center X-ray crystal structure analysis can provide great detail about the average structure of a macromolecule. During the refinement process, regions of the molecule are sometimes found to be disordered; high B-values and poorly defined electron density indicate the absences of single well-ordered conformations. To analyze the structure further, crystallographers have modeled alternate conformations and ensembles of structures to fit the Bragg data better [Clarage \& Phillips, Jr., 1993][Gros et al., 1990][Kuriyan et al., 1991]. The Bragg data used in each of these refinement techniques, however, contain no information about the correlations in the disorder. Information in the form of diffuse, or variational, X-ray scattering is excluded from the usual structural analysis scheme for proteins and nucleic acids. This unused scattering contains the information about inter- and intra-molecular motions and their correlations in the crystal.
X-ray diffuse scattering cannot generally be used to differentiate between static and dynamic disorder. Dynamic disorder can often be distinguished by changing the temperature of the system. Decreasing the temperature during data collection often results in an increase in the resolution and intensity of the high-angle Bragg reflections, indicating increased ordering in the crystals [Parak et al., 1987][Frauenfelder et al., 1979][Phillips et al., 1980]. Experimental evidence supporting significant dynamic disorder within macromolecular crystals has been reviewed by Petsko and Ringe (1984) . Moreover, inelastic diffuse scattering experiments on myoglobin crystals using a Mössbauer radiation source demonstrated that much of the disorder in crystals is indeed dynamic [Nienhaus et al., 1989]. Such data are not available for the yeast initiator tRNA crystals. However, based on the data from protein crystals, it seems clear that much of the disorder seen in tRNA crystals must be dynamic. Even if the interconversion of conformations within crystallized tRNA molecules does not occur on fast time scales, diffuse scattering studies still reveal the conformational flexibility of the molecules, which is crucial to understanding their biological function.
Application of diffuse scattering analysis to protein and nucleic acid crystals has provided information about a variety of systems. Although diffuse scattering intensities cannot be Fourier-inverted to produce directly the description of the motions, the diffuse scattering can be calculated and compared with experimental results to yield insights about the macromolecular motions. Analysis of tropomyosin crystals reveals considerable motion in the filamentous protein lattice [Chacko \& Phillips Jr., 1992][Boylan \& Phillips, 1986]. Similarly, globular protein crystals have also been analyzed for diffuse scattering. Insulin crystals have been shown to contain movements that are predominantly correlated over distances of approximately 6 Å [Caspar et al., 1988]. Short-range correlated motions have also been found to dominate in triclinic and tetragonal lysozyme crystals [Clarage et al., 1992]. Orthorhombic lysozyme crystals produce diffuse streaks which have been calculated by a long-range lattice-coupled model [Doucet \& Benoit, 1987]. Diffuse scattering from crystals of a DNA octamer revealed partially disordered B-DNA present in the solvent channels formed by A-DNA [Doucet et al., 1989].
The studies on lysozyme and insulin share some assumptions. First, a certain homogeneity in the disorder is assumed in the diffuse scattering studies mentioned above. That is, all parts of the molecule are assumed to undergo the same specified disorder. The limitation in this assumption is that diffuse scattering from a portion of the molecule cannot be modeled by these methods. Furthermore, correlations have been modeled as isotropically distributed disorder. These assumptions are valid in some cases but may not always apply.
In this study, we describe the analysis of X-ray diffuse scattering from yeast initiator transfer RNA (tRNA) crystals. The analysis shows that the assumptions of homogeneous and isotropic disorder do not suffice in this case. Therefore, existing techniques have been modified and extended to overcome these assumptions.
The structure of yeast initiator tRNA (space group P) has been solved to 3 Å resolution [Basavappa \& Sigler, 1991][Basavappa, 1991] (see Figure 1). The 3 end of this nucleic acid molecule forms a complex with the amino acid, methionine, and is called the acceptor stem. The end of the other arm of this L-shaped molecule is responsible for the specificity in the binding of the tRNA to messenger RNA (mRNA) in the ribosome; the three bases (or anti-codon) on the tip of this arm interact with the codon bases on mRNA. In the crystal, the acceptor arms of adjacent tRNA molecules line up to form a pseudo-helix along the c axis of the unit cell with the anticodon arms extending out almost perpendicularly from this pseudo-helix axis (see Figures 2c and 3c). Adjacent pseudo-helices contact each other through their extended anticodon loops. The electron density for the anti-codon loop region, however, is not localized, and B-values can be greater than 100 Å corresponding to rms displacements on the order of an Angstrom. Solvent content in this crystal form is high (approximately 82%) indicating that there is room for large scale molecular motions in the unit cell.