  The capacity of proteins to interact specifically with one another underlies
our conceptual understanding of how living systems function. Systems-level
study of specificity in protein-protein interactions is complicated by the fact
that the cellular environment is crowded and heterogeneous; interaction pairs
may exist at low relative concentrations and thus be presented with many more
opportunities for promiscuous interactions compared to specific interaction
possibilities. Here we address these questions using a simple computational
model that includes specifically designed interacting model proteins immersed
in a mixture containing hundreds of different unrelated ones; all of them
undergo simulated diffusion and interaction. We find that specific complexes
are quite robust to interference from promiscuous interaction partners, only in
the range of temperatures Tdesign>T>Trand. At T>Tdesign specific complexes
become unstable, while at T<Trand formation of specific complexes is suppressed
by promiscuous interactions. Specific interactions can form only if
Tdesign>Trand. This condition requires an energy gap between binding energy in
a specific complex and set of binding energies between randomly associating
proteins, providing a general physical constraint on evolutionary selection or
design of specific interacting protein interfaces. This work has implications
for our understanding of how the protein repertoire functions and evolves
within the context of cellular systems.
