The number of protein-protein structural families in nature is then estimated from the sequence families and structural folds currently present in PDB, under the assumption that the current PDB is a random subset of the structural universe. Since dimeric protein-protein interaction is the basic unit of all higher-order oligomers, our calculation is focused on the dimer structures. Protein quaternary structure universe dictates possible ways that proteins interact with each other. Despite the extensive analysis on the universe of protein tertiary folds for which a general consensus exists, very few such studies were conducted on protein-protein complexes. Using a non-redundant set of protein dimeric structures in the PDB and the complex structural alignment tool MM-align, this study proposed a quantitative estimate of quaternary folds possibly existing in nature. First, a new scoring function, rTM-score, was introduced to measure the “similarity” between complex structures, which accounts for both chain orientation and monomer structural similarity into a single sensitive parameter. All non-redundant complex structures in the PDB screened at a sequence identity cutoff 90% were classified into “quaternary families” by mapping both sequences of each dimer onto the Pfam database. The 3,629 unique quaternary families were thereby clustered by rTM-score into 1,761 quaternary folds, with the largest cluster comprising 47 complex structures. About 60% of the structures were found to be structural orphans, indicating that the protein complex structure library is largely incomplete. A power-law dependence was observed between the cluster size and the number of clusters, which may implicate a cascade mechanism in the evolution of the protein-protein complexes. Based on the maximum probability principle, the number of possible quaternary structure folds in nature was estimated. The number of folds in our estimation varies when the number of quaternary families changes which follows a strict logarithmic dependence. If we OTX015 assume that the number of quaternary families in nature is similar to the number of monomeric protein families, it was estimated that the number of expected quaternary folds in nature is approximately 4,000-5,000. This number is about two times lower than the previous estimation that defined protein folds based on a sequence identity cutoff. Based on the definition of rTM-score.0.5, the rate of quaternary fold determination is low, i.e. 130 per year in last 6 years. This means we need about a quarter of century before a complete set of quaternary protein structures can be experimentally solved under the current fold solution rate. There are several uncertainties in our model which can be improved in the future studies. First, quaternary structural folds are defined by rTM-score.0.5, which only accounts for global topology and corresponds to the complexes of the same chainorientation and similar monomer fold.