AbstractThis paper examines the topological properties of protein disulfide bonding patterns. First, a description of these patterns in terms of partially directed graphs is developed. The topologically distinct disulfide bonding patterns available to a polypeptide chain containing n disulfide bonds are enumerated, and their symmetry and reducibility properties are examined. The theoretical probabilities are calculated that a randomly chosen pattern of n bonds will have any combination of symmetry and reducibility properties, given that all patterns have equal probability of being chosen. Next, the National Biomedical Research Foundation protein sequence and Brookhaven National Laboratories protein structure (PDB) databases are examined, and the occurrences of disulfide bonding patterns in them are determined. The frequencies of symmetric and/or reducible patterns are found to exceed theoretical predictions based on equiprobable pattern selection. Kauzmann's model, in which disulfide bonds form during random encounters as the chain assumes random coil conformations, finds that bonds are more likely to form with near neighbor cysteines than with remote cysteines. The observed frequencies of occurrence of disulfide patterns are found here to be virtually uncorrelated with the predictions of this alternative random bonding model. These results strongly suggest that disulfide bond pattern formation is not the result of random factors, but instead is a directed process.Finally, the PDB structure database is examined to determine the extrinsic topologies of polypeptides containing disulfide bonds. A complete survey of all structures in the database found no instances in which two loops formed by disulfide bonds within the same polypeptide chain are topologically linked. Similarly, no instances are found in which two loops present on different polypeptide chains in a structure are catenated. Further, no examples of topologically knotted loops occur. In contrast, pseudolinking has been found to be a relatively frequent event. These results show a complete avoidance of nontrivial topological entanglements that is unlikely to be the result of chance events. A hypothesis is presented to account for some of these observations.