Models of protein interactions: How to choose one

Background: There have been many attempts to approximate realistic protein interaction energies by coarse graining (i.e. considering interactions between amino acids rather than those between atoms). In particular, many 20-letter models have been derived (corresponding to the 20 naturally occurring amino acids). Because such models remain computationally infeasible, many two-letter models have been proposed as further simplifications. The choice of which model to use remains arbitrary, however. In this work, we formulate the framework within which the quality of approximate interaction potentials with respect to folding can be defined explicitly. Results: Using a recently proposed criterion for comparing interaction matrices, we compare various 20 x 20 interaction matrices and obtain the two-letter model that most closely approximates each 20 x 20 matrix. We find that there are considerable differences among the 20 x 20 matrices. In particular, some matrices are much more similar to the hydrophobic model than others. Furthermore, we find that although the best two-letter approximation of a 20-letter model is a significantly better approximation than a random two-letter model, it is still a poor approximation of realistic protein interactions. Conclusions: The determination of the best two-letter approximations of various 20-letter models of protein interaction energies reveals the degree to which hydrophobic interactions dominate in each of the models and hence in proteins.