Co-operative interactions during protein folding

Abstract

The theory for measuring co-operativity between interactions in proteins by protein engineering experiments is developed by introducing a procedure for analysing increasing orders of synergy in a protein with increasing numbers of residues. The (pairwise) interaction energy (Δ 2 G int) between two side-chains may be measured experimentally by a double-mutant cycle consisting of the wild-type protein, the two single mutants and the double mutant. This procedure may be extended to three residues to give a value for Δ 3 G int for a triple-mutant cube, and to higher orders using multi-dimensional mutant space. We now show that Δ 3 G int is the excess energy of adding all three chains compared with the sum of all the pairwise values of (Δ 2 G int) for each of the constituent double-mutant cycles and the sum of all the single addition energies. This physical interpretation extends to higher orders of mutation. Δ n G int (i.e. the interaction energy for n residues), thus, reveals the layers of synergy in interactions as a protein is built up. This procedure is applied to measuring changes in synergy during the refolding of barnase for the triad of salt-linked residues Asp8, Asp12 and Arg110, which are mutated to alanine residues. The value of Δ 3 G int in the folded structure is 0.77(±0.06) kcal mol −1 (i.e. the triad is 0.77 kcal mol −1 more stable than expected from the sum of the individual pairwise interactions and single contributions). The value of Δ 3 G int is still significant in the transition state for unfolding (0.60(±0.07) kcal mol −1) and in the folding intermediate (0.60(±0.13 kcal mol −1). These results show that synergistic interactions exist in barnase, in its transition state for unfolding and in a refolding intermediate. A direct measurement of the change of co-operativity between the folded state and the transition state for unfolding shows a decrease of 0.17(±0.04) kcal mol −1, suggesting that the initial stages of protein unfolding may be accompanied by some loosening of structure in parts that still interact. The similar extent of co-operativity in the transition state for unfolding and the intermediate in refolding suggests that the intermediate is homogeneous, at least in the region of the salt-linked triad, as heterogeneity would lower the co-operativity.