  We study the formation of protein-protein encounter complexes with a Langevin
equation approach that considers direct, steric and thermal forces. As three
model systems with distinctly different properties we consider the pairs
barnase:barstar, cytochrome c:cytochrome c peroxidase and p53:MDM2. In each
case, proteins are modeled either as spherical particles, as dipolar spheres or
as collection of several small beads with one dipole. Spherical reaction
patches are placed on the model proteins according to the known experimental
structures of the protein complexes. In the computer simulations, concentration
is varied by changing box size. Encounter is defined as overlap of the reaction
patches and the corresponding first passage times are recorded together with
the number of unsuccessful contacts before encounter. We find that encounter
frequency scales linearly with protein concentration, thus proving that our
microscopic model results in a well-defined macroscopic encounter rate. The
number of unsuccessful contacts before encounter decreases with increasing
encounter rate and ranges from 20-9000. For all three models, encounter rates
are obtained within one order of magnitude of the experimentally measured
association rates. Electrostatic steering enhances association up to 50-fold.
If diffusional encounter is dominant (p53:MDM2) or similarly important as
electrostatic steering (barnase:barstar), then encounter rate decreases with
decreasing patch radius. More detailed modeling of protein shapes decreases
encounter rates by 5-95 percent. Our study shows how generic principles of
protein-protein association are modulated by molecular features of the systems
under consideration. Moreover it allows us to assess different coarse-graining
strategies for the future modelling of the dynamics of large protein complexes.
