  The native conformation of structured proteins is stabilized by a complex
network of interactions. We analyzed the elementary patterns that constitute
such network and ranked them according to their importance in shaping protein
sequence design. To achieve this goal, we employed a cluster expansion of the
partition function in the space of sequences and evaluated numerically the
statistical importance of each cluster. An important feature of this procedure
is that it is applied to a dense, finite system. We found that patterns that
contribute most to the partition function are cycles with even numbers of
nodes, while cliques are typically detrimental. Each cluster also gives a
contribute to the sequence entropy, which is a measure of the evolutionary
designability of a fold. We compared the entropies associated with different
interaction patterns to their abundances in the native structures of real
proteins.
