An Application of the Eigenproblem for Biochemical Similarity

Abstract

Protein alignment finds its application in refining results of sequence alignment and understanding protein function. A previous study aligned single molecules, making use of the minimization of sums of the squares of eigenvalues, obtained for the antisymmetric Cartesian coordinate distance matrices Dx and Dy. This is used in our program to search for similarities between amino acids by comparing the sums of the squares of eigenvalues associated with the Dx, Dy, and Dz distance matrices. These matrices are obtained by removing atoms that could lead to low similarity. Candidates are aligned, and trilateration is used to attach all previously striped atoms. A TM-score is the scoring function that chooses the best alignment from supplied candidates. Twenty essential amino acids that take many forms in nature are selected for comparison. The correct alignment is taken into account most of the time by the alignment algorithm. It was numerically detected by the TM-score 70% of the time, on average, and 15% more cases with close scores can be easily distinguished by human observation.

Keywords

• eigenproblem
• eigenvalues
• molecular alignment
• orthogonal alignment
• biochemical similarity
• antisymmetric matrix