INTRODUCTIONDistance geometry is a general and powerful method for building approximate models of complex molecular structures, although it is best known as a method for determining the solution conformation of molecules from NMR data.*-4 NMR structure determination is an important but small subset of the problems that can be solved with distance geometry. Our goal in this chapter is to describe how to use distance geometry for other molecular modeling applications ranging from conformational analysis of small molecules to drugreceptor docking.Molecular model-building (conformational search) methods fall into two general classes: systematic and random.5-7 Systematic methods search all possible combinations of torsional angles, whereas random methods usually involve a Monte Carlo (with Metropolis samplings) or molecular dynamics trajectory.9 Both approaches attempt to search large areas of conformational space and eventually converge on the desired conformation or structure. Dis-Reviews in Computational Chemistry, Volume V tance geometry is a random method, but it differs greatly from standard Monte Carlo or molecular dynamics techniques. Distance geometry directly generates structures to satisfy the constraints of the model, rather than searching most or all of the conformational space to find the appropriate structures. It can therefore rapidly find one or more possible solutions, but it shares with other random methods the inability to guarantee finding all solutions.A distance geometry program requires at least 2N2 (N = number of atoms) words of memory, which until recently restricted the method's applicability to relatively small problems. Modern workstations' speed and memory now easily satisfy the computational demands of distance geometry for structures up to about 2000 atoms. Several programs are now available that run on machines from small workstations to supercomputers.2~4~~~-~3
Overview of Distance Geometry as a General Model BuilderDistance geometry has proven to be useful for conformational analysis,14-*6 protein homology model building,17J* pharmacophore modeling,19-21 docking722J3 generating complex cyclic structures724J5 and converting two-dimensional sketches into three-dimensional coordinates.26P Many special-purpose algorithms and methods have been developed for these problems, but none has the broad applicability of distance geometry. Surprisingly, distance geometry is often competitive with these custom methods15916J8J9 and is frequently the best method for particularly complex structure modeling problems such as polycyclic systems.Distance geometry does not require a starting conformation or force field parameters; distance geometry is a purely geometric method that generates structures directly to satisfy the constraints of the model. Flexible rings are handled easily by the method without any special consideration or modification. Distance geometry is also unusual in that it performs well with qualitative information: a large number of approximate distance bounds are more valuable in defi...