Figure 3. Estimating E_c for a general interaction matrix.

We are interested in the contribution to the second moment of the energy distribution from residue types i and j, with frequencies p_i and p_j and interaction energy U_ij. Diagonalization of interaction matrix U introduces a new set of quasi-residues (polyhedrals) with interaction energy given by and quasi-frequencies . Each eigencomponent l has the simplified interaction matrix shown in the red box, for which can be easily estimated (Eq. (8)). The overall estimate of E_c is the summation of estimates for each l.