Protein-protein bond formations, such as antibody-antigen complexation or aggregation of protein monomers into dimers and larger aggregates, occur with bimolecular rate constants on the order of 10(6) M-1.s-1, which is only 3 orders of magnitude slower than the diffusion-limited Smoluchowski rate. However, since the protein-protein bond requires rotational alignment to within a few angstroms of tolerance, purely geometric estimates would suggest that the observed rates might be 6 orders of magnitude below the Smoluchowski rate. Previous theoretical treatments have not been solved for the highly specific docking criteria of protein-protein association--the entire subunit interface must be aligned within 2 A of the correct position. Several studies have suggested that diffusion alone could not produce the rapid association kinetics and have postulated "lengthy collisions" and/or the operation of electrostatic or hydrophobic steering forces to accelerate the association. In the present study, the Brownian dynamics simulation method is used to compute the rate of association of neutral spherical model proteins with the stated docking criteria. The Brownian simulation predicts a rate of 2 x 10(6) M-1.s-1 for this generic protein-protein association, a rate that is 2000 times faster than that predicted by the simplest geometric calculation and is essentially equal to the rates observed for protein-protein association in aqueous solution. This high rate is obtained by simple diffusive processes and does not require any attractive or steering forces beyond those achieved for a partially formed bond. The rate enhancement is attributed to a diffusive entrapment effect, in which a protein pair surrounded and trapped by water undergoes multiple collisions with rotational reorientation during each encounter.