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Dynamics of protein-protein encounter: A Langevin equation approach with reaction patches
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Image of FIG. 1.
FIG. 1.

Scheme to visualize the different variants of the model for the three considered model systems. The color code is yellow for barnase, cytochrome c, and p53; green for barstar, cytochrome c peroxidase, and MDM2. The respective reaction patches are shown in white. only includes a simple steric interaction. has an additional effective electrostatic interaction, here denoted with red arrows showing the direction of the dipole of the model particles. In , the excluded volume is modeled in more detail as a collection of smaller beads. The transparent blue spherical surface marks the volume used in and for the sake of comparison. Finally, the bottom row shows surface representations of the atomistic structures taken from the protein database atomistic structures taken from the protein data bank (PDB).

Image of FIG. 2.
FIG. 2.

Logarithmic plot of the distribution of the FPT to encounter between a single pair of barnase and barstar model particles in a cubic boundary box of edge length , representing a concentration of for each protein. The dashed line represents a single exponential fit to the data points, which shows the expected behavior with respect to the encounter frequency .

Image of FIG. 3.
FIG. 3.

Simulated encounter frequencies for a single pair of barnase and barstar model particles in cubic boundary boxes of different sizes representing different concentrations. The dashed line is a linear fit to the data.

Image of FIG. 4.
FIG. 4.

Encounter frequency for different numbers of barnase:barstar pairs leaving the size of the boundary box constant. The data points show the encounter frequencies as obtained from simulations, while the dashed line represents the function , where is the number of particle pairs and is a fitted prefactor.

Image of FIG. 5.
FIG. 5.

Different alignment states during the encounter process. proteins are completely unaligned. In state , referred to as contact in this paper, the proteins are translationally aligned, i.e., they are close enough to actually encounter (denoted by the overlap of the lightened area around the model particles), but lack the correct orientation. proteins reached the encounter meaning that the reactive patches are in translational and rotational alignments.

Image of FIG. 6.
FIG. 6.

Logarithmically plotted distribution of the number of approaches between a barnase and a barstar particle with incorrect rotational alignment. The dashed line is an exponential fit to the data.

Image of FIG. 7.
FIG. 7.

Double-logarithmic plot of the distribution of resting and return times of the translationally aligned state ( in Fig. 5).

Image of FIG. 8.
FIG. 8.

Correlation plot of encounter rate and mean number of contacts with all the data from Table II.

Image of FIG. 9.
FIG. 9.

Encounter rates in dependency of the patch size for the barnase:barstar model system in the variant.

Image of FIG. 10.
FIG. 10.

Comparison of and similar to Fig. 9 for small patch sizes. For larger patch sizes there is no substantial difference.


Generic image for table
Table I.

Protein structures and parameters used in the study. The coordinates of the patches and the dipole moment are given relative to the center of mass.

Generic image for table
Table II.

Encounter rates which have been averaged over several simulations at different concentrations as given in the text. The values are given in for the three different versions of our model. are average values for the number of unsuccessful contacts before encounter. is basically independent of the concentration. Therefore it is again averaged over the different simulations for each of the chosen systems. The errors were determined by one standard deviation from the eight values obtained at different concentrations. Some of the choices for the patch radius were not applicable to , as for these cases an encounter was completely prevented by the detailed excluded volume model.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamics of protein-protein encounter: A Langevin equation approach with reaction patches