Systematic Extraction of Dynamically Relevant Order Parameters
Isolated n-alkane chains in water serve as useful model systems in which to study the role of hydrophobicity in protein folding. A nonlinear dimensionality reduction technique known as the diffusion map, was applied to long molecular dynamics simulations of n-alkane chains to systematically extract order parameters describing the slow, fundamental dynamics of the chain. A reconstruction of the free energy surface in these variables for n-tetracosane (C24H50) reveals kinetically meaningful low free energy pathways between metastable states. For sufficiently long chains, we find collapse from an extended conformation to a planar hairpin to proceed by a "kink and slide" mechanism, whereby a bend in the head or tail migrates to the middle of the chain and is accompanied by an expulsion of interior solvent molecules. This is followed by further collapse into a helical coil.