Title |
Nonlinear reconstruction of single-molecule free-energy surfaces from univariate time series
|
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Published in |
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, March 2016
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DOI | 10.1103/physreve.93.032412 |
Pubmed ID | |
Authors |
Jiang Wang, Andrew L. Ferguson |
Abstract |
The stable conformations and dynamical fluctuations of polymers and macromolecules are governed by the underlying single-molecule free energy surface. By integrating ideas from dynamical systems theory with nonlinear manifold learning, we have recovered single-molecule free energy surfaces from univariate time series in a single coarse-grained system observable. Using Takens' Delay Embedding Theorem, we expand the univariate time series into a high dimensional space in which the dynamics are equivalent to those of the molecular motions in real space. We then apply the diffusion map nonlinear manifold learning algorithm to extract a low-dimensional representation of the free energy surface that is diffeomorphic to that computed from a complete knowledge of all system degrees of freedom. We validate our approach in molecular dynamics simulations of a C_{24}H_{50} n-alkane chain to demonstrate that the two-dimensional free energy surface extracted from the atomistic simulation trajectory is - subject to spatial and temporal symmetries - geometrically and topologically equivalent to that recovered from a knowledge of only the head-to-tail distance of the chain. Our approach lays the foundations to extract empirical single-molecule free energy surfaces directly from experimental measurements. |
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