The same dataset of 4024 nonredundant structures was used to derive the torsion angles φ and ψ after running DSSP for the whole dataset. The minimum bin size for the torsion angles was set to 1o comprising the bins ranging from 180 to 180 for both the torsion angles. Before the potential was developed, the torsion angle bins were initialised with a constant to avoid null values for the development of Boltzmann energy values. Then, the bins were normalised with a standard procedure using the circular Gaussian function for φ and ψ having the bivariate normal distribution.
Here, σ is the standard deviation and A(φ,ψ) is the Gaussian apodisation function for the torsion angles φ and ψ where the distribution of torsion angle potential is tapered around the peaks to accommodate torsion angle perturbation in the mutants.
The torsion angle count exhibits different frequencies and the population of angles bins differ from one amino acid to other. In order to avoid this problem, the torsion angle bins for all 20 amino acids were further normalised individually for the angles φ and ψ. Then, they were used to calculate the Boltzmann energy values for mean force potentials of all amino acids:
Here, the g(φ,ψ) and g_{ref}(φ,ψ) and are torsion angle distribution of a specific amino acid and the average distribution over all the amino acids respectively.

