Many biological macromolecules are very difficult to crystallize and thus are not amenable for electron or X-ray crystallography. Fortunately, techniques have been developed over the past two decades for image averaging and three-dimensional reconstruction of individual macromolecules with low or no symmetry. Presently, the attainable resolution for reconstructing these molecules in 3D is 1.5-4 nm. Radiation damage of biological material remains the principal problem, since low-dose imaging requires averaging of thousands of individual images in order to boost the specimen signal to a level sufficient to allow construction of an atomic model. In theory, low-dose images provide enough information about the position and orientation of individual macromolecules or assemblies to provide atomic resolution if the molecular weight is greater than ~105dal and more than 10,000 particles are averaged (1). However, the quality of the best images as yet does not match theoretical calculations, which means that the molecular weight limit and the number of averaged particles required for atomic resolution may need to be an order of magnitude higher. The limitation in resolution comes about because of inaccuracies in determining the five orientation parameters needed to align low-dose images that are inherently noisy. Larger molecules or assemblies can be more accurately aligned simply because more orientational information is produced by the imaging process. The poor image contrast at high resolution of ice-embedded specimens needs to be overcome before atomic resolution can be challenged. This low contrast is thought to be caused by blurring of the image due to charging of the specimen by the electron beam and to beam-induced specimen movement (2).
Computer analysis of single-particle images was developed initially from methods to align individual images of macromolecules based upon cross-correlation functions versus a common reference. For 2-D images, three alignment parameters must be determined, a rotational orientation angle and two translational vectors. These can be determined from a rotational cross-correlation function (performed on the modulus of the Fourier transform of the images, since this function is translationally invariant) and from a subsequent translational cross-correlation function, respectively (3). Typically a second alignment procedure is performed using the averaged structure from the first alignment as a reference in the second. A second major development in single-particle methods was the use of correspondence analysis (a type of multivariate statistical analysis) to determine the most significant factors by which a collection of images varies (4). Typically images of identical molecules will cluster into groups that differ in their orientations, and if the orientation of each group can be determined, a 3-D reconstruction can be calculated using established computer algorithms such as the filtered backprojection. The strategy for collecting different tilted views of a specimen varies, but one common approach is the "random conical tilt" procedure (5). In this example, two electron micrographs are recorded of an area containing dozens or hundreds of molecules. The first micrograph is a low-dose exposure with the specimen grid tilted at some predetermined angle; the second exposure is a higher-dose exposure of the untilted grid. The higher-dose image is used to identify individual particles and the orientations using cross-correlation alignment and correspondence analysis. From this information, the same particles can be identified in the low-dose, high-tilt exposure, and their orientations can be calculated knowing the orientations of the untilted views, the known tilt angle, and the orientation of the tilt axis. The 3-D structure of the molecule can then be calculated from the various images of the molecules identified in the low-dose image.
Although performed at relatively low resolution, single-particle approaches have provided significant insight into the operation of large macromolecular complexes. The structure and function of ribosomes have been explored (6-8), which has also produced the sites of association of the 30S and 50S subunits (9) and a direct visualization of tRNAs bound to the 70S ribosome (10, 11). Other large complexes studied in 3-D are the NADH-dehydrogenase complex (see Dehydrogenase (12)), the calcium release channel/ryanodine receptor (13, 14), the nuclear pore complex (15), and hemoglobins (16, 17). Not all structural characterizations need to be performed in 3-D as evidenced by the ligand and subunit locations found in 2-D in photosystem I and II (18, 19).
