Examining a Thermodynamic Order Parameter of Protein Folding

Song-Ho Chong,Sihyun Ham

doi:10.1038/s41598-018-25406-8

Song-Ho Chong, Sihyun Ham

Open Access

https://doi.org/10.1038/s41598-018-25406-8

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Journal: Scientific Reports	Publication Date: May 8, 2018
Citations: 8	License type: open-access

Affiliation: Sookmyung Women's University

Abstract

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.

Highlights

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
We start from overviewing the geometric order parameters commonly used in protein folding studies: Cα-root mean square deviation (RMSD) to the native structure (Fig. 2a) and the fraction (Q) of native amino acid contacts (Fig. 2b)
The solvent-averaged effective energy f–the thermodynamic order parameter that we argue in the present study–is introduced as follows[21,26]

Summary

Introduction

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. More systematically derived collective reaction coordinates have been commonly adopted, for example, those determined by the time-lagged independent component analysis (TICA)[17,18] or the principal component analysis (PCA)[19] of internal coordinates, which best characterize rare or large conformational fluctuations, respectively These order parameters can be classified into two groups depending on whether external information other than raw simulation trajectories is utilized. We examine the suitability of the solvent-averaged effective energy[20,21], to be denoted as f from here on, as a reaction coordinate of protein folding This is a thermodynamic quantity since it involves the solvation free energy (i.e., averaging over solvent molecules), but like the geometric order parameters mentioned above, it can be defined and computed for individual protein conformations. Thereby, we would like to establish the usefulness of this thermodynamic order parameter for investigating the protein folding

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Results

Conclusion