9] Distance geometry

Abstract

Publisher Summary This chapter discusses a descriptive introduction to the mathematics and a user's guide to the distance geometry computer programs. The chapter also discusses other approaches to the problem of determining molecular structures in noncrystalline environments. Distance geometry is concerned with building structures from internal distances. This chapter will explain the method and its application to the interpretation of nuclear magnetic resonance (NMR) data. The approach is quite general and can be used to search conformation space subject to a wide variety of constraints beyond those obtainable from NMR. The same mathematics has also been used as a tool for statistical analysis of data that is known as “multidimensional scaling.” While it is difficult to determine systematic errors, the rather close correspondence of X-ray and NMR structures of rigid proteins, such as BPTI and tendamistat suggests that the systematic errors for proteins are not much worse than the random errors. The same may not be true for nucleic acid structures. These molecules have lower hydrogen densities than proteins do, leading to fewer NOEs. They are frequently more elongated, and the long distances in such systems may be significantly distorted.