Multiscale complex network of protein conformational fluctuations in single-molecule time series

Abstract

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy-different physical states having the same value for a measured observable-as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctutation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion.single-molecule experiment ͉ anomalous diffusion ͉ time series analysis O ptical single-molecule spectroscopy has provided unique insights into both the distribution of molecular properties and their dynamic behavior, which are inaccessible using ensemble-averaged measurements (1-5). In principle, the complexity observed in the dynamics and kinetics of a protein originates in the underlying multidimensional energy landscape (6-12). The dynamics can be understood as the protein traversing from one state (node) to another along a complex network in conformational space or, more generally, in state space. The network properties of biological systems can provide a new perspective for addressing the nature of their hierarchical organization in multidimensional state space (10,11,13,14), enabling us to ask such questions as: Is there any distinctive network topology that is characteristic for the native basin into which a protein folds? Are there any common network features that biological systems may have evolved by adapting to the changes in the environment? Motivated by questions of this nature, we address how one can extract the state space network (SSN) of multiscale biological systems explicitly from a single-molecule time series, free from a priori assumptions on the underlying physical model or rules. These theoretical studies underscore the difficulties in establishing a minimal physical model for the origin of complexity in the kinetics or dynamics of biomolecules. Instead of postulating or constructing a physical model to characterize experimental results, we take a different approach to "let the system speak for itself'' through the single-molecule time series. Such unbiased solutions, which are data-driven instead of model-driven, have been provided in the context of single-molecule FRET experiments (24) and emission intermittency, demonstrated in resolving quantum dot bl...

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