(713d) Systematic Characterization of Protein Folding Pathways Using Diffusion Maps and Molecular Simulation

Understanding the detailed mechanisms by which proteins fold from linear chains of amino acids to unique secondary/tertiary structures is still an active area of research. In complement to experimental studies, molecular simulations provide the necessary temporal and spatial resolutions to probe the detailed mechanisms and dynamics of protein folding. Conventional observables, such as root-mean-square deviation from the folded structure and radius of gyration, are commonly used to characterize the structural evolution but often fail to effectively capture the underlying dynamics of the protein folding process. It is therefore advantageous to adopt a method that can systematically analyze simulation data to extract relevant structural as well as dynamical information. We present the first study of the explicit characterization of folding pathways of Trp-cage miniprotein that utilizes the combination of molecular dynamics simulation and the nonlinear dimensionality reduction technique known as diffusion maps. Diffusion maps automatically embeds the high-dimensional protein folding trajectories into a low-dimensional space. From this low-dimensional embedding, the folding pathways and the relevant intermediate structures can be easily visualized. The eigenvectors that parameterize the low-dimensional space, furthermore, are determined systematically, rather than chosen heuristically, as is done with phenomenological observables. From the two-dimensional diffusion maps embedding of the Trp-cage molecular dynamics simulation data, we successfully identified two distinct folding pathways and several important intermediate structures, whose mechanistic details can be captured only imperfectly by the conventional phenomenological observables. Importantly, the identified pathways and intermediates are consistent with previous experimental and simulation studies. This demonstrates that the diffusion maps technique can be employed to effectively analyze and construct protein folding pathways from molecular simulations, without prior knowledge of the order parameters required to characterize the folding dynamics.

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