The folding of an enzyme. I. Theory of protein engineering analysis of stability and pathway of protein folding.

The theory, assumptions and limitations are outlined for a simple protein engineering approach to the problem of the stability and pathway of protein folding. It is a general procedure for analysing structure-activity relationships in non-covalent bonding, including enzyme catalysis, that relates experimentally accessible data to changes in non-covalent bonding. Kinetic and equilibrium measurements on the unfolding and refolding of mutant proteins can be used to map the formation of structure in transition states and folding intermediates. For example, the ratio of the changes in the activation energy of unfolding and the free energy of unfolding on mutation is measured to give a parameter phi. There are two extreme values of phi that are often found in practice and may be interpreted in a simple manner. A value of phi = 0 implies that the structure at the site of mutation is as folded in the transition state as it is in the folded state. Conversely, phi = 1 shows that the structure at the site of mutation is as unfolded in the transition state as it is in the unfolded structure. Fractional values of phi are more difficult to interpret and require a more sophisticated approach. The most suitable mutations involve truncation of side-chains to remove moieties that preferably make few interactions with the rest of the protein and do not pair with buried charges. Fractional values of phi found for this type of mutation may imply that there is partial non-covalent bond formation or a mixture of states. The major assumptions of the method are: (1) mutation does not alter the pathway of folding; (2) mutation does not significantly change the structure of the folded state; (3) mutation does not perturb the structure of the unfolded state; and (4) the target groups do not make new interactions with new partners during the course of reaction energy. Assumptions (2) and (3) are not necessarily essential for the simple cases of phi = 0 or 1, the most common values, since effects of disruption of structure can cancel out. Assumption (4) may be checked by the double-mutant cycle procedure, which may be analysed to isolate the effects of just a pair of interactions against a complicated background. This analysis provides the formal basis of the accompanying studies on the stability and pathway of folding of barnase, where it is seen that the theory holds very well in practice.