1. The symmetry of proteins composed of identical polypeptide chains has been investigated by means of cross-linking with bifunctional reagents and subsequent sodium dodecylsulfate -polyacrylamide gel electrophoresis. The majority of the investigations were performed with diimidates of different chain lengths (C, -C,z), which react exclusively with amino groups. Aldolase, catalase, fumarase, pyruvate kinase, tetrameric proteins with identical polypeptide chains, reveal a D2 symmetry, i.e. they appear to be composed of two pairs of polypeptide chains. The validity of this conclusion is demonstrated with lactate dehydrogenase. This enzyme, shown by X-ray analysis to have a D, symmetry, yields after cross-linking and subsequent polyacrylamide electrophoresis the band pattern expected for a protein with this quaternary structure and similar to the pattern obtained with the above enzymes.2. The influence of the experimental conditions on the cross-linking reaction has been investigated. The selectivity of the bifunctional reagent for the different contact domains within the quaternary structure of a protein depends on the reaction time, the chain length and on the concentration of the reagent. In general the D2 symmetry becomes more obvious with increasing chain length and with increasing concentration of the diimidate. Diethylpyrocarbonate showed very little selectivity.3. Problems and limitations of the method have been investigated. The four polypeptide chains of B-galactosidase could not be cross-linked with the investigated reagents. Glyceraldehyde-phosphate dehydrogenase barely showed the predicted cross-linking pattern, although its D, symmetry has been demonstrated by X-ray analysis. Yeast alcohol dehydrogenase shows a pattern which did not indicate any substructure with respect to the quaternary structure. Catalase yielded a complicated band pattern indicating that the cross-linking prevented complete unfolding of the polypeptide chains in sodium dodecylsulfate. These pattern did not occur after cross-linking with diethyl pyrocarbonate.4. The applicability of molecular-weight determinations with sodium dodecylsulfate -polyacrylamide gel electrophoresis to cross-linked proteins has been investigated. Calibrations obtained with cross-linked proteins are very similar to that obtained with non-cross-linked polypeptide chains.Even with catalase the R, values of the predominant bands fit into this calibration.The allosteric properties of a protein are closely related to its subunit assembly. In recent years the interest focussed on the interaction between polypeptide chains because knowledge of the structure of subunit contacts and the symmetry of the oligomer This work has been dcscribed in a preliminary report [l]. Enzymes. Alcohol dehydrogcnase or alcohol : NAD+ oxidorcductase (EC 1.1.1.1); aldolase or D-fructose-1,6-bisphosphate Dglyceraldehyde-3-phosphate-lyase (EC 4.1.2.1 3) : catalase or hydrogen-peroxide : hydrogen-peroxide oxidoreductase (EC 1.1 1.1 .h) appears to be of great importance for the understand...