Fast three-color single-molecule FRET using statistical inference

Unravelling molecular dynamics in living cells: Fluorescent protein biosensors for cell biology

Genetically encoded, fluorescent protein (FP)-based Förster resonance energy transfer (FRET) biosensors are microscopy imaging tools tailored for the precise monitoring and detection of molecular dynamics within subcellular microenvironments. They are characterised by their ability to provide an outstanding combination of spatial and temporal resolutions in live-cell microscopy. In this review, we begin by tracing back on the historical development of genetically encoded FP labelling for detection in live cells, which lead us to the development of early biosensors and finally to the engineering of single-chain FRET-based biosensors that have become the state-of-the-art today. Ultimately, this review delves into the fundamental principles of FRET and the design strategies underpinning FRET-based biosensors, discusses their diverse applications and addresses the distinct challenges associated with their implementation. We place particular emphasis on single-chain FRET biosensors for the Rho family of guanosine triphosphate hydrolases (GTPases), pointing to their historical role in driving our understanding of the molecular dynamics of this important class of signalling proteins and revealing the intricate relationships and regulatory mechanisms that comprise Rho GTPase biology in living cells.

Maximum Likelihood Analysis of Diffusing Molecules with Conformational Dynamics in Single-Molecule FRET

In single-molecule Förster resonance energy transfer (FRET) experiments, characterizing conformational dynamics from photon bursts emitted by diffusing molecules can be challenging due to the interplay of molecular transitions, translational diffusion, and background noise. This paper extends the maximum likelihood analysis of photon bursts (burstML) to incorporate both conformational dynamics and diffusion through the laser spot, offering a comprehensive analysis of photon bursts from single diffusing molecules. The new approach integrates two previously developed methods: one accounting for diffusion without conformational dynamics and the other addressing conformational dynamics without diffusion. By combining these approaches, the extended burstML method allows determination of brightness, diffusion time, FRET efficiency in each state, and transition rates, even under challenging conditions, such as fast (comparable to photon count rates) and slow (one transition per several bursts) transition rates, high background noise, and unequal brightness or diffusivity of the states. The performance of burstML was demonstrated on simulated data of a two-state diffusing molecule and compared with the colorML method, which simplifies analysis by excluding translational diffusion. While colorML is computationally efficient and performs well under ideal conditions (low background noise and equal brightness and diffusivity of states), its accuracy diminishes when these conditions are not met. In contrast, burstML remains accurate across a broader range of experimental scenarios. Both burstML and colorML were applied to analyze folding of several proteins (Pin1 WW domain, FiP35 WW domain, FBP28 WW domain, villin, and a synthetic protein α3D) under various experimental conditions, highlighting where colorML differs from burstML and providing insights into the applicability of the methods in diverse experimental settings.

Tailorable biosensors for real-time monitoring of stress distribution in soft biomaterials and living tissues

Visualizing mechanical stress distribution in soft and live biomaterials is essential for understanding biological processes and improving material design. However, it remains challenging due to their complexity, dynamic nature, and sensitivity requirements, necessitating innovative techniques. Since polysaccharides are common in various biomaterials, a biosensor integrating a Förster resonance energy transfer (FRET)-based tension sensor module and carbohydrate-binding modules (FTSM-CBM) has been designed for real-time monitoring of the stress distribution of these biomaterials. By simple dripping or soaking, FTSM-CBM enables fast, reproducible and semiquantitative detection of both 2D and 3D stress distributions in polysaccharide-based hydrogels. Additionally, it provides valuable information such as microstructure hints and fracture site warnings. FTSM-CBM can also monitor the locomotion of maggots, which is not feasible with most existing techniques. Furthermore, by changing the CBM, FTSM-CBM can be expanded for various polysaccharide-based biomaterials. This study provides a powerful tool that may promote related research in life and materials science.

Characterizing heterogeneity in amyloid formation processes

Protein aggregation is a complex process, consisting of a large number of pathways connecting monomers and mature amyloid fibrils. Recent advances in structure determination techniques, such as solid-state NMR and cryoEM, have allowed the determination of atomic resolution structures of fibril polymorphs, but most of the intermediate stages of the process including oligomer formation remain unknown. Proper characterization of the heterogeneity of the process is critical not only for physical and chemical understanding of the aggregation process but also for elucidation of the disease mechanisms and identification of therapeutic targets. This article reviews recent developments in the characterization of heterogeneity in amyloid formation processes.

Identifying the minimal sets of distance restraints for FRET-assisted protein structural modeling

Proteins naturally occur in crowded cellular environments and interact with other proteins, nucleic acids, and organelles. Since most previous experimental protein structure determination techniques require that proteins occur in idealized, non-physiological environments, the effects of realistic cellular environments on protein structure are largely unexplored. Recently, Förster resonance energy transfer (FRET) has been shown to be an effective experimental method for investigating protein structure in vivo. Inter-residue distances measured in vivo can be incorporated as restraints in molecular dynamics (MD) simulations to model protein structural dynamics in vivo. Since most FRET studies only obtain inter-residue separations for a small number of amino acid pairs, it is important to determine the minimum number of restraints in the MD simulations that are required to achieve a given root-mean-square deviation (RMSD) from the experimental structural ensemble. Further, what is the optimal method for selecting these inter-residue restraints? Here, we implement several methods for selecting the most important FRET pairs and determine the number of pairsN r $$ {N}_r $$ that are needed to induce conformational changes in proteins between two experimentally determined structures. We find that enforcing only a small fraction of restraints,N r / N ≲ 0.08 $$ {N}_r/N\lesssim 0.08 $$ , whereN $$ N $$ is the number of amino acids, can induce the conformational changes. These results establish the efficacy of FRET-assisted MD simulations for atomic scale structural modeling of proteins in vivo.

Single-Molecule Characterization of Heterogeneous Oligomer Formation during Co-Aggregation of 40- and 42-Residue Amyloid-β

The two most abundant isoforms of amyloid-β (Aβ) are the 40- (Aβ40) and 42-residue (Aβ42) peptides. Since they coexist and there is a correlation between toxicity and the ratio of the two isoforms, quantitative characterization of their interactions is crucial for understanding the Aβ aggregation mechanism. In this work, we follow the aggregation of individual isoforms in a mixture using single-molecule FRET spectroscopy by labeling Aβ42 and Aβ40 with the donor and acceptor fluorophores, respectively. We found that there are two phases of aggregation. The first phase consists of coaggregation of Aβ42 with a small amount of Aβ40, while the second phase results mostly from aggregation of Aβ40. We also found that the aggregation of Aβ42 is slowed by Aβ40 while the aggregation of Aβ40 is accelerated by Aβ42 in a concentration-dependent manner. The formation of oligomers was monitored by incubating mixtures in a plate reader and performing a single-molecule free-diffusion experiment at several different stages of aggregation. The detailed properties of the oligomers were obtained by maximum likelihood analysis of fluorescence bursts. The FRET efficiency distribution is much broader than that of the Aβ42 oligomers, indicating the diversity in isoform composition of the oligomers. Pulsed interleaved excitation experiments estimate that the fraction of Aβ40 in the co-oligomers in a 1:1 mixture of Aβ42 and Aβ40 varies between 0 and 20%. The detected oligomers were mostly co-oligomers especially at the physiological ratio of Aβ42 and Aβ40 (1:10), suggesting the critical role of Aβ40 in oligomer formation and aggregation.

Efficient, nonparametric removal of noise and recovery of probability distributions from time series using nonlinear-correlation functions: Photon and photon-counting noise

A preceding paper [M. Dhar, J. A. Dickinson, and M. A. Berg, J. Chem. Phys. 159, 054110 (2023)] shows how to remove additive noise from an experimental time series, allowing both the equilibrium distribution of the system and its Green's function to be recovered. The approach is based on nonlinear-correlation functions and is fully nonparametric: no initial model of the system or of the noise is needed. However, single-molecule spectroscopy often produces time series with either photon or photon-counting noise. Unlike additive noise, photon noise is signal-size correlated and quantized. Photon counting adds the potential for bias. This paper extends noise-corrected-correlation methods to these cases and tests them on synthetic datasets. Neither signal-size correlation nor quantization is a significant complication. Analysis of the sampling error yields guidelines for the data quality needed to recover the properties of a system with a given complexity. We show that bias in photon-counting data can be corrected, even at the high count rates needed to optimize the time resolution. Using all these results, we discuss the factors that limit the time resolution of single-molecule spectroscopy and the conditions that would be needed to push measurements into the submicrosecond region.

Direct observation of tRNA-chaperoned folding of a dynamic mRNA ensemble

T-box riboswitches are multi-domain noncoding RNAs that surveil individual amino acid availabilities in most Gram-positive bacteria. T-boxes directly bind specific tRNAs, query their aminoacylation status to detect starvation, and feedback control the transcription or translation of downstream amino-acid metabolic genes. Most T-boxes rapidly recruit their cognate tRNA ligands through an intricate three-way stem I-stem II-tRNA interaction, whose establishment is not understood. Using single-molecule FRET, SAXS, and time-resolved fluorescence, we find that the free T-box RNA assumes a broad distribution of open, semi-open, and closed conformations that only slowly interconvert. tRNA directly binds all three conformers with distinct kinetics, triggers nearly instantaneous collapses of the open conformations, and returns the T-box RNA to their pre-binding conformations upon dissociation. This scissors-like dynamic behavior is enabled by a hinge-like pseudoknot domain which poises the T-box for rapid tRNA-induced domain closure. This study reveals tRNA-chaperoned folding of flexible, multi-domain mRNAs through a Venus flytrap-like mechanism.

Single-molecule FRET and molecular diffusion analysis characterize stable oligomers of amyloid-β 42 of extremely low population

Soluble oligomers produced during protein aggregation have been thought to be toxic species causing various diseases. Characterization of these oligomers is difficult because oligomers are a heterogeneous mixture, which is not readily separable, and may appear transiently during aggregation. Single-molecule spectroscopy can provide valuable information by detecting individual oligomers, but there have been various problems in determining the size and concentration of oligomers. In this work, we develop and use a method that analyzes single-molecule fluorescence burst data of freely diffusing molecules in solution based on molecular diffusion theory and maximum likelihood method. We demonstrate that the photon count rate, diffusion time, population, and Förster resonance energy transfer (FRET) efficiency can be accurately determined from simulated data and the experimental data of a known oligomerization system, the tetramerization domain of p53. We used this method to characterize the oligomers of the 42-residue amyloid-β (Aβ42) peptide. Combining peptide incubation in a plate reader and single-molecule free-diffusion experiments allows for the detection of stable oligomers appearing at various stages of aggregation. We find that the average size of these oligomers is 70-mer and their overall population is very low, less than 1 nM, in the early and middle stages of aggregation of 1 µM Aβ42 peptide. Based on their average size and long diffusion time, we predict the oligomers have a highly elongated rod-like shape.

Analysis of photon trajectories from diffusing single molecules

In single-molecule free diffusion experiments, molecules spend most of the time outside a laser spot and generate bursts of photons when they diffuse through the focal spot. Only these bursts contain meaningful information and, therefore, are selected using physically reasonable criteria. The analysis of the bursts must take into account the precise way they were chosen. We present new methods that allow one to accurately determine the brightness and diffusivity of individual molecule species from the photon arrival times of selected bursts. We derive analytical expressions for the distribution of inter-photon times (with and without burst selection), the distribution of the number of photons in a burst, and the distribution of photons in a burst with recorded arrival times. The theory accurately treats the bias introduced due to the burst selection criteria. We use a Maximum Likelihood (ML) method to find the molecule's photon count rate and diffusion coefficient from three kinds of data, i.e., the bursts of photons with recorded arrival times (burstML), inter-photon times in bursts (iptML), and the numbers of photon counts in a burst (pcML). The performance of these new methods is tested on simulated photon trajectories and on an experimental system, the fluorophore Atto 488.

Single-photon smFRET. I: Theory and conceptual basis

We present a unified conceptual framework and the associated software package for single-molecule Förster resonance energy transfer (smFRET) analysis from single-photon arrivals leveraging Bayesian nonparametrics, BNP-FRET. This unified framework addresses the following key physical complexities of a single-photon smFRET experiment, including: 1) fluorophore photophysics; 2) continuous time kinetics of the labeled system with large timescale separations between photophysical phenomena such as excited photophysical state lifetimes and events such as transition between system states; 3) unavoidable detector artefacts; 4) background emissions; 5) unknown number of system states; and 6) both continuous and pulsed illumination. These physical features necessarily demand a novel framework that extends beyond existing tools. In particular, the theory naturally brings us to a hidden Markov model with a second-order structure and Bayesian nonparametrics on account of items 1, 2, and 5 on the list. In the second and third companion articles, we discuss the direct effects of these key complexities on the inference of parameters for continuous and pulsed illumination, respectively.

Single-photon smFRET: II. Application to continuous illumination

Here we adapt the Bayesian nonparametrics (BNP) framework presented in the first companion article to analyze kinetics from single-photon, single-molecule Förster resonance energy transfer (smFRET) traces generated under continuous illumination. Using our sampler, BNP-FRET, we learn the escape rates and the number of system states given a photon trace. We benchmark our method by analyzing a range of synthetic and experimental data. Particularly, we apply our method to simultaneously learn the number of system states and the corresponding kinetics for intrinsically disordered proteins using two-color FRET under varying chemical conditions. Moreover, using synthetic data, we show that our method can deduce the number of system states even when kinetics occur at timescales of interphoton intervals.

Host-Guest Doping in Flexible Organic Crystals for Room-Temperature Phosphorescence

Organic single crystals (OSCs) with excellent flexibility and unique optical properties are of great importance due to their broad applicability in optical/optoelectronic devices and sensors. Nevertheless, fabricating flexible OSCs with room-temperature phosphorescence (RTP) remains a great challenge. Herein, we propose a host-guest doping strategy to achieve both RTP and flexibility of OSCs. The single-stranded crystal is highly bendable upon external force application and can immediately return to its original straight shape after removal of the stress, impressively emitting bright deep-red phosphorescence. The theoretical and experimental results demonstrate that the bright RTP arises from Förster resonance energy transfer (FRET) from the triphenylene molecules to the dopants. This strategy is both conceptually and synthetically simple and offers a universal approach for the preparation of flexible OSCs with RTP.

Learning continuous potentials from smFRET

Potential energy landscapes are useful models in describing events such as protein folding and binding. While single-molecule fluorescence resonance energy transfer (smFRET) experiments encode information on continuous potentials for the system probed, including rarely visited barriers between putative potential minima, this information is rarely decoded from the data. This is because existing analysis methods often model smFRET output assuming, from the onset, that the system probed evolves in a discretized state space to be analyzed within a hidden Markov model (HMM) paradigm. By contrast, here, we infer continuous potentials from smFRET data without discretely approximating the state space. We do so by operating within a Bayesian nonparametric paradigm by placing priors on the family of all possible potential curves. As our inference accounts for a number of required experimental features raising computational cost (such as incorporating discrete photon shot noise), the framework leverages a structured-kernel-interpolation Gaussian process prior to help curtail computational cost. We show that our structured-kernel-interpolation priors for potential energy reconstruction from smFRET analysis accurately infers the potential energy landscape from a smFRET binding experiment. We then illustrate advantages of structured-kernel-interpolation priors for potential energy reconstruction from smFRET over standard HMM approaches by providing information, such as barrier heights and friction coefficients, that is otherwise inaccessible to HMMs.

Single-photon smFRET. III. Application to pulsed illumination

Förster resonance energy transfer (FRET) using pulsed illumination has been pivotal in leveraging lifetime information in FRET analysis. However, there remain major challenges in quantitative single-photon, single-molecule FRET (smFRET) data analysis under pulsed illumination including 1) simultaneously deducing kinetics and number of system states; 2) providing uncertainties over estimates, particularly uncertainty over the number of system states; and 3) taking into account detector noise sources such as cross talk and the instrument response function contributing to uncertainty; in addition to 4) other experimental noise sources such as background. Here, we implement the Bayesian nonparametric framework described in the first companion article that addresses all aforementioned issues in smFRET data analysis specialized for the case of pulsed illumination. Furthermore, we apply our method to both synthetic as well as experimental data acquired using Holliday junctions.

Unsupervised selection of optimal single-molecule time series idealization criterion

Single-molecule (SM) approaches have provided valuable mechanistic information on many biophysical systems. As technological advances lead to ever-larger data sets, tools for rapid analysis and identification of molecules exhibiting the behavior of interest are increasingly important. In many cases the underlying mechanism is unknown, making unsupervised techniques desirable. The divisive segmentation and clustering (DISC) algorithm is one such unsupervised method that idealizes noisy SM time series much faster than computationally intensive approaches without sacrificing accuracy. However, DISC relies on a user-selected objective criterion (OC) to guide its estimation of the ideal time series. Here, we explore how different OCs affect DISC’s performance for data typical of SM fluorescence imaging experiments. We find that OCs differing in their penalty for model complexity each optimize DISC’s performance for time series with different properties such as signal/noise and number of sample points. Using a machine learning approach, we generate a decision boundary that allows unsupervised selection of OCs based on the input time series to maximize performance for different types of data. This is particularly relevant for SM fluorescence data sets, which often have signal/noise near the derived decision boundary and include time series of nonuniform length because of stochastic bleaching. Our approach, AutoDISC, allows unsupervised per-molecule optimization of DISC, which will substantially assist in the rapid analysis of high-throughput SM data sets with noisy samples and nonuniform time windows.

Illuminating amyloid fibrils: Fluorescence-based single-molecule approaches

The aggregation of proteins into insoluble filamentous amyloid fibrils is a pathological hallmark of neurodegenerative diseases that include Parkinson's disease and Alzheimer's disease. Since the identification of amyloid fibrils and their association with disease, there has been much work to describe the process by which fibrils form and interact with other proteins. However, due to the dynamic nature of fibril formation and the transient and heterogeneous nature of the intermediates produced, it can be challenging to examine these processes using techniques that rely on traditional ensemble-based measurements. Single-molecule approaches overcome these limitations as rare and short-lived species within a population can be individually studied. Fluorescence-based single-molecule methods have proven to be particularly useful for the study of amyloid fibril formation. In this review, we discuss the use of different experimental single-molecule fluorescence microscopy approaches to study amyloid fibrils and their interaction with other proteins, in particular molecular chaperones. We highlight the mechanistic insights these single-molecule techniques have already provided in our understanding of how fibrils form, and comment on their potential future use in studying amyloid fibrils and their intermediates.

Recent advances in FRET-Based biosensors for biomedical applications

Fluorescence resonance energy transfer (FRET)-based biosensors are effective analytical tools extensively used in fields of biomedicine, pharmacology, toxicology, and food sciences. Ratiometric imaging of substantial cellular processes, molecular components, and biological interactions is widely performed by these biosensors. A variety of FRET-based biosensors have provided comprehensive insights into underlying mechanisms of pathological conditions in live cells, tissues, and organisms. Moreover, integration of FRET-based biosensors with the current bioanalytical techniques allows for accurate, rapid, and sensitive diagnosis and proposes the advanced strategies for treatment. Precise analysis of ligand-receptor interactions by FRET-based biosensors has presented a basis for determination of novel therapeutic agents. Therefore, this study was designed to review the recent developments in FRET-based biosensors and their biomedical applications. In addition, characteristics, challenges, and outlooks of these biosensors were discussed.

Combining Rapid Microfluidic Mixing and Three-Color Single-Molecule FRET for Probing the Kinetics of Protein Conformational Changes

Single-molecule Förster resonance energy transfer (FRET) is well suited for studying the kinetics of protein conformational changes, owing to its high sensitivity and ability to resolve individual subpopulations in heterogeneous systems. However, the most common approach employing two fluorophores can only monitor one distance at a time, and the use of three fluorophores for simultaneously monitoring multiple distances has largely been limited to equilibrium fluctuations. Here we show that three-color single-molecule FRET can be combined with rapid microfluidic mixing to investigate conformational changes in a protein from milliseconds to minutes. In combination with manual mixing, we extended the kinetics to 1 h, corresponding to a total range of 5 orders of magnitude in time. We studied the monomer-to-protomer conversion of the pore-forming toxin cytolysin A (ClyA), one of the largest protein conformational transitions known. Site-specific labeling of ClyA with three fluorophores enabled us to follow the kinetics of three intramolecular distances at the same time and revealed a previously undetected intermediate. The combination of three-color single-molecule FRET with rapid microfluidic mixing thus provides an approach for probing the mechanisms of complex biomolecular processes with high time resolution.

Extraction of rapid kinetics from smFRET measurements using integrative detectors

Hidden Markov models (HMMs) are used to learn single-molecule kinetics across a range of experimental techniques. By their construction, HMMs assume that single-molecule events occur on slower timescales than those of data acquisition. To move beyond that HMM limitation and allow for single-molecule events to occur on any timescale, we must treat single-molecule events in continuous time as they occur in nature. We propose a method to learn kinetic rates from single-molecule Förster resonance energy transfer (smFRET) data collected by integrative detectors, even if those rates exceed data acquisition rates. To achieve that, we exploit our recently proposed "hidden Markov jump process" (HMJP), with which we learn transition kinetics from parallel measurements in donor and acceptor channels. HMJPs generalize the HMM paradigm in two critical ways: (1) they deal with physical smFRET systems as they switch between conformational states in continuous time, and (2) they estimate transition rates between conformational states directly without having recourse to transition probabilities or assuming slow dynamics. Our continuous-time treatment learns the transition kinetics and photon emission rates for dynamic regimes that are inaccessible to HMMs, which treat system kinetics in discrete time. We validate our framework's robustness on simulated data and demonstrate its performance on experimental data from FRET-labeled Holliday junctions.

A Combined Acceptor Photobleaching and Donor Fluorescence Lifetime Imaging Microscopy Approach to Analyze Multi-Protein Interactions in Living Cells

Protein-protein interaction studies often provide new insights, i.e., into the formation of protein complexes relevant for structural oligomerization, regulation of enzymatic activity or information transfer within signal transduction pathways. Mostly, biochemical approaches have been used to study such interactions, but their results are limited to observations from lysed cells. A powerful tool for the non-invasive investigation of protein-protein interactions in the context of living cells is the microscopic analysis of Förster Resonance Energy Transfer (FRET) among fluorescent proteins. Normally, FRET is used to monitor the interaction state of two proteins, but in addition, FRET studies have been used to investigate three or more interacting proteins at the same time. Here we describe a fluorescence microscopy-based method which applies a novel 2-step acceptor photobleaching protocol to discriminate between non-interacting, dimeric interacting and trimeric interacting states within a three-fluorophore setup. For this purpose, intensity- and fluorescence lifetime-related FRET effects were analyzed on representative fluorescent dimeric and trimeric FRET-constructs expressed in the cytosol of HEK293 cells. In particular, by combining FLIM- and intensity-based FRET data acquisition and interpretation, our method allows to distinguish trimeric from different types of dimeric (single-, double- or triple-dimeric) protein-protein interactions of three potential interaction partners in the physiological setting of living cells.

FRET-based dynamic structural biology: Challenges, perspectives and an appeal for open-science practices

Single-molecule FRET (smFRET) has become a mainstream technique for studying biomolecular structural dynamics. The rapid and wide adoption of smFRET experiments by an ever-increasing number of groups has generated significant progress in sample preparation, measurement procedures, data analysis, algorithms and documentation. Several labs that employ smFRET approaches have joined forces to inform the smFRET community about streamlining how to perform experiments and analyze results for obtaining quantitative information on biomolecular structure and dynamics. The recent efforts include blind tests to assess the accuracy and the precision of smFRET experiments among different labs using various procedures. These multi-lab studies have led to the development of smFRET procedures and documentation, which are important when submitting entries into the archiving system for integrative structure models, PDB-Dev. This position paper describes the current 'state of the art' from different perspectives, points to unresolved methodological issues for quantitative structural studies, provides a set of 'soft recommendations' about which an emerging consensus exists, and lists openly available resources for newcomers and seasoned practitioners. To make further progress, we strongly encourage 'open science' practices.

Modulation of a protein-folding landscape revealed by AFM-based force spectroscopy notwithstanding instrumental limitations

Single-molecule force spectroscopy is a powerful tool for studying protein folding. Over the last decade, a key question has emerged: how are changes in intrinsic biomolecular dynamics altered by attachment to μm-scale force probes via flexible linkers? Here, we studied the folding/unfolding of α₃D using atomic force microscopy (AFM)-based force spectroscopy. α₃D offers an unusual opportunity as a prior single-molecule fluorescence resonance energy transfer (smFRET) study showed α₃D's configurational diffusion constant within the context of Kramers theory varies with pH. The resulting pH dependence provides a test for AFM-based force spectroscopy's ability to track intrinsic changes in protein folding dynamics. Experimentally, however, α₃D is challenging. It unfolds at low force (<15 pN) and exhibits fast-folding kinetics. We therefore used focused ion beam-modified cantilevers that combine exceptional force precision, stability, and temporal resolution to detect state occupancies as brief as 1 ms. Notably, equilibrium and nonequilibrium force spectroscopy data recapitulated the pH dependence measured using smFRET, despite differences in destabilization mechanism. We reconstructed a one-dimensional free-energy landscape from dynamic data via an inverse Weierstrass transform. At both neutral and low pH, the resulting constant-force landscapes showed minimal differences (∼0.2 to 0.5 k _B T) in transition state height. These landscapes were essentially equal to the predicted entropic barrier and symmetric. In contrast, force-dependent rates showed that the distance to the unfolding transition state increased as pH decreased and thereby contributed to the accelerated kinetics at low pH. More broadly, this precise characterization of a fast-folding, mechanically labile protein enables future AFM-based studies of subtle transitions in mechanoresponsive proteins.

DeepFRET, a software for rapid and automated single-molecule FRET data classification using deep learning

Single-molecule Förster Resonance energy transfer (smFRET) is an adaptable method for studying the structure and dynamics of biomolecules. The development of high throughput methodologies and the growth of commercial instrumentation have outpaced the development of rapid, standardized, and automated methodologies to objectively analyze the wealth of produced data. Here we present DeepFRET, an automated, open-source standalone solution based on deep learning, where the only crucial human intervention in transiting from raw microscope images to histograms of biomolecule behavior, is a user-adjustable quality threshold. Integrating standard features of smFRET analysis, DeepFRET consequently outputs the common kinetic information metrics. Its classification accuracy on ground truth data reached >95% outperforming human operators and commonly used threshold, only requiring ~1% of the time. Its precise and rapid operation on real data demonstrates DeepFRET's capacity to objectively quantify biomolecular dynamics and the potential to contribute to benchmarking smFRET for dynamic structural biology.