How the excluded volume architecture influences ion-mediated forces between proteins

The effective interactions between model proteins of various shapes are computed by means of Monte Carlo simulations. In particular, we determine how the modification of the excluded volume architecture influences both entropic and purely electrostatic ion-mediated forces between proteins. We find that interprotein interactions are strongly affected by protein shape, which results in a high decrease of electrostatic screening for typical active site geometries. Effective interactions are then closer to the direct Coulombic interactions, and both affinity and selectivity are enhanced by several orders of magnitude.

Figure 1

Anion density field $\rho ∕\rho (R=\infty )$ around spherical proteins (a) in the case of a protein alone, and in both cases of (b) two oppositely charged proteins, and (c) two like-charged proteins, for the reduced interprotein distance $R∕R_c$=1.5. The bonding and antibonding regions are separated by a line, and the coordinates $(r,z)$ are indicated.

Figure 2

Schematic view of the different model proteins. The charges of the proteins are placed on $\alpha$. The interactions are computed as a function of the distance $R$ between the charges, for the geometries sketched in the box.

Figure 3

Different contributions to the scaled effective force $F_{\mathrm{eff}}{R}_c∕k_{B}T$ exerted on a protein $S$ as functions of the reduced distance $R∕R_c$ between two proteins $S$ and $A$, which are either like charged ($+10$ and $+10$) or oppositely charged ($+10$ and $-10$). The same is plotted for two spherical proteins $S$ (the three thickest curves of each graph).

Figure 4

Anion density field $\rho ∕\rho (R=\infty )$ for the reduced distance between like-charged proteins $R∕R_c=1.4$, for a system with two spherical proteins $S$ (left) and a system with proteins $A$ and $S$. On the right, the difference of those fields is presented.

Figure 5

Same as Fig. 3, but now the two proteins are of types $S$ and $B$.

Figure 6

Scaled potentials of mean force PMF (in units of $k_{B}T$) as a function of the reduced interprotein distance $R∕R_c$ for different protein shapes.