Extracting the underlying effective free energy landscape from single-molecule time series--local equilibrium states and their network

We present a new self-consistent procedure to construct a multidimensional effective free energy landscape from a scalar single molecule time series, when single molecules experience the landscape within a given timescale of "observation." The theory is based on a framework we recently developed to extract a set of local equilibrium states (LESs) and their network from a scalar time series, such as distance between dye molecules tagged in a biomolecule. We scrutinize the appropriateness of the assumptions of local equilibration and local detailed balance among LESs at the single molecule level within the given timescale, rather than postulating them a priori. The self-consistent procedure in this article incorporates the effect of local correlation of the system dynamics inside potential basins, and the effect of finiteness of the sampled data points in assigning the boundary between different LESs. We propose a new simple scheme to assign the dimensionality of the energy landscape from a single molecule time series. We also address the question of what the molecules actually "feel" from the underlying landscape at the single molecule level.