Structural heterogeneity and quantitative FRET efficiency distributions of polyprolines through a hybrid atomistic simulation and Monte Carlo approach

Accounting for Fast vs Slow Exchange in Single Molecule FRET Experiments Reveals Hidden Conformational States

Proteins are dynamic systems whose structural preferences determine their function. Unfortunately, building atomically detailed models of protein structural ensembles remains challenging, limiting our understanding of the relationships between sequence, structure, and function. Combining single molecule Förster resonance energy transfer (smFRET) experiments with molecular dynamics simulations could provide experimentally grounded, all-atom models of a protein's structural ensemble. However, agreement between the two techniques is often insufficient to achieve this goal. Here, we explore whether accounting for important experimental details like averaging across structures sampled during a given smFRET measurement is responsible for this apparent discrepancy. We present an approach to account for this time-averaging by leveraging the kinetic information available from Markov state models of a protein's dynamics. This allows us to accurately assess which time scales are averaged during an experiment. We find this approach significantly improves agreement between simulations and experiments in proteins with varying degrees of dynamics, including the well-ordered protein T4 lysozyme, the partially disordered protein apolipoprotein E (ApoE), and a disordered amyloid protein (Aβ40). We find evidence for hidden states that are not apparent in smFRET experiments because of time averaging with other structures, akin to states in fast exchange in nuclear magnetic resonance, and evaluate different force fields. Finally, we show how remaining discrepancies between computations and experiments can be used to guide additional simulations and build structural models for states that were previously unaccounted for. We expect our approach will enable combining simulations and experiments to understand the link between sequence, structure, and function in many settings. Understanding protein dynamics is crucial for understanding protein function, yet few methodologies report on protein motion at an atomic level. Combining single molecule Förster resonance energy transfer (smFRET) experiments with computer simulations could provide atomistic models of protein ensembles which are grounded in experiments, however, there has been limited agreement between the two methods to date. Here, we present an algorithm to recapitulate smFRET experiments from molecular dynamics simulations. This approach significantly improves agreement between simulations and experiments for proteins across the ordered spectrum. Moreover, with this approach we can confidently create atomic models for states observed during smFRET experiments which were otherwise difficult to model due to high amounts of flexibility, disorder, or large deviations from crystal-like states.

FRET-guided modeling of nucleic acids

The functional diversity of RNAs is encoded in their innate conformational heterogeneity. The combination of single-molecule spectroscopy and computational modeling offers new attractive opportunities to map structural transitions within nucleic acid ensembles. Here, we describe a framework to harmonize single-molecule Förster resonance energy transfer (FRET) measurements with molecular dynamics simulations and de novo structure prediction. Using either all-atom or implicit fluorophore modeling, we recreate FRET experiments in silico, visualize the underlying structural dynamics and quantify the reaction coordinates. Using multiple accessible-contact volumes as a post hoc scoring method for fragment assembly in Rosetta, we demonstrate that FRET can be used to filter a de novo RNA structure prediction ensemble by refuting models that are not compatible with in vitro FRET measurement. We benchmark our FRET-assisted modeling approach on double-labeled DNA strands and validate it against an intrinsically dynamic manganese(II)-binding riboswitch. We show that a FRET coordinate describing the assembly of a four-way junction allows our pipeline to recapitulate the global fold of the riboswitch displayed by the crystal structure. We conclude that computational fluorescence spectroscopy facilitates the interpretability of dynamic structural ensembles and improves the mechanistic understanding of nucleic acid interactions.

Accounting for fast vs slow exchange in single molecule FRET experiments reveals hidden conformational states

Proteins are dynamic systems whose structural preferences determine their function. Unfortunately, building atomically detailed models of protein structural ensembles remains challenging, limiting our understanding of the relationships between sequence, structure, and function. Combining single molecule Förster resonance energy transfer (smFRET) experiments with molecular dynamics simulations could provide experimentally grounded, all-atom models of a protein's structural ensemble. However, agreement between the two techniques is often insufficient to achieve this goal. Here, we explore whether accounting for important experimental details like averaging across structures sampled during a given smFRET measurement is responsible for this apparent discrepancy. We present an approach to account for this time-averaging by leveraging the kinetic information available from Markov state models of a protein's dynamics. This allows us to accurately assess which timescales are averaged during an experiment. We find this approach significantly improves agreement between simulations and experiments in proteins with varying degrees of dynamics, including the well-ordered protein T4 lysozyme, the partially disordered protein apolipoprotein E (ApoE), and a disordered amyloid protein (Aβ40). We find evidence for hidden states that are not apparent in smFRET experiments because of time averaging with other structures, akin to states in fast exchange in NMR, and evaluate different force fields. Finally, we show how remaining discrepancies between computations and experiments can be used to guide additional simulations and build structural models for states that were previously unaccounted for. We expect our approach will enable combining simulations and experiments to understand the link between sequence, structure, and function in many settings.

FRETpredict: a Python package for FRET efficiency predictions using rotamer libraries

Förster resonance energy transfer (FRET) is a widely-used and versatile technique for the structural characterization of biomolecules. Here, we introduce FRETpredict, an easy-to-use Python software to predict FRET efficiencies from ensembles of protein conformations. FRETpredict uses a rotamer library approach to describe the FRET probes covalently bound to the protein. The software efficiently and flexibly operates on large conformational ensembles such as those generated by molecular dynamics simulations to facilitate the validation or refinement of molecular models and the interpretation of experimental data. We provide access to rotamer libraries for many commonly used dyes and linkers and describe a general methodology to generate new rotamer libraries for FRET probes. We demonstrate the performance and accuracy of the software for different types of systems: a rigid peptide (polyproline 11), an intrinsically disordered protein (ACTR), and three folded proteins (HiSiaP, SBD2, and MalE). FRETpredict is open source (GPLv3) and is available at github.com/KULL-Centre/FRETpredict and as a Python PyPI package at pypi.org/project/FRETpredict .

A new twist on PIFE: photoisomerisation-related fluorescence enhancement

PIFE was first used as an acronym for protein-induced fluorescence enhancement, which refers to the increase in fluorescence observed upon the interaction of a fluorophore, such as a cyanine, with a protein. This fluorescence enhancement is due to changes in the rate ofcis/transphotoisomerisation. It is clear now that this mechanism is generally applicable to interactions with any biomolecule. In this review, we propose that PIFE is thereby renamed according to its fundamental working principle as photoisomerisation-related fluorescence enhancement, keeping the PIFE acronym intact. We discuss the photochemistry of cyanine fluorophores, the mechanism of PIFE, its advantages and limitations, and recent approaches to turning PIFE into a quantitative assay. We provide an overview of its current applications to different biomolecules and discuss potential future uses, including the study of protein-protein interactions, protein-ligand interactions and conformational changes in biomolecules.

A new twist on PIFE: photoisomerisation-related fluorescence enhancement

PIFE was first used as an acronym for protein-induced fluorescence enhancement, which refers to the increase in fluorescence observed upon the interaction of a fluorophore, such as a cyanine, with a protein. This fluorescence enhancement is due to changes in the rate of cis/trans photoisomerisation. It is clear now that this mechanism is generally applicable to interactions with any biomolecule and, in this review, we propose that PIFE is thereby renamed according to its fundamental working principle as photoisomerisation-related fluorescence enhancement, keeping the PIFE acronym intact. We discuss the photochemistry of cyanine fluorophores, the mechanism of PIFE, its advantages and limitations, and recent approaches to turn PIFE into a quantitative assay. We provide an overview of its current applications to different biomolecules and discuss potential future uses, including the study of protein-protein interactions, protein-ligand interactions and conformational changes in biomolecules.

Reliability and accuracy of single-molecule FRET studies for characterization of structural dynamics and distances in proteins

Single-molecule Förster-resonance energy transfer (smFRET) experiments allow the study of biomolecular structure and dynamics in vitro and in vivo. We performed an international blind study involving 19 laboratories to assess the uncertainty of FRET experiments for proteins with respect to the measured FRET efficiency histograms, determination of distances, and the detection and quantification of structural dynamics. Using two protein systems with distinct conformational changes and dynamics, we obtained an uncertainty of the FRET efficiency ≤0.06, corresponding to an interdye distance precision of ≤2 Å and accuracy of ≤5 Å. We further discuss the limits for detecting fluctuations in this distance range and how to identify dye perturbations. Our work demonstrates the ability of smFRET experiments to simultaneously measure distances and avoid the averaging of conformational dynamics for realistic protein systems, highlighting its importance in the expanding toolbox of integrative structural biology.

Wild-Type α-Synuclein and Variants Occur in Different Disordered Dimers and Pre-Fibrillar Conformations in Early Stage of Aggregation

α-Synuclein is a 140 amino-acid intrinsically disordered protein mainly found in the brain. Toxic α-synuclein aggregates are the molecular hallmarks of Parkinson’s disease. In vitro studies showed that α-synuclein aggregates in oligomeric structures of several 10th of monomers and into cylindrical structures (fibrils), comprising hundred to thousands of proteins, with polymorphic cross-β-sheet conformations. Oligomeric species, formed at the early stage of aggregation remain, however, poorly understood and are hypothezised to be the most toxic aggregates. Here, we studied the formation of wild-type (WT) and mutant (A30P, A53T, and E46K) dimers of α-synuclein using coarse-grained molecular dynamics. We identified two principal segments of the sequence with a higher propensity to aggregate in the early stage of dimerization: residues 36–55 and residues 66–95. The transient α-helices (residues 53–65 and 73–82) of α-synuclein monomers are destabilized by A53T and E46K mutations, which favors the formation of fibril native contacts in the N-terminal region, whereas the helix 53–65 prevents the propagation of fibril native contacts along the sequence for the WT in the early stages of dimerization. The present results indicate that dimers do not adopt the Greek key motif of the monomer fold in fibrils but form a majority of disordered aggregates and a minority (9–15%) of pre-fibrillar dimers both with intra-molecular and intermolecular β-sheets. The percentage of residues in parallel β-sheets is by increasing order monomer < disordered dimers < pre-fibrillar dimers. Native fibril contacts between the two monomers are present in the NAC domain for WT, A30P, and A53T and in the N-domain for A53T and E46K. Structural properties of pre-fibrillar dimers agree with rupture-force atomic force microscopy and single-molecule Förster resonance energy transfer available data. This suggests that the pre-fibrillar dimers might correspond to the smallest type B toxic oligomers. The probability density of the dimer gyration radius is multi-peaks with an average radius that is 10 Å larger than the one of the monomers for all proteins. The present results indicate that even the elementary α-synuclein aggregation step, the dimerization, is a complicated phenomenon that does not only involve the NAC region.

Unraveling multi-state molecular dynamics in single-molecule FRET experiments. I. Theory of FRET-lines

Conformational dynamics of biomolecules are of fundamental importance for their function. Single-molecule studies of Förster Resonance Energy Transfer (smFRET) between a tethered donor and acceptor dye pair are a powerful tool to investigate the structure and dynamics of labeled molecules. However, capturing and quantifying conformational dynamics in intensity-based smFRET experiments remains challenging when the dynamics occur on the sub-millisecond timescale. The method of multiparameter fluorescence detection addresses this challenge by simultaneously registering fluorescence intensities and lifetimes of the donor and acceptor. Together, two FRET observables, the donor fluorescence lifetime τD and the intensity-based FRET efficiency E, inform on the width of the FRET efficiency distribution as a characteristic fingerprint for conformational dynamics. We present a general framework for analyzing dynamics that relates average fluorescence lifetimes and intensities in two-dimensional burst frequency histograms. We present parametric relations of these observables for interpreting the location of FRET populations in E-τD diagrams, called FRET-lines. To facilitate the analysis of complex exchange equilibria, FRET-lines serve as reference curves for a graphical interpretation of experimental data to (i) identify conformational states, (ii) resolve their dynamic connectivity, (iii) compare different kinetic models, and (iv) infer polymer properties of unfolded or intrinsically disordered proteins. For a simplified graphical analysis of complex kinetic networks, we derive a moment-based representation of the experimental data that decouples the motion of the fluorescence labels from the conformational dynamics of the biomolecule. Importantly, FRET-lines facilitate exploring complex dynamic models via easily computed experimental observables. We provide extensive computational tools to facilitate applying FRET-lines.

Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure

The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains with atomic detail from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve very good agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structure such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301L, P301S, and P301T mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically detailed view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Recent Efforts and Milestones for Simulating Nucleic Acid FRET Experiments through Computational Methods

Computational methods can greatly aid nucleic acid fluorescence experiments by either offering fully detailed atomic insights into the conformations and interactions present in the studied system or by providing accurate simulations of the fundamental parameters. Fluorescence-based optical biosensors show great potential for clinical diagnosis of life-altering diseases with a very high specificity. Many of the designs for such rely on the concept of Förster resonance energy transfer (FRET). Currently, the methods used experimentally make use of theoretical assumptions which fundamentally affect the results. Having a detailed atomistic overview or significant simulated parameters could improve the understanding of the calculations and provide much more accurate outcomes. However, there are many challenges that need to be addressed before standardized computational protocols can be employed. This review is meant to highlight the progress made for computational methods used to simulate FRET experiments for nucleic acid probes. Recent advances have been made in computational tools, such as force field parametrizations and improved protocols. Complementary simulations to experimental data are also comprised in the this review.

Theory and Analysis of Single-Molecule FRET Experiments

Inter-dye distances and conformational dynamics can be studied using single-molecule FRET measurements. We consider two approaches to analyze sequences of photons with recorded photon colors and arrival times. The first approach is based on FRET efficiency histograms obtained from binned photon sequences. The experimental histograms are compared with the theoretical histograms obtained using the joint distribution of acceptor and donor photons or the Gaussian approximation. In the second approach, a photon sequence is analyzed without binning. The parameters of a model describing conformational dynamics are found by maximizing the appropriate likelihood function. The first approach is simpler, while the second one is more accurate, especially when the population of species is small and transition rates are fast. The likelihood-based analysis as well as the recoloring method has the advantage that diffusion of molecules through the laser focus can be rigorously handled.

Resolving distance variations by single-molecule FRET and EPR spectroscopy using rotamer libraries

Förster resonance energy transfer (FRET) and electron paramagnetic resonance (EPR) spectroscopy are complementary techniques for quantifying distances in the nanometer range. Both approaches are commonly employed for probing the conformations and conformational changes of biological macromolecules based on site-directed fluorescent or paramagnetic labeling. FRET can be applied in solution at ambient temperature and thus provides direct access to dynamics, especially if used at the single-molecule level, whereas EPR requires immobilization or work at cryogenic temperatures but provides data that can be more reliably used to extract distance distributions. However, a combined analysis of the complementary data from the two techniques has been complicated by the lack of a common modeling framework. Here, we demonstrate a systematic analysis approach based on rotamer libraries for both FRET and EPR labels to predict distance distributions between two labels from a structural model. Dynamics of the fluorophores within these distance distributions are taken into account by diffusional averaging, which improves the agreement with experiment. Benchmarking this methodology with a series of surface-exposed pairs of sites in a structured protein domain reveals that the lowest resolved distance differences can be as small as ∼0.25 nm for both techniques, with quantitative agreement between experimental and simulated transfer efficiencies within a range of ±0.045. Rotamer library analysis thus establishes a coherent way of treating experimental data from EPR and FRET and provides a basis for integrative structural modeling, including studies of conformational distributions and dynamics of biological macromolecules using both techniques.

FRETraj: Integrating single-molecule spectroscopy with molecular dynamics

SUMMARY

Quantitative interpretation of single-molecule FRET experiments requires a model of the dye dynamics to link experimental energy transfer efficiencies to distances between atom positions. We have developed FRETraj, a Python module to predict FRET distributions based on accessible-contact volumes (ACV) and simulated photon statistics. FRETraj helps to identify optimal fluorophore positions on a biomolecule of interest by rapidly evaluating donor-acceptor distances. FRETraj is scalable and fully integrated into PyMOL and the Jupyter ecosystem. Here we describe the conformational dynamics of a DNA hairpin by computing multiple ACVs along a molecular dynamics trajectory and compare the predicted FRET distribution with single-molecule experiments. FRET-assisted modeling will accelerate the analysis of structural ensembles in particular dynamic, non-coding RNAs and transient protein-nucleic acid complexes.

AVAILABILITY

FRETraj is implemented as a cross-platform Python package available under the GPL-3.0 on Github (https://github.com/RNA-FRETools/fretraj) and is documented at https://RNA-FRETools.github.io/fretraj.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Recent advances in computational methods for biosensor design

Biosensors are analytical tools with a great application in healthcare, food quality control, and environmental monitoring. They are of considerable interest to be designed by using cost-effective and efficient approaches. Designing biosensors with improved functionality or application in new target detection has been converted to a fast-growing field of biomedicine and biotechnology branches. Experimental efforts have led to valuable successes in the field of biosensor design; however, some deficiencies restrict their utilization for this purpose. Computational design of biosensors is introduced as a promising key to eliminate the gap. A set of reliable structure prediction of the biosensor segments, their stability, and accurate descriptors of molecular interactions are required to computationally design biosensors. In this review, we provide a comprehensive insight into the progress of computational methods to guide the design and development of biosensors, including molecular dynamics simulation, quantum mechanics calculations, molecular docking, virtual screening, and a combination of them as the hybrid methodologies. By relying on the recent advances in the computational methods, an opportunity emerged for them to be complementary or an alternative to the experimental methods in the field of biosensor design.

Quantitative comparison between sub-millisecond time resolution single-molecule FRET measurements and 10-second molecular simulations of a biosensor protein

Molecular Dynamics (MD) simulations seek to provide atomic-level insights into conformationally dynamic biological systems at experimentally relevant time resolutions, such as those afforded by single-molecule fluorescence measurements. However, limitations in the time scales of MD simulations and the time resolution of single-molecule measurements have challenged efforts to obtain overlapping temporal regimes required for close quantitative comparisons. Achieving such overlap has the potential to provide novel theories, hypotheses, and interpretations that can inform idealized experimental designs that maximize the detection of the desired reaction coordinate. Here, we report MD simulations at time scales overlapping with in vitro single-molecule Förster (fluorescence) resonance energy transfer (smFRET) measurements of the amino acid binding protein LIV-BP^SS at sub-millisecond resolution. Computationally efficient all-atom structure-based simulations, calibrated against explicit solvent simulations, were employed for sampling multiple cycles of LIV-BP^SS clamshell-like conformational changes on the time scale of seconds, examining the relationship between these events and those observed by smFRET. The MD simulations agree with the smFRET measurements and provide valuable information on local dynamics of fluorophores at their sites of attachment on LIV-BP^SS and the correlations between fluorophore motions and large-scale conformational changes between LIV-BP^SS domains. We further utilize the MD simulations to inform the interpretation of smFRET data, including Förster radius (R₀) and fluorophore orientation factor (κ²) determinations. The approach we describe can be readily extended to distinct biochemical systems, allowing for the interpretation of any FRET system conjugated to protein or ribonucleoprotein complexes, including those with more conformational processes, as well as those implementing multi-color smFRET.

Förster (fluorescence) resonance energy transfer (FRET) has been used extensively by biophysicists as a molecular-scale ruler that yields fundamental structural and kinetic insights into transient processes including complex formation and conformational rearrangements required for biological function. FRET techniques require the identification of informative fluorophore labeling sites, spaced at defined distances to inform on a reaction coordinate of interest and consideration of noise sources that have the potential to obscure quantitative interpretations. Here, we describe an approach to leverage advancements in computationally efficient all-atom structure-based molecular dynamics simulations in which structural dynamics observed via FRET can be interpreted in full atomistic detail on commensurate time scales. We demonstrate the potential of this approach using a model FRET system, the amino acid binding protein LIV-BP^SS conjugated to self-healing organic fluorophores. LIV-BP^SS exhibits large scale, sub-millisecond clamshell-like conformational changes between open and closed conformations associated with ligand unbinding and binding, respectively. Our findings inform on the molecular basis of the dynamics observed by smFRET and on strategies to optimize fluorophore labeling sites, the manner of fluorophore attachment, and fluorophore composition.

Enhancement of Energy Transfer Efficiency with Structural Control of Multichromophore Light-Harvesting Assembly

Multichromophore systems (MCSs) are envisioned as building blocks of molecular optoelectronic devices. While it is important to understand the characteristics of energy transfer in MCSs, the effect of multiple donors on energy transfer has not been understood completely, mainly due to the lack of a platform to investigate such an effect systematically. Here, a systematic study on how the number of donors (n D) and interchromophore distances affect the efficiency of energy transfer (η FRET) is presented. Specifically, η FRET is calculated for a series of model MCSs using simulations, a series of multiporphyrin dendrimers with systematic variation of n D and interdonor distances is synthesized, and η FRETs of those dendrimers using transient absorption spectroscopy are measured. The simulations predict η FRET in the multiporphyrin dendrimers well. In particular, it is found that η FRET is enhanced by donor-to-donor energy transfer only when structural heterogeneity exists in an MCS, and the relationships between the η FRET enhancement and the structural parameters of the MCS are revealed.

Kappaphobia is the elephant in the fret room

FRET is both a phenomenon and a spectroscopic technique, capable of measuring one geometric quantity: kappa-squared divided by the sixth power of the donor-acceptor distance. Kappa-squared is often replaced by a constant even though such a replacement may lead to serious errors. Kappaphobia, the fear of kappa or the reluctance to deal with kappa-squared adequately, is a looming presence in the FRET community. Unfortunately, this reluctance, or fear, is often tolerated, and sometimes encouraged. A decrease in kappaphobia will lead to an increase in the impact and success of FRET.

How the dyes affect folding of small proteins in single-molecule FRET experiments: A simulation study

A key question in the application of the single-molecule Förster resonance energy transfer (smFRET) technique to study protein folding is how the dyes affect the protein behavior. Understanding of these effects is particularly important for small proteins, for which the dyes, along with their linkers, can be comparable in size (mass) with the protein. Using a coarse-grained model, we simulated folding of BBL protein and two of its FRET constructs. The obtained results suggest that even for small proteins, such as the 45-residue BBL, the appearance of the excluded volume in the protein conformation space due to the presence of dyes does not change the overall picture of folding. At the same time, some deviations from folding of the original protein are observed, in particular, the FRET constructs fold considerably slower than the original protein because the protein collapse in the initial state of folding is slowed down due to the protein loading with relatively massive dyes.

Monte Carlo Diffusion-Enhanced Photon Inference: Distance Distributions and Conformational Dynamics in Single-Molecule FRET

Single-molecule Förster resonance energy transfer (smFRET) is utilized to study the structure and dynamics of many biomolecules, such as proteins, DNA, and their various complexes. The structural assessment is based on the well-known Förster relationship between the measured efficiency of energy transfer between a donor (D) and an acceptor (A) dye and the distance between them. Classical smFRET analysis methods called photon distribution analysis (PDA) take into account photon shot-noise, D-A distance distribution, and, more recently, interconversion between states in order to extract accurate distance information. It is known that rapid D-A distance fluctuations on the order of the D lifetime (or shorter) can increase the measured mean FRET efficiency and thus decrease the estimated D-A distance. Nonetheless, this effect has been so far neglected in smFRET experiments, potentially leading to biases in estimated distances. Here we introduce a PDA approach dubbed Monte Carlo diffusion-enhanced photon inference (MC-DEPI). MC-DEPI recolor detected photons of smFRET experiments taking into account dynamics of D-A distance fluctuations, multiple interconverting states, and photoblinking. Using this approach, we show how different underlying conditions may yield identical FRET histograms and how the additional information from fluorescence decays helps in distinguishing between the different conditions. We also introduce a machine learning fitting approach for retrieving the D-A distance distribution, decoupled from the above-mentioned effects. We show that distance interpretation of smFRET experiments of even the simplest dsDNA is nontrivial and requires decoupling the effects of rapid D-A distance fluctuations on FRET in order to avoid systematic biases in the estimation of the D-A distance distribution.

48-spot single-molecule FRET setup with periodic acceptor excitation

Single-molecule Förster resonance energy transfer (smFRET) allows measuring distances between donor and acceptor fluorophores on the 3-10 nm range. Solution-based smFRET allows measurement of binding-unbinding events or conformational changes of dye-labeled biomolecules without ensemble averaging and free from surface perturbations. When employing dual (or multi) laser excitation, smFRET allows resolving the number of fluorescent labels on each molecule, greatly enhancing the ability to study heterogeneous samples. A major drawback to solution-based smFRET is the low throughput, which renders repetitive measurements expensive and hinders the ability to study kinetic phenomena in real-time. Here we demonstrate a high-throughput smFRET system that multiplexes acquisition by using 48 excitation spots and two 48-pixel single-photon avalanche diode array detectors. The system employs two excitation lasers allowing separation of species with one or two active fluorophores. The performance of the system is demonstrated on a set of doubly labeled double-stranded DNA oligonucleotides with different distances between donor and acceptor dyes along the DNA duplex. We show that the acquisition time for accurate subpopulation identification is reduced from several minutes to seconds, opening the way to high-throughput screening applications and real-time kinetics studies of enzymatic reactions such as DNA transcription by bacterial RNA polymerase.

Structure-Based Theory of Fluctuation-Induced Energy Transfer in a Molecular Dyad

We present a microscopic theory for the description of fluctuation-induced excitation energy transfer in chromophore dimers to explain experimental data on a perylene biscarboximide dyad with orthogonal transition dipole moments. Our non-Condon extension of Förster theory takes into account the fluctuations of excitonic couplings linear and quadratic in the normal coordinates, treated microscopically by quantum chemical/electrostatic calculations. The modulation of the optical transition energies of the chromophores is inferred from optical spectra of the isolated chromophores. The application of the theory to the considered dyad reveals a two to three order of magnitude increase in the rate constant by non-Condon effects. These effects are found to be dominated by fluctuations linear in the normal coordinates and provide a structure-based qualitative interpretation of the experimental time constant for energy transfer as well as its dependence on temperature.

Dispersion Correction Alleviates Dye Stacking of Single-Stranded DNA and RNA in Simulations of Single-Molecule Fluorescence Experiments

We combine single-molecule Förster resonance energy transfer (single-molecule FRET) experiments with extensive all-atom molecular dynamics (MD) simulations (>100 μs) to characterize the conformational ensembles of single-stranded (ss) DNA and RNA in solution. From MD simulations with explicit dyes attached to single-stranded nucleic acids via flexible linkers, we calculate FRET efficiencies and fluorescence anisotropy decays. We find that dispersion-corrected water models alleviate the problem of overly abundant interactions between fluorescent dyes and the aromatic ring systems of nucleobases. To model dye motions in a computationally efficient and conformationally exhaustive manner, we introduce a dye-conformer library, built from simulations of dinucleotides with covalently attached dye molecules. We use this library to calculate FRET efficiencies for dT₁₉, dA₁₉, and rA₁₉ simulated without explicit labels over a wide range of salt concentrations. For end-labeled homopolymeric pyrimidine ssDNA, MD simulations with the parmBSC1 force field capture the overall trend in salt-dependence of single-molecule FRET based distance measurements. For homopolymeric purine ssRNA and ssDNA, the DESRES and parmBSC1 force fields, respectively, provide useful starting points, even though our comparison also identifies clear deviations from experiment.

Linking time-series of single-molecule experiments with molecular dynamics simulations by machine learning

Single-molecule experiments and molecular dynamics (MD) simulations are indispensable tools for investigating protein conformational dynamics. The former provide time-series data, such as donor-acceptor distances, whereas the latter give atomistic information, although this information is often biased by model parameters. Here, we devise a machine-learning method to combine the complementary information from the two approaches and construct a consistent model of conformational dynamics. It is applied to the folding dynamics of the formin-binding protein WW domain. MD simulations over 400 μs led to an initial Markov state model (MSM), which was then "refined" using single-molecule Förster resonance energy transfer (FRET) data through hidden Markov modeling. The refined or data-assimilated MSM reproduces the FRET data and features hairpin one in the transition-state ensemble, consistent with mutation experiments. The folding pathway in the data-assimilated MSM suggests interplay between hydrophobic contacts and turn formation. Our method provides a general framework for investigating conformational transitions in other proteins.

Deciphering Design Principles of Förster Resonance Energy Transfer-Based Protease Substrates: Thermolysin-Like Protease from Geobacillus stearothermophilus as a Test Case

Protease activity is frequently assayed using short peptides that are equipped with a Förster resonance energy transfer (FRET) reporter system. Many frequently used donor-acceptor pairs are excited in the ultraviolet range and suffer from low extinction coefficients and quantum yields, limiting their usefulness in applications where a high sensitivity is required. A large number of alternative chromophores are available that are excited in the visible range, for example, based on xanthene or cyanine core structures. These alternatives are not only larger in size but also more hydrophobic. Here, we show that the hydrophobicity of these chromophores not only affects the solubility of the resulting FRET-labeled peptides but also their kinetic parameters in a model enzymatic reaction. In detail, we have compared two series of 4-8 amino acid long peptides, designed to serve as substrates for the thermolysin-like protease (TLP-ste) from Geobacillus stearothermophilus. These peptides were equipped with a carboxyfluorescein donor and either Cy5 or its sulfonated derivative Alexa Fluor 647 as the acceptor. We show that the turnover rate k _cat is largely unaffected by the choice of the acceptor fluorophore, whereas the K _M value is significantly lower for the Cy5- than for the Alexa Fluor 647-labeled substrates. TLP-ste is a rather nonspecific protease with a large number of hydrophobic amino acids surrounding the catalytic site, so that the fluorophore itself may form additional interactions with the enzyme. This hypothesis is supported by the result that the difference between Cy5- and Alexa Fluor 647-labeled substrates becomes less pronounced with increasing peptide length, that is, when the fluorophore is positioned at a larger distance from the catalytic site. These results suggest that fluorophores may become an integral part of FRET-labeled peptide substrates and that K _M and k _cat values are generally only valid for a specific combination of the peptide sequence and FRET pair.

Lipid Configurations from Molecular Dynamics Simulations

The extent to which current force fields faithfully reproduce conformational properties of lipids in bilayer membranes, and whether these reflect the structural principles established for phospholipids in bilayer crystals, are central to biomembrane simulations. We determine the distribution of dihedral angles in palmitoyl-oleoyl phosphatidylcholine from molecular dynamics simulations of hydrated fluid bilayer membranes. We compare results from the widely used lipid force field of Berger et al. with those from the most recent C36 release of the CHARMM force field for lipids. Only the CHARMM force field produces the chain inequivalence with sn-1 as leading chain that is characteristic of glycerolipid packing in fluid bilayers. The exposure and high partial charge of the backbone carbonyls in Berger lipids leads to artifactual binding of Na+ ions reported in the literature. Both force fields predict coupled, near-symmetrical distributions of headgroup dihedral angles, which is compatible with models of interconverting mirror-image conformations used originally to interpret NMR order parameters. The Berger force field produces rotamer populations that correspond to the headgroup conformation found in a phosphatidylcholine lipid bilayer crystal, whereas CHARMM36 rotamer populations are closer to the more relaxed crystal conformations of phosphatidylethanolamine and glycerophosphocholine. CHARMM36 alone predicts the correct relative signs of the time-average headgroup order parameters, and reasonably reproduces the full range of NMR data from the phosphate diester to the choline methyls. There is strong motivation to seek further experimental criteria for verifying predicted conformational distributions in the choline headgroup, including the 31P chemical shift anisotropy and 14N and CD3 NMR quadrupole splittings.

Hypothesis: structural heterogeneity of the unfolded proteins originating from the coupling of the local clusters and the long-range distance distribution

We propose a hypothesis that explains two apparently contradicting observations for the heterogeneity of the unfolded proteins. First, the line confocal method of the single-molecule Förster resonance energy transfer (sm-FRET) spectroscopy revealed that the unfolded proteins possess broad peaks in the FRET efficiency plot, implying the significant heterogeneity that lasts longer than milliseconds. Second, the fluorescence correlation method demonstrated that the unfolded proteins fluctuate in the time scale shorter than 100 ns. To formulate the hypothesis, we first summarize the recent consensus for the structure and dynamics of the unfolded proteins. We next discuss the conventional method of the sm-FRET spectroscopy and its limitations for the analysis of the unfolded proteins, followed by the advantages of the line confocal method that revealed the heterogeneity. Finally, we propose that the structural heterogeneity formed by the local clustering of hydrophobic residues modulates the distribution of the long-range distance between the labeled chromophores, resulting in the broadening of the peak in the FRET efficiency plot. A clustering of hydrophobic residues around the chromophore might further contribute to the broadening. The proposed clusters are important for the understanding of protein folding mechanism.

Theory of FRET "Spectroscopic Ruler" for Short Distances: Application to Polyproline

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory.

Combining Graphical and Analytical Methods with Molecular Simulations To Analyze Time-Resolved FRET Measurements of Labeled Macromolecules Accurately

Förster resonance energy transfer (FRET) measurements from a donor, D, to an acceptor, A, fluorophore are frequently used in vitro and in live cells to reveal information on the structure and dynamics of DA labeled macromolecules. Accurate descriptions of FRET measurements by molecular models are complicated because the fluorophores are usually coupled to the macromolecule via flexible long linkers allowing for diffusional exchange between multiple states with different fluorescence properties caused by distinct environmental quenching, dye mobilities, and variable DA distances. It is often assumed for the analysis of fluorescence intensity decays that DA distances and D quenching are uncorrelated (homogeneous quenching by FRET) and that the exchange between distinct fluorophore states is slow (quasistatic). This allows us to introduce the FRET-induced donor decay, ε_D(t), a function solely depending on the species fraction distribution of the rate constants of energy transfer by FRET, for a convenient joint analysis of fluorescence decays of FRET and reference samples by integrated graphical and analytical procedures. Additionally, we developed a simulation toolkit to model dye diffusion, fluorescence quenching by the protein surface, and FRET. A benchmark study with simulated fluorescence decays of 500 protein structures demonstrates that the quasistatic homogeneous model works very well and recovers for single conformations the average DA distances with an accuracy of < 2%. For more complex cases, where proteins adopt multiple conformations with significantly different dye environments (heterogeneous case), we introduce a general analysis framework and evaluate its power in resolving heterogeneities in DA distances. The developed fast simulation methods, relying on Brownian dynamics of a coarse-grained dye in its sterically accessible volume, allow us to incorporate structural information in the decay analysis for heterogeneous cases by relating dye states with protein conformations to pave the way for fluorescence and FRET-based dynamic structural biology. Finally, we present theories and simulations to assess the accuracy and precision of steady-state and time-resolved FRET measurements in resolving DA distances on the single-molecule and ensemble level and provide a rigorous framework for estimating approximation, systematic, and statistical errors.

Design and Properties of Genetically Encoded Probes for Sensing Macromolecular Crowding

Cells are highly crowded with proteins and polynucleotides. Any reaction that depends on the available volume can be affected by macromolecular crowding, but the effects of crowding in cells are complex and difficult to track. Here, we present a set of Förster resonance energy transfer (FRET)-based crowding-sensitive probes and investigate the role of the linker design. We investigate the sensors in vitro and in vivo and by molecular dynamics simulations. We find that in vitro all the probes can be compressed by crowding, with a magnitude that increases with the probe size, the crowder concentration, and the crowder size. We capture the role of the linker in a heuristic scaling model, and we find that compression is a function of size of the probe and volume fraction of the crowder. The FRET changes observed in Escherichia coli are more complicated, where FRET-increases and scaling behavior are observed solely with probes that contain the helices in the linker. The probe with the highest sensitivity to crowding in vivo yields the same macromolecular volume fractions as previously obtained from cell dry weight. The collection of new probes provides more detailed readouts on the macromolecular crowding than a single sensor.

Covalent dye attachment influences the dynamics and conformational properties of flexible peptides

Fluorescence spectroscopy techniques like Förster resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) have become important tools for the in vitro and in vivo investigation of conformational dynamics in biomolecules. These methods rely on the distance-dependent quenching of the fluorescence signal of a donor fluorophore either by a fluorescent acceptor fluorophore (FRET) or a non-fluorescent quencher, as used in FCS with photoinduced electron transfer (PET). The attachment of fluorophores to the molecule of interest can potentially alter the molecular properties and may affect the relevant conformational states and dynamics especially of flexible biomolecules like intrinsically disordered proteins (IDP). Using the intrinsically disordered S-peptide as a model system, we investigate the impact of terminal fluorescence labeling on the molecular properties. We perform extensive molecular dynamics simulations on the labeled and unlabeled peptide and compare the results with in vitro PET-FCS measurements. Experimental and simulated timescales of end-to-end fluctuations were found in excellent agreement. Comparison between simulations with and without labels reveal that the π-stacking interaction between the fluorophore labels traps the conformation of S-peptide in a single dominant state, while the unlabeled peptide undergoes continuous conformational rearrangements. Furthermore, we find that the open to closed transition rate of S-peptide is decreased by at least one order of magnitude by the fluorophore attachment. Our approach combining experimental and in silico methods provides a benchmark for the simulations and reveals the significant effect that fluorescence labeling can have on the conformational dynamics of small biomolecules, at least for inherently flexible short peptides. The presented protocol is not only useful for comparing PET-FCS experiments with simulation results but provides a strategy to minimize the influence on molecular properties when chosing labeling positions for fluorescence experiments.

High Precision FRET at Single-molecule Level for Biomolecule Structure Determination

A protocol on how to perform high-precision interdye distance measurements using Förster resonance energy transfer (FRET) at the single-molecule level in multiparameter fluorescence detection (MFD) mode is presented here. MFD maximizes the usage of all "dimensions" of fluorescence to reduce photophysical and experimental artifacts and allows for the measurement of interdye distance with an accuracy up to ~1 Å in rigid biomolecules. This method was used to identify three conformational states of the ligand-binding domain of the N-methyl-D-aspartate (NMDA) receptor to explain the activation of the receptor upon ligand binding. When comparing the known crystallographic structures with experimental measurements, they agreed within less than 3 Å for more dynamic biomolecules. Gathering a set of distance restraints that covers the entire dimensionality of the biomolecules would make it possible to provide a structural model of dynamic biomolecules.

Recent advances in FRET for the study of protein interactions and dynamics

Förster/fluorescence resonance energy transfer (FRET) has been extensively used to detect the binding state or conformation of biomolecules. In the past few decades, various in vitro and in vivo applications of FRET measurement have been developed, including FRET probes, in-cell measurements, single-molecule measurements, and combination with computer simulation. In this review, we describe recent advances in FRET methods for examining biomolecular interactions and dynamics: (i) phasor plot analysis for quantitative analysis of protein interactions, (ii) single-molecule FRET measurement for detecting conformational dynamics in live cells, and (iii) data assimilation using molecular dynamics simulation to evaluate conformation of the whole protein.

Computational refinement of spectroscopic FRET measurements

This article supplies raw data related to a research article entitled “Joint refinement of FRET measurements using spectroscopic and computational tools” (Kyrychenko et al., 2017) [1], in which we demonstrate the use of molecular dynamics simulations to estimate FRET orientational factors in a benchmark donor-linker-acceptor system of enhanced cyan (ECFP) and enhanced yellow (EYFP) fluorescent proteins. This can improve the recalculation of donor-acceptor distance information from single-molecule FRET measurements.

Joint refinement of FRET measurements using spectroscopic and computational tools

The variability of the orientation factor is a long-standing challenge in converting FRET efficiency measurements into donor-acceptor distances. We propose the use of molecular dynamics (MD) simulations to characterize orientation distributions and thus improve the accuracy of distance measurements. Here, we test this approach by comparing experimental and simulated FRET efficiencies for a model donor-acceptor pair of enhanced cyan and enhanced yellow FPs connected by a flexible linker. Several spectroscopic techniques were used to characterize FRET in solution. In addition, a series of atomistic MD simulations of a total length of 1.5 μs were carried out to calculate the distances and the orientation factor in the FRET-pair. The resulting MD-based and experimentally measured FRET efficiency histograms coincided with each other, allowing for direct comparison of distance distributions. Despite the fact that the calculated average orientation factor was close to 2/3, the application of the average κ² to the entire histogram of FRET efficiencies resulted in a substantial artificial broadening of the calculated distribution of apparent donor-acceptor distances. By combining single pair-FRET measurements with computational tools, we demonstrate that accounting for the donor and acceptor orientation heterogeneity is critical for accurate representation of the donor-acceptor distance distribution from FRET measurements.

Quantitative FRET studies and integrative modeling unravel the structure and dynamics of biomolecular systems

Förster Resonance Energy Transfer (FRET) combined with single-molecule spectroscopy probes macromolecular structure and dynamics and identifies coexisting conformational states. We review recent methodological developments in integrative structural modeling by satisfying spatial restraints on networks of FRET pairs (hybrid-FRET). We discuss procedures to incorporate prior structural knowledge and to obtain optimal distance networks. Finally, a workflow for hybrid-FRET is presented that automates integrative structural modeling and experiment planning to put hybrid-FRET on rails. To test this workflow, we simulate realistic single-molecule experiments and resolve three protein conformers, exchanging at 30μs and 10ms, with accuracies of 1-3Å RMSD versus the target structure. Incorporation of data from other spectroscopies and imaging is also discussed.

Deriving Structural Information from Experimentally Measured Data on Biomolecules

During the past half century, the number and accuracy of experimental techniques that can deliver values of observables for biomolecular systems have been steadily increasing. The conversion of a measured value Q^exp of an observable quantity Q into structural information is, however, a task beset with theoretical and practical problems: 1) insufficient or inaccurate values of Q^exp , 2) inaccuracies in the function Q(r→) used to relate the quantity Q to structure r→ , 3) how to account for the averaging inherent in the measurement of Q^exp , 4) how to handle the possible multiple-valuedness of the inverse r→(Q) of the function Q(r→) , to mention a few. These apply to a variety of observable quantities Q and measurement techniques such as X-ray and neutron diffraction, small-angle and wide-angle X-ray scattering, free-electron laser imaging, cryo-electron microscopy, nuclear magnetic resonance, electron paramagnetic resonance, infrared and Raman spectroscopy, circular dichroism, Förster resonance energy transfer, atomic force microscopy and ion-mobility mass spectrometry. The process of deriving structural information from measured data is reviewed with an eye to non-experts and newcomers in the field using examples from the literature of the effect of the various choices and approximations involved in the process. A list of choices to be avoided is provided.

Evaluation and characterization of thyroid-disrupting activities in soil samples along the Second Songhua River, China

In this study, a recombinant thyroid receptor (TR) gene yeast assay combined with Monte Carlo simulation were used to evaluate and characterize soil samples collected from Jilin (China) along the Second Songhua River, for their ant/agonist effect on TR. No TR agonistic activity was found in soils, but many soil samples exhibited TR antagonistic activities, and the bioassay-derived amiodarone hydrochloride equivalents, which was calculated based on Monte Carlo simulation, ranged from not detected (N.D.) to 35.5μg/g. Hydrophilic substance fractions were determined to be the contributors to TR antagonistic activity in these soil samples. Our results indicate that the novel calculation method is effective for the quantification and characterization of TR antagonists in soil samples, and these data could provide useful information for future management and remediation efforts for contaminated soils.

Dynamics of the Orientational Factor in Fluorescence Resonance Energy Transfer

A one-dimensional diffusion equation is derived for the time evolution of the orientational factor, κ², in the Förster energy transfer rate. The κ²-dependent diffusion coefficient is obtained in three different ways: (1) by requiring the κ² autocorrelation function, calculated using the κ² diffusion equation, to be single-exponential with the exact characteristic time; (2) by projecting the multidimensional diffusion equation for the transition dipoles onto κ² using the local equilibrium approximation; and (3) by requiring exact and approximate κ² trajectories to be as close as possible using a Bayesian approach. Within the framework of this simple theory, the distance dependence of the fluorescence resonance energy transfer (FRET) efficiency can be calculated for all values of the ratio of the rotational correlation time of the transition dipoles to the lifetime of the donor excited state. The theoretical predictions are compared to the exact values obtained from Brownian dynamics simulations of the reorientation of the donor and acceptor transition dipoles.

Probing the Action of Chemical Denaturant on an Intrinsically Disordered Protein by Simulation and Experiment

Chemical denaturants are the most commonly used agents for unfolding proteins and are thought to act by better solvating the unfolded state. Improved solvation is expected to lead to an expansion of unfolded chains with increasing denaturant concentration, providing a sensitive probe of the denaturant action. However, experiments have so far yielded qualitatively different results concerning the effects of chemical denaturation. Studies using Förster resonance energy transfer (FRET) and other methods found an increase in radius of gyration with denaturant concentration, but most small-angle X-ray scattering (SAXS) studies found no change. This discrepancy therefore challenges our understanding of denaturation mechanism and more generally the accuracy of these experiments as applied to unfolded or disordered proteins. Here, we use all-atom molecular simulations to investigate the effect of urea and guanidinium chloride on the structure of the intrinsically disordered protein ACTR, which can be studied by experiment over a wide range of denaturant concentration. Using unbiased molecular simulations with a carefully calibrated denaturant model, we find that the protein chain indeed swells with increasing denaturant concentration. This is due to the favorable association of urea or guanidinium chloride with the backbone of all residues and with the side-chains of almost all residues, with denaturant-water transfer free energies inferred from this association in reasonable accord with experimental estimates. Interactions of the denaturants with the backbone are dominated by hydrogen bonding, while interactions with side-chains include other contributions. By computing FRET efficiencies and SAXS intensities at each denaturant concentration, we show that the simulation trajectories are in accord with both experiments on this protein, demonstrating that there is no fundamental inconsistency between the two types of experiment. Agreement with experiment also supports the picture of chemical denaturation described in our simulations, driven by weak association of denaturant with the protein. Our simulations support some assumptions needed for each experiment to accurately reflect changes in protein size, namely, that the commonly used FRET chromophores do not qualitatively alter the results and that possible effects such as preferential solvent partitioning into the interior of the chain do not interfere with the determination of radius of gyration from the SAXS experiments.