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.

Single-Molecule Förster Resonance Energy Transfer Measurement Reveals the Dynamic Partially Ordered Structure of the Epidermal Growth Factor Receptor C-Tail Domain

“… The existence of multiple structural states near Grb2-binding sites has been previously suggested. For example, relatively slow transitions between hidden states were elucidated from in vitro single-molecule imaging experiments of EGFR and Grb2-binding kinetics, in which multiple rates in both association and dissociation processes were detected . Coincidence of different rates of Grb2 dissociation was also detected in living cells .…”

Single Molecule Data Analysis: An Introduction

“…Statistical approaches have been invaluable in generating detailed mechanistic insight into realms previously inaccessible at every step along biology's central dogma [42,43]. They have also unveiled basic molecular mechanisms from noisy single molecule data that have given rise to detailed energy landscape [44][45][46][47][48][49][50] and kinetic scheme [31,[51][52][53][54][55] models. Furthermore, one's choice of analysis methods can deeply alter the interpretation of experiment [56,57].…”

From Prescriptive to Predictive: an Interdisciplinary Perspective on the Future of Computational Chemistry

“…259 Recent advances in measuring theoretical quantities directly instead of using numerical approximations or intermediate models include: the prediction of protein assemblies from cryo-electron microscopy data, 260 the extraction of time-averaged equilibrium probability distributions for an individual molecule via tunnelling microscopy, 261 or the direct construction of energy landscapes 219 from experimental single-molecule time-series. 172,262,263 The mechanical forces between two covalently bound atoms can now be measured and, thus, the forces can act as control parameters to design potential energy landscapes, 264 rather than being structural constraints. 265 By putting more effort, time, and expenses into the measurement stage of the modelling cycle, physical and chemical sciences can gain detailed knowledge about risks and uncertainties in large and complex systems.…”