Development of a thermodynamic approach to clustering ensemble structures for a native state of a protein from NMR experiment: Application to a cancer suppressor protein P53

NMR experiments for resolving protein structures provide ensemble structures that have different features from the unique ones obtained from X-ray crystallography experiments. Currently, the conventional methods to select good structures for a native state from NMR rely on choosing structures with geometrical similarity, for example root-mean-square deviation (RMSD), in the ensemble of protein structures. However, the conventional approach can clarify nothing but a geometrical convergence of ensemble structures, with which one assumes that the structures of low energies and with smaller RMSD values are candidates for a native-state structure of a target protein. Here, we suggest a statistical physics approach to probe the thermodynamic stability of ensemble structures resolved in NMR experiment and to identify a set of ensemble structures possessing thermodynamic equivalence as candidates for a native-state structure. We employed a coarse-grained description for a global protein energy function based on the environmental energy parameters of 20 amino acids, which were constructed by perceptron learning and protein threading of 1,006 representative proteins. We constructed an approximate partition function in the conformational space of decoy conformations, although it was not albeit exact. We calculated the unfolded fraction and the specific heat of the tetramerization domain of an important cancer suppressor protein p53 as a function of temperature. Applying our approach to the 20 (78) ensemble structures of the 1HS5 (1SAK) group, 9 (72) out of 20 (78) ensemble structures were interpreted as thermodynamically equivalent and could be considered as a good set of native-state structures with relatively high thermodynamic stabilities whereas the remaining 11 (6) ensemble structures should have been removed from the candidate structures for a native state in the NMR, experiment. After refining the ensemble structures of 1SAK to have 3SAK experimentally, the 23 new ensemble structures of 3SAK showed a good thermodynamic equivalence in their unfolded fraction and specific heat curves. Our statistical physics approach is a new alternative method for characterizing the thermodynamic behavior of ensemble structures of a target protein in NMR experiments and to select a good set of ensemble structures for a native state. If our approach is combined with the conventional geometrical method, it will greatly facilitate the identification and characterization of ensemble structures of a target protein in NMR experiments.