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

doi:10.1073/pnas.0707378105

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

*Nonlinear Sciences Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan;
^†Core Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan;
^§Department of Chemistry, University of California, Berkeley, CA 94720; and
^¶Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Edited by R. Stephen Berry, University of Chicago, Chicago, IL, and approved November 20, 2007 (received for review August 6, 2007)

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.

Footnotes

^‖To whom correspondence should be addressed. E-mail: tamiki{at}es.hokudai.ac.jp
Author contributions: C.-B.L. and T.K. designed research; C.-B.L. and T.K. performed research; C.-B.L., H.Y., and T.K. contributed new reagents/analytic tools; C.-B.L. analyzed data; and C.-B.L., H.Y., and T.K. wrote the paper.
↵ ^‡Present address: Research Institute for Electronic Science, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0707378105/DC1.