Our seminar will be in CSL 141.

**Recovery of single molecule folding landscapes from univariate time series**

Andrew L. Ferguson, Materials Science and Engineering, UIUC

The stable conformations and structural fluctuations of biomolecules and polymers are governed by the underlying molecular free energy surface (FES). We have previously developed nonlinear machine learning tools to synthesize from molecular dynamics simulations low-dimensional representations of the FES parameterized by collective coordinates, which are, in principle, functions of all molecular degrees of freedom. Experimentally, the full set of molecular degrees of freedom as a function of time is inaccessible, with sophisticated single-molecule techniques limited to tracking a handful of coarse-grained observables, such as the molecular radius of gyration, or an intra-molecular distance between fluorescent molecular tags. By integrating Takens’ theorem of delay embeddings with nonlinear manifold learning techniques, we have developed a computational approach to recover smooth transformations of a molecular FES from time series following the temporal evolution of a single molecular observable. We have validated our approach in molecular dynamics simulations of an n-tetracosane (C_24H_50) hydrocarbon chain in water, and demonstrated that the FES computed from a time series of the chain head-to-tail distance is a C^1 transformation of the FES recovered from a complete knowledge of all molecular degrees of freedom. In future work, we will extend our approach to proteins, confront issues of finite sampling, sample noise, and non-generic observables, and partner with single-molecule biophysicists to apply our methodology to experimental data.

This work was partially supported by a 2013 IMSE Small Grant to A.L. Ferguson (MatSE), and R.E.L. DeVille (Math).

BIO

Andrew L. Ferguson is Assistant Professor of Materials Science and Engineering, and an Affiliated Assistant Professor of Chemical and Biomolecular Engineering, and Computational Science and Engineering at the University of Illinois at Urbana-Champaign. He received an M.Eng. in Chemical Engineering from Imperial College London in 2005, and a PhD in Chemical and Biological Engineering from Princeton University in 2010. From 2010 to 2012 he was a Postdoctoral Fellow of the Ragon Institute of MGH, MIT, and Harvard in the Department of Chemical Engineering at MIT. He commenced his appointment at UIUC in August 2012. His research interests lie at the intersection of biomolecular simulation, nonlinear machine learning, and computational immunology. He is the recipient of a 2014 NSF CAREER Award, a 2014 ACS PRF Doctoral New Investigator, and was named the Institution of Chemical Engineers North America 2013 Young Chemical Engineer of the Year for his work in the application of thermodynamic principles to HIV and hepatitis C vaccine design.

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