An outstanding challenge in cell biology is to define at atomic resolution, the molecular events that occur at biological membranes such as the transduction of extracellular signals into intracellular responses, energy conversion, and the generation or transport of small molecules and ions. A full understanding of these processes will require atomic resolution structures of membrane proteins trapped in their basal and activated states, as well as atomic views of multi-protein complexes that nucleate at cellular membranes. A major focus of my laboratory is the structure determination of such large multiprotein assemblies by analysis of high resolution images of single particles. In this method, large numbers of images of individual protein molecules are recorded using very low electron doses, sorted into distinct classes, and then added together to obtain distinct views of the molecule that have a high signal to noise ratio. The averaged views are then oriented with respect to each other, and used to reconstruct a model of the three-dimensional structure. The pace of recent progress in this field suggests that this approach of crystallography without crystals may have great potential to probe biologically-relevant complexes that are too large to be analyzed by NMR methods or that do not crystallize easily in the two- or three-dimensional arrays required for electron microscopic or X-ray crystallographic studies. The catalytic core of the pyruvate dehydrogenase is an excellent model system for refinement of single particle methods. Sixty copies of this enzyme, E2CD, assemble into a 1,800 kDa icosahedral complex that is readily purified and that shows a number of distinct orientations on electron micrographs. We are optimizing methods to accurately orient the single molecules and to correct distortions introduced during image collection on the electron microscope. Currently, processing of 4500 individual molecular images has led to a three-dimensional model that has a resolution of 14 +. The predicted envelope of this structure is in excellent agreement with the recently determined X-ray structure. Analysis of the catalytic core when it is complexed to the accessory enzymes E1 or E3 has yielded a three-dimensional model that has a resolution of 35 +. The study of such complexes is useful even at modest resolution since three dimensional structures of the individual components solved by X-ray crystallography can be docked into density maps determined by electron microscopy. Refinement of these methods will also be useful for the analysis of human P-glycoprotein and for related structural projects of other membrane proteins currently underway in the laboratory.