Figure 1

(a) Model of two interacting proteins, where interacting surfaces are flat disks of radius $R$ with randomly placed amino acids. (b) Snapshot of a random surface pattern.Reuse & Permissions

Figure 2

Computed probability distribution $P(E)$, and EVD, $P_{\min }(E)$, for heterodimers and homodimers, respectively. We generated ${10}^6$ surfaces with random patterns, where each surface has the diameter, $D=140\AA$. We placed $N_0=350$ particles (at random) on each surface, with the hard-core diameter of a particle being $d_0=5\AA$, (and the average surface fraction of each pattern is thus $N_0{d}_0^2/D^2\simeq 0.446$). The potential $U(r)$ was chosen to be a square well with the amplitude, $U_0=-2k_{B}T$, where $k_B$ is the Boltzmann constant and $T$ is the temperature, and with the length $\xi =8\AA$ [i.e., $U(r)=U_0$, if $5\AA <r\le 8\AA$, and $U(r)=0$, if $r>8\AA$], $E$ is plotted in the units of $k_{B}T$, and normalized by the total number of interface particles. $P(E)$ is normalized in such a way that $\int P(E)dE=1$. The intersurface separation, $h$, was chosen to be $h=5.01\AA$, i.e., such that the surfaces are practically in contact. Inset: computed dependence of $\sigma$ as a function of $\xi$ for heterodimers and homodimers, respectively. Straight lines represent the linear fits to the data. The linear correlation coefficient is $R\simeq 0.99$ in both cases. The computed ratio of the fits’ slopes, ${\sigma }_{\mathrm{homo}}/{\sigma }_{\mathrm{hetero}}\simeq 1.416$, is in excellent agreement with the theoretical prediction, $\sqrt{2}\simeq 1.414$. Error bars correspond to 1 standard deviation; most of error bars are smaller than the symbol size.Reuse & Permissions