Examining a Thermodynamic Order Parameter of Protein Folding

Dimensionality reduction with a suitable choice of order parameters or reaction coordinates is commonly used for analyzing high-dimensional time-series data generated by atomistic biomolecular simulations. So far, geometric order parameters, such as the root mean square deviation, fraction of native amino acid contacts, and collective coordinates that best characterize rare or large conformational transitions, have been prevailing in protein folding studies. Here, we show that the solvent-averaged effective energy, which is a thermodynamic quantity but unambiguously defined for individual protein conformations, serves as a good order parameter of protein folding. This is illustrated through the application to the folding-unfolding simulation trajectory of villin headpiece subdomain. We rationalize the suitability of the effective energy as an order parameter by the funneledness of the underlying protein free energy landscape. We also demonstrate that an improved conformational space discretization is achieved by incorporating the effective energy. The most distinctive feature of this thermodynamic order parameter is that it works in pointing to near-native folded structures even when the knowledge of the native structure is lacking, and the use of the effective energy will also find applications in combination with methods of protein structure prediction.