Improved resolution of complex single-molecule FRET systems via wavelet shrinkage

Time-Frequency Analysis of Two-Dimensional Electron Spin Resonance Signals

Two-dimensional electron spin resonance (2D ESR) spectroscopy is a unique experimental technique for probing protein structure and dynamics, including processes that occur at the microsecond time scale. While it provides significant resolution enhancement over the one-dimensional experimental setup, spectral broadening and noise make extraction of spectral information highly challenging. Traditionally, two-dimensional Fourier transform (2D FT) is applied for the analysis of 2D ESR signals, although its efficiency is limited to stationary signals. In addition, it often fails to resolve overlapping peaks in 2D ESR. In this work, we propose a time-frequency analysis of 2D time-domain signals, which identifies all frequency peaks by decoupling a signal into its distinct constituent components via projection on the time-frequency plane. The method utilizes 2D undecimated discrete wavelet transform (2D UDWT) as an intermediate step in the analysis, followed by signal reconstruction and 2D FT. We have applied the method to a simulated 2D double quantum coherence (DQC) signal for validation and a set of experimental 2D ESR signals, demonstrating its efficiency in resolving overlapping peaks in the frequency domain, while displaying frequency evolution with time in case of non-stationary data.

Extraction of Weak Spectroscopic Signals with High Fidelity: Examples from ESR

Noise impedes experimental studies by reducing signal resolution and/or suppressing weak signals. Signal averaging and filtering are the primary methods used to reduce noise, but they have limited effectiveness and lack capabilities to recover signals at low signal-to-noise ratios (SNRs). We utilize a wavelet transform-based approach to effectively remove noise from spectroscopic data. The wavelet denoising method we use is a significant improvement on standard wavelet denoising approaches. We demonstrate its power in extracting signals from noisy spectra on a variety of signal types ranging from hyperfine lines to overlapped peaks to weak peaks overlaid on strong ones, drawn from electron-spin-resonance spectroscopy. The results show that one can accurately extract details of complex spectra, including retrieval of very weak ones. It accurately recovers signals at an SNR of ∼1 and improves the SNR by about 3 orders of magnitude with high fidelity. Our examples show that one is now able to address weaker SNR signals much better than by previous methods. This new wavelet approach can be successfully applied to other spectroscopic signals.

Single molecule FRET methodology for investigating glutamate receptors

Single molecule Förster Resonance Energy Transfer (smFRET) allows us to measure variation in distances between donor and acceptor fluorophores attached to a protein, providing the conformational landscape of the protein with respect to this specific distance. smFRET can be performed on freely diffusing molecules or on tethered molecules. Here, we describe the tethered method used to study ionotropic glutamate receptors, which allows us to track the changes in FRET as a function of time, thus providing information on the conformations sampled and kinetics of conformational changes in the millisecond to second time scale. Strategies for attaching fluorophores to the proteins, methods for acquiring and analyzing the smFRET trajectories, and limitations are discussed.

Mechanism of modulation of AMPA receptors by TARP-γ8

Using single-channel recordings and single-molecule FRET, Carrillo et al. show that resensitization of α-amino-5-methyl-3-hydroxy-4-isoxazole propionate receptors by the regulatory protein γ8 is characterized by transitions to high conductance levels associated with tighter conformational coupling similar to those seen in the presence of cyclothiazide.

Fast excitatory synaptic transmission in the mammalian central nervous system is mediated by glutamate-activated α-amino-5-methyl-3-hydroxy-4-isoxazole propionate (AMPA) receptors. In neurons, AMPA receptors coassemble with transmembrane AMPA receptor regulatory proteins (TARPs). Assembly with TARP γ8 alters the biophysical properties of the receptor, producing resensitization currents in the continued presence of glutamate. Using single-channel recordings, we show that under resensitizing conditions, GluA2 AMPA receptors primarily transition to higher conductance levels, similar to activation of the receptors in the presence of cyclothiazide, which stabilizes the open state. To study the conformation associated with these states, we have used single-molecule FRET and show that this high-conductance state exhibits tighter coupling between subunits in the extracellular parts of the receptor. Furthermore, the dwell times for the transition from the tightly coupled state to the decoupled states correlate to longer open durations of the channels, thus correlating conformation and function at the single-molecule level.

Dissection of Interaction Kinetics through Single-Molecule Interaction Simulation

The ability to extract kinetic interaction parameters from single-molecule fluorescence resonance energy transfer trajectories without the need for solving complex single-molecule differential equations has the potential to address some of the critical biophysical questions. Here, we provide a noise-free single-molecule interaction simulation (SMIS) tool to give the expected dwell-time distributions and relative populations of each FRET level based on the assigned kinetic model and to dissect kinetic interaction parameters from single-molecule FRET trajectories. The method provides the expected dwell-time distributions, average transition rates, and relative populations of each FRET level based on the assigned kinetic model. By comparing with ground truth data and experimental data, we demonstrated that SMIS is useful to quantify the interaction kinetic rate constants without using the traditional single-molecule analytical solution approach.

Mechanistic Understanding of the Phosphorylation-Induced Conformational Rigidity at the AMPA Receptor C-terminal Domain

Phosphorylation at the intracellular C-terminal domain (CTD) of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors induces conformational rigidity. Such intracellular alterations to the AMPA receptor influence its functional responses, which are involved in multiple synaptic processes and neuronal signaling. The structure of the CTD still remains unresolved, which poses challenges toward providing a mechanism for the process of phosphorylation and deciphering the role of each phosphorylation step in causing the resultant conformational behavior. Herein, we utilize smFRET spectroscopy to understand the mechanism of phosphorylation, with the help of strategic point mutations that mimic phosphorylation. Our results reveal that first, phosphorylation at three target sites (S818, S831, and T840) is necessary for the change in the secondary structure of the existing disordered native sequence. Also, the results suggest that the formation of the tertiary structure through electrostatic interaction involving one specific phosphorylation site (S831) stabilizes the structure and renders conformational rigidity.

Phosphorylation Induces Conformational Rigidity at the C-Terminal Domain of AMPA Receptors

The intracellular C-terminal domain (CTD) of AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) receptor undergoes phosphorylation at specific locations during long-term potentiation. This modification enhances conductance through the AMPA receptor ion channel and thus potentially plays a crucial role in modulating receptor trafficking and signaling. However, because the CTD structure is largely unresolved, it is difficult to establish if phosphorylation induces conformational changes that might play a role in enhancing channel conductance. Herein, we utilize single-molecule Förster resonance energy transfer (smFRET) spectroscopy to probe the conformational changes of a section of the AMPA receptor CTD, under the conditions of point-mutated phosphomimicry. Multiple analysis algorithms fail to identify stable conformational states within the smFRET distributions, consistent with a lack of well-defined secondary structure. Instead, our results show that phosphomimicry induces conformational rigidity to the CTD, and such rigidity is electrostatically tunable.

Reliable State Identification and State Transition Detection in Fluorescence Intensity-Based Single-Molecule Förster Resonance Energy-Transfer Data

Single-molecule Förster resonance energy transfer (smFRET) is a powerful technique to probe biomolecular structure and dynamics. A popular implementation of smFRET consists of recording fluorescence intensity time traces of surface-immobilized, chromophore-tagged molecules. This approach generates large and complex data sets, the analysis of which is to date not standardized. Here, we address a key challenge in smFRET data analysis: the generation of thermodynamic and kinetic models that describe with statistical rigor the behavior of FRET trajectories recorded from surface-tethered biomolecules in terms of the number of FRET states, the corresponding mean FRET values, and the kinetic rates at which they interconvert. For this purpose, we first perform Monte Carlo simulations to generate smFRET trajectories, in which a relevant space of experimental parameters is explored. Then, we provide an account on current strategies to achieve such model selection, as well as a quantitative assessment of their performances. Specifically, we evaluate the performance of each algorithm (change-point analysis, STaSI, HaMMy, vbFRET, and ebFRET) with respect to accuracy, reproducibility, and computing time, which yields a range of algorithm-specific referential benchmarks for various data qualities. Data simulation and analysis were performed with our MATLAB-based multifunctional analysis software for handling smFRET data (MASH-FRET).

The structure-energy landscape of NMDA receptor gating

N-Methyl-D-aspartate (NMDA) receptors are the main calcium-permeable excitatory receptors in the mammalian central nervous system. The NMDA receptor gating is complex, exhibiting multiple closed, open, and desensitized states; however, central questions regarding the conformations and energetics of the transmembrane domains as they relate to the gating states are still unanswered. Here, using single-molecule Förster resonance energy transfer (smFRET), we map the energy landscape of the first transmembrane segment of the Rattus norvegicus NMDA receptor under resting and various liganded conditions. These results show kinetically and structurally distinct changes associated with apo, agonist-bound, and inhibited receptors linked by a linear mechanism of gating at this site. Furthermore, the smFRET data suggest that allosteric inhibition by zinc occurs by an uncoupling of the agonist-induced changes at the extracellular domains from the gating motions leading to an apo-like state, while dizocilpine, a pore blocker, stabilizes multiple closely packed transmembrane states.

Conformational transitions in the glycine-bound GluN1 NMDA receptor LBD via single-molecule FRET

The N-methyl-D-aspartate receptor (NMDAR) is a member of the glutamate receptor family of proteins and is responsible for excitatory transmission. Activation of the receptor is thought to be controlled by conformational changes in the ligand binding domain (LBD); however, glutamate receptor LBDs can occupy multiple conformations even in the activated form. This work probes equilibrium transitions among NMDAR LBD conformations by monitoring the distance across the glycine-bound LBD cleft using single-molecule Förster resonance energy transfer (smFRET). Recent improvements in photoprotection solutions allowed us to monitor transitions among the multiple conformations. Also, we applied a recently developed model-free algorithm called "step transition and state identification" to identify the number of states, their smFRET efficiencies, and their interstate kinetics. Reversible interstate conversions, corresponding to transitions among a wide range of cleft widths, were identified in the glycine-bound LBD, on much longer timescales compared to channel opening. These transitions were confirmed to be equilibrium in nature by shifting the distribution reversibly via denaturant. We found that the NMDAR LBD proceeds primarily from one adjacent smFRET state to the next under equilibrium conditions, consistent with a cleft-opening/closing mechanism. Overall, by analyzing the state-to-state transition dynamics and distributions, we achieve insight into specifics of long-lived LBD equilibrium structural dynamics, as well as obtain a more general description of equilibrium folding/unfolding in a conformationally dynamic protein. The relationship between such long-lived LBD dynamics and channel function in the full receptor remains an open and interesting question.

Error-based extraction of states and energy landscapes from experimental single-molecule time-series

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.

Structural dynamics of the glycine-binding domain of the N-methyl-D-aspartate receptor

N-Methyl-D-aspartate receptors mediate the slow component of excitatory neurotransmission in the central nervous system. These receptors are obligate heteromers containing glycine- and glutamate-binding subunits. The ligands bind to a bilobed agonist-binding domain of the receptor. Previous x-ray structures of the glycine-binding domain of NMDA receptors showed no significant changes between the partial and full agonist-bound structures. Here we have used single molecule fluorescence resonance energy transfer (smFRET) to investigate the cleft closure conformational states that the glycine-binding domain of the receptor adopts in the presence of the antagonist 5,7-dichlorokynurenic acid (DCKA), the partial agonists 1-amino-1-cyclobutanecarboxylic acid (ACBC) and L-alanine, and full agonists glycine and D-serine. For these studies, we have incorporated the unnatural amino acid p-acetyl-L-phenylalanine for specific labeling of the protein with hydrazide derivatives of fluorophores. The single molecule fluorescence resonance energy transfer data show that the agonist-binding domain can adopt a wide range of cleft closure states with significant overlap in the states occupied by ligands of varying efficacy. The difference lies in the fraction of the protein in a more closed-cleft form, with full agonists having a larger fraction in the closed-cleft form, suggesting that the ability of ligands to select for these states could dictate the extent of activation.

Fast Step Transition and State Identification (STaSI) for Discrete Single-Molecule Data Analysis

We introduce a step transition and state identification (STaSI) method for piecewise constant single-molecule data with a newly derived minimum description length equation as the objective function. We detect the step transitions using the Student's t test and group the segments into states by hierarchical clustering. The optimum number of states is determined based on the minimum description length equation. This method provides comprehensive, objective analysis of multiple traces requiring few user inputs about the underlying physical models and is faster and more precise in determining the number of states than established and cutting-edge methods for single-molecule data analysis. Perhaps most importantly, the method does not require either time-tagged photon counting or photon counting in general and thus can be applied to a broad range of experimental setups and analytes.

BOBA FRET: bootstrap-based analysis of single-molecule FRET data

Time-binned single-molecule Förster resonance energy transfer (smFRET) experiments with surface-tethered nucleic acids or proteins permit to follow folding and catalysis of single molecules in real-time. Due to the intrinsically low signal-to-noise ratio (SNR) in smFRET time traces, research over the past years has focused on the development of new methods to extract discrete states (conformations) from noisy data. However, limited observation time typically leads to pronounced cross-sample variability, i.e., single molecules display differences in the relative population of states and the corresponding conversion rates. Quantification of cross-sample variability is necessary to perform statistical testing in order to assess whether changes observed in response to an experimental parameter (metal ion concentration, the presence of a ligand, etc.) are significant. However, such hypothesis testing has been disregarded to date, precluding robust biological interpretation. Here, we address this problem by a bootstrap-based approach to estimate the experimental variability. Simulated time traces are presented to assess the robustness of the algorithm in conjunction with approaches commonly used in thermodynamic and kinetic analysis of time-binned smFRET data. Furthermore, a pair of functionally important sequences derived from the self-cleaving group II intron Sc.ai5γ (d3'EBS1*/IBS1*) is used as a model system. Through statistical hypothesis testing, divalent metal ions are shown to have a statistically significant effect on both thermodynamic and kinetic aspects of their interaction. The Matlab source code used for analysis (bootstrap-based analysis of smFRET data, BOBA FRET), as well as a graphical user interface, is available via http://www.aci.uzh.ch/rna/.

Diagnosing heterogeneous dynamics in single-molecule/particle trajectories with multiscale wavelets

We describe a simple automated method to extract and quantify transient heterogeneous dynamical changes from large data sets generated in single-molecule/particle tracking experiments. Based on wavelet transform, the method transforms raw data to locally match dynamics of interest. This is accomplished using statistically adaptive universal thresholding, whose advantage is to avoid a single arbitrary threshold that might conceal individual variability across populations. How to implement this multiscale method is described, focusing on local confined diffusion separated by transient transport periods or hopping events, with three specific examples: in cell biology, biotechnology, and glassy colloid dynamics. The discussion is generalized within the framework of continuous time random walk. This computationally efficient method can run routinely on hundreds of millions of data points analyzed within an hour on a desktop personal computer.

Numerical construction of estimators for single-molecule fluorescence measurements

A novel scheme to estimate the values of the underlying physical quantity and those of any functions of the quantity from measured observable(s) contaminated with stochastic noise is presented for any arbitrary probability distribution. The constructed estimators can either maximize the unbiasedness (i.e., minimize the amount of the deviation of the expectation value from the true value buried in the measurement) or minimize the risk (the average deviation from the true value) depending on the relative priority of unbiasedness and risk in the data analysis. The performance of the constructed estimators is demonstrated with computer simulations of Förster-type resonance energy transfer (FRET) measurements and also with FRET experimental data of the agonist-binding domain of the GluA2 subunit of AMPA receptors with agonists chloro- and iodo-willardiines and with adenylate kinase both in the apo form and with substrates AMP-PNP and AMP. It is shown that the estimators constructed by the present method can quantify faithfully not only the physical quantity to be monitored but also the functions of that quantity for a wide range of values.

Photobleaching lifetimes of cyanine fluorophores used for single-molecule Förster resonance energy transfer in the presence of various photoprotection systems

Lengthening smFRET lifetimes: We investigated various photoprotection system combinations to find the combination that optimally extended the photobleach lifetime of a Cy3/Cy5 smFRET pair attached to a DNA hairpin in a single-molecule environment. We found that the glucose/glucose oxygen-scavenging solution in combination with redox-based photostabilization solutions yielded the longest average photobleaching lifetimes.

Role of conformational dynamics in α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA) receptor partial agonism

We have investigated the range of cleft closure conformational states that the agonist-binding domains of the α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA) receptors occupy when bound to a series of willardiine derivatives using single-molecule FRET. These studies show that the agonist-binding domain exhibits varying degrees of dynamics when bound to the different willardiines with differing efficacies. The chlorowillardiine- and nitrowillardiine-bound form of the agonist-binding domain probes a narrower range of cleft closure states relative to the iodowillardiine bound form of the protein, with the antagonist (αS)-α-amino-3-[(4-carboxyphenyl)methyl]-3,4-dihydro-2,4-dioxo-1(2H)-pyrimidinepropanoic acid (UBP-282)-bound form exhibiting the widest range of cleft closure states. Additionally, the average cleft closure follows the order UBP-282 > iodowillardiine > chlorowillardiine > nitrowillardiine-bound forms of agonist-binding domain. These single-molecule FRET data, along with our previously reported data for the glutamate-bound forms of wild type and T686S mutant proteins, show that the mean currents under nondesensitizing conditions can be directly correlated to the fraction of the agonist-binding domains in the "closed" cleft conformation. These results indicate that channel opening in the AMPA receptors is controlled by both the ability of the agonist to induce cleft closure and the dynamics of the agonist-binding domain when bound to the agonist.

Advances in quantitative FRET-based methods for studying nucleic acids

Förster resonance energy transfer (FRET) is a powerful tool for monitoring molecular distances and interactions at the nanoscale level. The strong dependence of transfer efficiency on probe separation makes FRET perfectly suited for "on/off" experiments. To use FRET to obtain quantitative distances and three-dimensional structures, however, is more challenging. This review summarises recent studies and technological advances that have improved FRET as a quantitative molecular ruler in nucleic acid systems, both at the ensemble and at the single-molecule levels.

Structural landscape of isolated agonist-binding domains from single AMPA receptors

α-amino-3-hydroxy-5-methyl-4-isoxazole propionate (AMPA) receptors mediate fast excitatory neurotransmission by converting chemical signals into electrical signals. Thus, it is important to understand the relationship between their chemical biology and their function. Single molecule fluorescence resonance energy transfer (smFRET) was used to examine the conformations explored by the agonist binding domain of the AMPA receptor for wild type and T686 mutant proteins. Each form of the agonist binding domain exhibited a dynamic, multi-state sequential equilibrium, which could only be identified using wavelet shrinkage, a signal processing technique that removes experimental shot-noise. These results illustrate that the extent of activation is dependent not on a rigid closed cleft, but instead on the probability that a given subunit will occupy a closed cleft conformation, which in turn is not only determined by the lowest energy state but by the range of states that the protein explores.