Do proteins always benefit from a stability increase? Relevant and residual stabilisation in a three-state protein by charge optimisation.

The vast majority of our knowledge on protein stability arises from the study of simple two-state models. However, proteins displaying equilibrium intermediates under certain conditions abound and it is unclear whether the energetics of native/intermediate equilibria is well represented in current knowledge. We consider here that the overall conformational stability of three-state proteins is made of a "relevant" term and a "residual" one, corresponding to the free energy differences of the native to intermediate (N-to-I) and intermediate to denatured (I-to-D) equilibria, respectively. The N-to-I free energy difference is considered to be the relevant stability because protein-unfolding intermediates are likely devoid of biological activity. We use surface charge optimisation to first increase the overall (N-to-D) stability of a model three-state protein (apoflavodoxin) and then investigate whether the stabilisation obtained is realised into relevant or into residual stability. Most of the mutations designed from electrostatic calculations or from simple sequence conservation analysis produce large increases in the overall stability of the protein. However, in most cases, this simply leads to similarly large increases of the residual stability. Two mutations, nevertheless, show a different trend and increase the relevant stability of the protein substantially. When all the mutations are mapped onto the structure of the apoflavodoxin thermal-unfolding intermediate (obtained independently by equilibrium phi-analysis and NMR) they cluster perfectly so that the mutations increasing the relevant stability appear in the small unstructured region of the intermediate and the others in the native-like region. This illustrates the need for specific investigation of N-to-I equilibria and the structure of protein intermediates, and indicates that it is possible to rationally stabilise a protein against partial unfolding once the structure of the intermediate conformation is known, even if at low resolution.