Pace collected unfolding free energy data for Tyr to Phe mutants and Thr to Val mutations in which the wild-type side chain was either hydrogen bonded or not hydrogen bonded. The analysis is illustrated for Tyr to Phe mutations. A mutation from Tyr to Phe will break the hydrogen bond, reflected in ΔG_HB. It may also alter other contributions of the side chain such as hydrophobicity, conformational entropy and packing, reflected in ΔG_SC(Tyr) and ΔG_SC(Phe) for the Tyr and Phe side chains, respectively. All other contributions to folding that are not involved in the mutation are lumped into ΔG_other. For the hydrogen bonded side chains, the difference in unfolding free energies, ΔG_u(1) and ΔG_u(2), reflects both ΔG_HB and the difference in other side chain contributions. For the non-hydrogen bonded side chains, the difference in unfolding free energies, ΔG_u(3) and ΔG_u(4), reflects only the difference in the other side chain contributions. By subtracting the average unfolding free energy changes for the mutants in the two classes (hydrogen bonded and not), the average other side chain contributions cancel, leaving the average hydrogen bond contribution.

In this example residue X and residue Y form a hydrogen bond. The change in unfolding free energy upon mutation of residue Y, ΔΔGu(Y), will reflect the hydrogen bond contribution, ΔG_HB, and any other interactions made by residue Y in the folded or unfolded state, ΔG_Yother. Similarly, the change in unfolding free energy upon mutation of residue X, ΔΔGu(X), will reflect the hydrogen bond contribution, ΔG_HB, and any other interactions made by residue X in the folded or unfolded state, ΔG_Xother. The change in unfolding free energy upon mutation of both residue X and Y, ΔΔGu(XY), will reflect the hydrogen bond contribution, ΔG_HB, and any other interactions made by residues X and Y in the folded or unfolded state, ΔG_Xother + ΔG_Yother. As illustrated below the cycle, adding the single mutant effects and subtracting the double mutant effects results in cancellation of the other contributions and leaves the hydrogen bond free energy. The key and rather bold assumption is that the effects of the mutants are additive and independent.

The figure illustrates a hypothetical hydrogen bond made between two threonine side chains on the left must compete with an alternative hydrogen bond. The alternative hydrogen bond could be made in either the folded or unfolded state because transmembrane helical structure can be maintained in unfolded membrane proteins. For the hydrogen bond on the left to be net stabilizing, it must be stronger than the hydrogen bond on the right.