Section 16.1.1. Introduction

Ab initio methods for solving the crystallographic phase problem rely on diffraction amplitudes alone and do not require prior knowledge of any atomic positions. General features that are not specific to the structure in question (e.g. the presence of disulfide bridges or solvent regions) can, however, be utilized. For the last three decades, most small-molecule structures have been routinely solved by direct methods, a class of ab initio methods in which probabilistic phase relations are used to derive reflection phases from the measured amplitudes. Direct methods, implemented in widely used highly automated computer programs such as MULTAN (Main et al., 1980), SHELXS (Sheldrick, 1990), SAYTAN (Debaerdemaeker et al., 1985) and SIR (Burla et al., 1989), provide computationaly efficient solutions for structures containing fewer than approximately 100 independent non-H atoms. However, larger structures are not consistently amenable to these programs and, in fact, few unknown structures with more than 200 independent equal atoms have ever been solved using these programs.

Successful applications to native data for structures that could legitimately be regarded as small macromolecules awaited the development of a direct-methods procedure (Weeks et al., 1993) that has come to be known as Shake-and-Bake. The distinctive feature of this procedure is the repeated and unconditional alternation of reciprocal-space phase refinement (Shaking) with a complementary real-space process that seeks to improve phases by applying constraints (Baking). Consequently, it yields a computer-intensive algorithm, requiring two Fourier transformations during each cycle, which has been made feasible in recent years due to the tremendous increases in computer speed. The first previously unknown structures determined by Shake-and-Bake were two forms of the 100-atom peptide ternatin (Miller et al., 1993). Subsequent applications of the Shake-and-Bake algorithm have involved structures containing as many as 2000 independent non-H atoms (Frazão et al., 1999) provided that accurate diffraction data have been measured to a resolution of 1.2 Å or better.

The basic theory underlying direct methods has been summarized in an excellent chapter (Giacovazzo, 2001) in IT B (Chapter 2.2 ) to which the reader is referred for details. The present chapter focuses on those aspects of direct methods that have proven useful for larger molecules (more than 250 independent non-H atoms) or are unique to the macromolecular field. These include direct-methods applications that utilize anomalous-dispersion measurements or multiple diffraction patterns [i.e., single isomorphous replacement (SIR), single anomalous scattering (SAS) and multiple-wavelength data]. The easiest way to combine isomorphous or anomalous-scattering information with direct methods is to first compute difference structure factors and then to apply direct methods to the difference data. Using this approach, the dual-space Shake-and-Bake procedure has been used to solve the anomalously scattering substructure of the selenomethionine derivative of an epimerase enzyme that has 70 selenium sites (Deacon & Ealick, 1999). Substructure applications require only the 2.5–3.0 Å data normally included in multiple wavelength anomalous dispersion (MAD) measurements, and data sets truncated even to 5 Å have led to solutions.

A formal integration of the probabilistic machinery of direct methods with isomorphous replacement and anomalous dispersion was initiated in 1982 (Hauptman, 1982a,b). Although practical applications of this and subsequent related theory have been limited so far, such applications are likely to have greater importance in the future, and progress is described in Sections 16.1.9.1 and 16.1.9.2. Similarly, the combination of direct methods with multiple-beam diffraction is still in its infancy. However, preliminary studies indicate that the information gleaned from multiple-beam data will greatly strengthen existing techniques (Weckert et al., 1993). Progress in this area is summarized in Section 16.1.9.3.