Error-based Extraction of States and Energy Landscapes from Experimental Single-Molecule Time-Series

Abstract

Characterization of states, the essential components of the underlying energy landscapes, is one of the most intriguing subjects in single-molecule (SM) experiments due to the existence of noise inherent to the measurements. Here we present a method to extract the underlying state sequences from experimental SM time-series. Taking into account empirical error and the finite sampling of the time-series, the method extracts a steady-state network which provides an approximation of the underlying effective free energy landscape. The core of the method is the application of rate-distortion theory from information theory, allowing the individual data points to be assigned to multiple states simultaneously. We demonstrate the method's proficiency in its application to simulated trajectories as well as to experimental SM fluorescence resonance energy transfer (FRET) trajectories obtained from isolated agonist binding domains of the AMPA receptor, an ionotropic glutamate receptor that is prevalent in the central nervous system.

Single Molecule Data Analysis: An Introduction

“…This gives us visual insight into cluster overlap as well as the breadth of the conditional distributions p(C k |s i ) detailed in Ref. [46]. Fig.…”

“…Since, as we will see in the next section, RDT clustering directly returns conditional probabilities that each data point belongs to each cluster [46,260], soft partitioning is directly built into the RDT framework.…”

“…The errors must be treated carefully on a case-by-case basis; this is detailed for the case of smFRET data in Ref. [46].…”

“…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].…”

Combining pressure and temperature control in dynamics on energy landscapes

“…The determination of such regions and flows requires finding the minima of the landscape and measuring the local volume in state space contained within the basins of the landscape, and furthermore the analysis of the connectivity of the landscape including the derivation of the energetic, entropic and kinetic barriers [10,28] that separate individual minima and the multi-minima basins [2]. In the a e-mail: c.schoen@fkf.mpg.de literature, one finds two complementary approaches to identifying such landscape features: indirectly via extraction from long molecular dynamics [29][30][31] and Monte Carlo simulations [32] or even from long time sequences of experimental signals [33,34], or directly from the landscape itself using various global optimization and exploration algorithms [23]. Of course, in practice, combinations of these methods are often employed, depending on the type of system and objective of the study.…”