ABSTRACT
Protein-protein interactions comprise both transport and reaction steps. During the transport step, anisotropy of proteins and their complexes is important both for hydrodynamic diffusion and accessibility of the binding site. Using a Brownian dynamics approach and extensive computer simulations, we quantify the effect of anisotropy on the encounter rate of ellipsoidal particles covered with spherical encounter patches. We show that the encounter rate k depends on the aspect ratios xi mainly through steric effects, while anisotropic diffusion has only a little effect. Calculating analytically the crossover times from anisotropic to isotropic diffusion in three dimensions, we find that they are much smaller than typical protein encounter times, in agreement with our numerical results.
Subject(s)
Models, Chemical , Models, Statistical , Proteins/chemistry , Proteins/ultrastructure , Anisotropy , Binding Sites , Computer Simulation , Diffusion , Protein BindingABSTRACT
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 to 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%. 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 modeling of the dynamics of large protein complexes.
Subject(s)
Models, Chemical , Bacterial Proteins/chemistry , Bacterial Proteins/metabolism , Cytochromes c/chemistry , Cytochromes c/metabolism , Models, Molecular , Peroxidase/chemistry , Peroxidase/metabolism , Protein Binding , Protein Conformation , Proto-Oncogene Proteins c-mdm2/chemistry , Proto-Oncogene Proteins c-mdm2/metabolism , Ribonucleases/chemistry , Ribonucleases/metabolism , Time Factors , Tumor Suppressor Protein p53/chemistry , Tumor Suppressor Protein p53/metabolismABSTRACT
Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nosé-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nosé-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nosé-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.
