Specific and nonspecific binding of proteins in simple interaction networks. (*A*) Basic topological units of the protein–protein interaction networks. Orange and green circles represent shared and unshared interfaces, respectively, and black lines indicate specific binding. The units are replicated to create networks, as illustrated in the oval for a Pairs and Threes network with *N* = 20 proteins. (*B*) Minimum-energy gap Δ*E* for networks of *N* proteins. Optimal gaps (symbols as in A) were found by MC optimization of interfaces with *L* = 25 amino acids. The gray dashed line is the Hamming bound of the binary model, scaled by an arbitrary factor 2/3 for comparison. Solid lines are power-law fits, with scaling exponents *γ* = 0.13 for the Pairs topology, 0.13 for Pairs and Threes in a 1∶1 ratio, 0.14 for Threes, 0.14 for Fives, and 0.19 for Chains. We also optimized the Pairs topology with different contact potentials. For the Betancourt–Thirumalai () and Skolnick et al. () potentials, we obtained *γ* = 0.12 and 0.13, respectively. (*C*) Concentration of proteins bound in nonspecific complexes, normalized by the concentration bound in specific complexes and free in solution. Individual protein concentrations are set at 100 nM each. With fixed total protein concentration the results are similar (*SI Text* and Fig. S5). Data are averaged over the two configurations of protein sequences with the largest minimum-energy gaps. (*D*) Hamming bound () on the minimum gap for *N* binary sequences of length *L*. For comparison, the gap of the Pairs network in B and the corresponding power law are shown as red symbols and line, multiplied by an arbitrary factor of 1.65.

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