. The problem with these algorithms is that the protein structures are represented using thousands of atomic coordinate variables. This results in a great computational burden due to the large number of degrees of freedom required to account for the flexibility. Past research in dimensionality reduction techniques has shown that a linear dimensionality reduction technique called Principal Component Analysis (PCA) is well suited for high dimensionality reduction. This thesis introduces a new flexible structural alignment algorithm called FlexSADRA, which uses PCA to perform flexible structural alignments. Test results show that FlexSADRA determines better alignments than rigid structural alignment algorithms. Unlike existing rigid and flexible algorithms, FlexSADRA addresses the problem in a significantly lower dimensionality problem space and assesses not only the structural fit but the structural feasibility of the final alignment.

A topic of research that is frequently studied in Structural Biology is the problem of determining the degree of similarity between two protein structures. The most common solution is to perform a three dimensional structural alignment on the two structures. Rigid structural alignment algorithms have been developed in the past to accomplish this but treat the protein molecules as immutable structures. Since protein structures can bend and flex, rigid algorithms do not yield accurate results and as a result, flexible structural alignment algorithms have been developed. The problem with these algorithms is that the protein structures are represented using thousands of atomic coordinate variables. This results in a great computational burden due to the large number of degrees of freedom required to account for the flexibility. Past research in dimensionality reduction techniques has shown that a linear dimensionality reduction technique called Principal Component Analysis (PCA) is well suited for high dimensionality reduction. This thesis introduces a new flexible structural alignment algorithm called FlexSADRA, which uses PCA to perform flexible structural alignments. Test results show that FlexSADRA determines better alignments than rigid structural alignment algorithms. Unlike existing rigid and flexible algorithms, FlexSADRA addresses the problem in a significantly lower dimensionality problem space and assesses not only the structural fit but the structural feasibility of the final alignment.