Oligomerization plays an important role in the function of many proteins. Thus, understanding, predicting, and, ultimately, engi-neering oligomerization presents a long-standing interest. From the perspective of structural biology, protein-protein interactions have mainly been analyzed in terms of the biophysical nature and evolution of protein interfaces. Here, our aim is to quantify the importance of the larger structural context of protein interfaces in protein interaction evolution. Specifically, we ask to what extent intersubunit geometry affects oligomerization state. We define a set of structural parameters describing the overall geometry and relative positions of interfaces of homomeric complexes with different oligomeric states. This allows us to quantify the contribution of direct sequence changes in interfaces versus indirect changes outside the interface that affect intersubunit geometry. We find that such indirect, or allosteric mutations affecting intersubunit geometry via indirect mechanisms are as important as interface sequence changes for evolution of oligomeric states.protein complex evolution | homomeric complexes | protein geometry D uring the course of evolution proteins are constrained by their stability, biochemical activity, and regulation. A specific level of evolutionary constraint is added by interactions with other proteins as a greater proportion of protein structure is involved in its function (1). The basic principles of protein recognition and interface formation have been understood for many years (2), and it has been clear for a long time that considerable differences exist between two functionally distinguishable groups-obligate and transient interfaces (3-5). The evolution of protein interfaces has been related to these two groups as well as other biophysical principles. For instance, Mintseris and Weng have, by appropriately grouping types of protein complexes, shown that protein interfaces are slightly more conserved than the surface but much less than the protein core (6). This makes sense in the light of the prediction where, on average, just two substitutions are sufficient to convert a patch on a protein surface into a protein interface (7). This in turn supports work on so-called hot spot (8-10) and anchor residues (11) or conserved residue clusters (12) in protein interfaces. The shared idea in all of these publications, that there are a few key interface residues, is in agreement with the nature of protein interface packing. Residues on the interface rim, which have more conformational freedom, can accommodate sequence changes more easily than ones in the interface core. More recently, there have been contributions to the field showing how interfaces can evolve through insertions of multiple residues forming so-called enabling loops (13,14).Interactions put additional constraints on protein sequences (15); however, in complexes where a subunit has multiple distinct surface regions that form interfaces (16), we would not expect the increase in evolutionary constraint ...