Recent paramagnetic relaxation enhancement (PRE) studies on several weakly interacting protein complexes have unequivocally demonstrated the existence of transient encounter complexes. Here, we present a computational method to study protein-protein binding by creating equilibrium ensembles that include both specific and nonspecific protein complexes. In a joint analysis of simulation and experiment we explore the physical nature and underlying physicochemical characteristics of encounter complexes involving three protein-protein interactions of the bacterial phosphotransferase system. Replica exchange Monte Carlo simulations using a coarse-grained energy function recover the structures of the specific complexes and produce binding affinities in good agreement with experiment. Together with the specific complex, a relatively small number of distinct nonspecific complexes largely accounts for the measured PRE data. The combined relative population of the latter is less than approximately 10%. The binding interfaces of the specific and nonspecific complexes differ primarily in size but exhibit similar amino acid compositions. We find that the overall funnel-shaped energy landscape of complex formation is dominated by the specific complex, a small number of structured nonspecific complexes, and a diffuse cloud of loosely bound complexes connecting the specific and nonspecific binding sites with each other and the unbound state. Nonspecific complexes may not only accelerate the binding kinetics by enhancing the rate of success of random diffusional encounters but also play a role in protein function as alternative binding modes.