title: Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series.
abstract: We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ~3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.
authors.affiliation: Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan.
authors.forename: Tahmina
authors.initials: T
authors.lastname: Sultana
authors.affiliation: Department of Physics, Nara Medical University, 840 Shijo-cho, Kashihara Nara 634-8521, Japan and Japan Science and Technology Agency (JST), CREST, Suita, Osaka, Japan.
authors.forename: Hiroaki
authors.initials: H
authors.lastname: Takagi
authors.affiliation: WPI Immunology Frontier Research Center (WPI-IFReC), Osaka University, 3-1 Yamadaoka, Suita, Osaka 565-0871, Japan.
authors.forename: Miki
authors.initials: M
authors.lastname: Morimatsu
authors.affiliation: Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Teramoto
authors.affiliation: Molecule and Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan.
authors.forename: Chun-Biu
authors.initials: CB
authors.lastname: Li
authors.affiliation: Cellular Informatics Laboratory, RIKEN, 2-1 Hirosawa, Wako 351-0198, Japan.
authors.forename: Yasushi
authors.initials: Y
authors.lastname: Sako
authors.affiliation: Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan.
authors.forename: Tamiki
authors.initials: T
authors.lastname: Komatsuzaki
mesh_terms: D002462:Cell Membrane / Q000378:metabolism; D066246:ErbB Receptors / Q000378:metabolism; D051380:GRB2 Adaptor Protein / Q000378:metabolism; D007700:Kinetics; D008390:Markov Chains; D008954:Models, Biological
chemical_list: D051380:GRB2 Adaptor Protein; D066246:ErbB Receptors