A contact is defined as 'minimally frustrated' if its native energy is at the lower end of the distribution of decoy energies, having a frustration index as measured with a Z-score of 0.78 or higher magnitude , that is, the majority of (but by no means all!) other amino acid pairs in that position would be unfavorable.
Conversely, a contact is defined as 'highly frustrated' if E0 is at the other end of the distribution with a local frustration index lower than -1, that is, most other amino acid pairs at that location would be more favorable for folding than the native ones by more than one standard deviation of that distribution. If the native energy is in between these limits, the contact is defined as 'neutral'.
A frustration index may depend on the choice of parts in which the protein's whole energy is divided. It therefore becomes natural to divide the energy up in a way that is at least roughly comparable to what natural selection can do: examine the changes in energy upon making mutations. The server provides two complementary ways for localizing frustration that differ in how the set of decoys is constructed:
(How favourable are the native residues relative to other residues in
The decoy set is made randomizing the identities of the interacting amino acids i,j, keeping all other interaction parameters at their native value. This scheme effectively evaluates every possible mutation of the amino acid pair that forms a particular contact in a robustly fixed structure. It is worth noting that the energy change upon a residue pair mutation not only comes directly from the particular contact probed, but also changes through interactions of each residue with other residues not in the mutated pair, and those contributions will also vary upon mutation.
(How favourable are the native interactions between two residues
relative to other interactions these residues can form in other
This way of measuring frustration imagines that the residues are not only changed in identity but are also displaced in location. The energy variance thus reflects contributions to different energies of other compact conformations. In this calculation the decoy set involves randomizing not just the identities but also the distance and densities of the interacting amino acids i,j. This scheme effectively evaluates the native pair with respect to a set of structural decoys that might be encountered in the folding process.
Most of the polipeptide sequences found in the biosphere fold into
defined structural elements forming domains. In order to fold robustly
in biologically relevant timescales, the heteropolymer must be
'minimally frustrated', and thus have an energy landscape that
resembles a rough funnel. It is not folding per se what determines
protein evolution, but the 'biological function' that the polipeptides
The complexity of protein sequences suggests they may contain conflicting signals encoding folding and function. Yet searching the immense energy landscape of a protein for the native structure would be slow if the landscape were very rugged due to many conflicting local interactions. Minimal frustration implies protein structure is also robust to mutation. Neither protein's kinetic foldability nor their mutational robustness deny the possibility that some frustration from conflicting signals may be present locally in some proteins. Such local frustration, being tolerable, might naturally arise from random neutral evolution. Local frustration also could be a functionally useful adaptation.
The possible adaptive value for a molecule to have spatially localized frustration arises from the way such frustration may sculpt protein dynamics for specific functions. In a monomeric protein the alternate configurations caused by locally frustrating an otherwise largely unfrustrated structure could provide specific control of the thermal motions, so the protein can function much like a macroscopic machine having only a few moving parts. Alternatively a site frustrated in a monomeric protein may become less frustrated in the final larger assembly containing that protein, thus guiding specific association.