  A method to search for local structural similarities in proteins at atomic
resolution is presented. It is demonstrated that a huge amount of structural
data can be handled within a reasonable CPU time by using a conventional
relational database management system with appropriate indexing of geometric
data. This method, which we call geometric indexing, can enumerate ligand
binding sites that are structurally similar to sub-structures of a query
protein among more than 160,000 possible candidates within a few hours of CPU
time on an ordinary desktop computer. After detecting a set of high scoring
ligand binding sites by the geometric indexing search, structural alignments at
atomic resolution are constructed by iteratively applying the Hungarian
algorithm, and the statistical significance of the final score is estimated
from an empirical model based on a gamma distribution. Applications of this
method to several protein structures clearly shows that significant
similarities can be detected between local structures of non-homologous as well
as homologous proteins.
