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Nonlinear reconstruction of single-molecule free-energy surfaces from univariate time series

Overview of attention for article published in Physical Review E, March 2016
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Nonlinear reconstruction of single-molecule free-energy surfaces from univariate time series
Published in
Physical Review E, March 2016
DOI 10.1103/physreve.93.032412
Pubmed ID

Jiang Wang, Andrew L. Ferguson


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.

Mendeley readers

The data shown below were compiled from readership statistics for 14 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Germany 1 7%
United States 1 7%
Unknown 12 86%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 8 57%
Researcher 4 29%
Student > Bachelor 1 7%
Student > Doctoral Student 1 7%
Readers by discipline Count As %
Physics and Astronomy 4 29%
Agricultural and Biological Sciences 3 21%
Mathematics 2 14%
Computer Science 2 14%
Chemistry 2 14%
Other 1 7%