Jakob Schluttig, Denitsa Alamanova, Volkhard Helms and Ulrich S. Schwarz

Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches

J. Chem. Phys. 129, 155106 (2008); DOI:10.1063/1.2996082

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.