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

Jiang Wang, Andrew L. Ferguson

Research output: Contribution to journalArticlepeer-review


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 C24H50 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.

Original languageEnglish (US)
Article number032412
JournalPhysical Review E
Issue number3
StatePublished - Mar 21 2016

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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