Stoichiometry and assembly of mTOR complexes revealed by single-molecule pulldown

The mammalian target of rapamycin (mTOR) kinase is a master regulator of cellular, developmental, and metabolic processes. Deregulation of mTOR signaling is implicated in numerous human diseases including cancer and diabetes. mTOR functions as part of either of the two multisubunit complexes, mTORC1 and mTORC2, but molecular details about the assembly and oligomerization of mTORCs are currently lacking. We use the single-molecule pulldown (SiMPull) assay that combines principles of conventional pulldown assays with single-molecule fluorescence microscopy to investigate the stoichiometry and assembly of mTORCs. After validating our approach with mTORC1, confirming a dimeric assembly as previously reported, we show that all major components of mTORC2 exist in two copies per complex, indicating that mTORC2 assembles as a homodimer. Interestingly, each mTORC component, when free from the complexes, is present as a monomer and no single subunit serves as the dimerizing component. Instead, our data suggest that dimerization of mTORCs is the result of multiple subunits forming a composite surface. SiMPull also allowed us to distinguish complex disassembly from stoichiometry changes. Physiological conditions that abrogate mTOR signaling such as nutrient deprivation or energy stress did not alter the stoichiometry of mTORCs. On the other hand, rapamycin treatment leads to transient appearance of monomeric mTORC1 before complete disruption of the mTOR–raptor interaction, whereas mTORC2 stoichiometry is unaffected. These insights into assembly of mTORCs may guide future mechanistic studies and exploration of therapeutic potential.The mammalian target of rapamycin (mTOR) is a master regulator of crucial cellular and developmental processes. As a serine/threonine protein kinase belonging to the phosphatidylinositol-3-kinase (PI3K)-related kinase family, mTOR integrates the sensing of nutrients, growth factors, oxygen, energy, and different types of stress to regulate a myriad of biological processes such as cell growth, proliferation, differentiation, and metabolism (1). mTOR functions as part of at least two biochemically and functionally distinct complexes—mTORC1 and mTORC2 (2). mTORC1, better characterized of the two complexes, is the rapamycin-sensitive complex, composed of the proteins raptor and mLST8, and it is regulated by the inhibitory proteins PRAS40 and DEPTOR (2, 3). mTORC1 is activated by nutrients (such as amino acids), growth factors, and cellular energy among other stimuli (1, 2). mTORC2 contains rictor, mLST8, and mSin, as well as the negative regulator DEPTOR (2, 3).PI3K-related kinases (PIKKs) such as ataxia telangiectasia mutated (ATM), ATM and Rad3-related protein (ATR), and DNA-dependent protein kinase (DNA-PK) are known to oligomerize (4–6). Biochemical and genetic analyses have identified self-association of mTOR and its orthologs in yeast and Drosophila (7–10). A cryoelectron microscopy (cryo-EM) study revealed that mTORC1 self-associates into a dimeric structure (11). Oligomerization of mTORC1 has been reported to be sensitive to nutrient status based on biochemical analyses of recombinant proteins (10, 12). Consensus is lacking on the oligomeric state of mTORC2, which has been proposed to be monomeric, dimeric, or multimeric (7, 10, 13, 14). High-resolution structural analysis of mTORC2 has not been possible thus far, likely owing to its large size and multiplicity of interaction partners.Ensemble biochemical methods have inherent limitations in analyzing multicomponent heterogeneous protein assemblies. These methods do not directly reveal the stoichiometry of interaction and offer low-resolution estimates of the sizes of protein complexes. Additionally, the lengthy procedures often associated with biochemical characterization may lead to loss or alteration of physiological protein complexes. We recently reported a single-molecule pulldown (SiMPull) technology that combines the principles of conventional pulldown assays with single-molecule fluorescence microscopy (15). In SiMPull, protein complexes are pulled down from freshly lysed cells directly onto chambers for single-molecule fluorescence microscopy. When proteins are stoichiometrically labeled for example using fluorescent protein tags, SiMPull can reveal the stoichiometry of the protein complexes via single-molecule fluorescence photobleaching step analysis (15).We have used SiMPull to investigate the oligomeric assembly of mTORCs. Upon validating our approach by demonstrating dimeric assembly of mTORC1, we find that mTORC2 is also dimeric and contains two molecules of mTOR and rictor per complex. Individual mTORC components are predominantly monomeric, but under physiological conditions there is no evidence of monomeric interaction between mTOR and raptor or rictor. Multicolor imaging of individual complexes revealed that although the two complexes are predominantly distinct, small fractions of mTORC1 and mTORC2 components coexist in the same complex. Physiological perturbations that abrogate mTOR signaling had no effect on the stoichiometry of mTOR complexes, indicating that inhibition of mTOR signaling can be achieved without requiring disassembly of mTOR complexes or changing their oligomeric state. On the other hand, treatment with rapamycin led to transient mTOR–raptor complexes containing one mTOR before complete disassembly of the interaction, whereas mTORC2 stoichiometry was unaffected.     

Functional importance of telomerase pseudoknot revealed by single-molecule analysis

Telomerase ribonucleoprotein (RNP) employs an RNA subunit to template the addition of telomeric repeats onto chromosome ends. Previous studies have suggested that a region of the RNA downstream of the template may be important for telomerase activity and that the region could fold into a pseudoknot. Whether the pseudoknot motif is formed in the active telomerase RNP and what its functional role is have not yet been conclusively established. Using single-molecule FRET, we show that the isolated pseudoknot sequence stably folds into a pseudoknot. However, in the context of the full-length telomerase RNA, interference by other parts of the RNA prevents the formation of the pseudoknot. The protein subunits of the telomerase holoenzyme counteract RNA-induced misfolding and allow a significant fraction of the RNPs to form the pseudoknot structure. Only those RNP complexes containing a properly folded pseudoknot are catalytically active. These results not only demonstrate the functional importance of the pseudoknot but also reveal the critical role played by telomerase proteins in pseudoknot folding.     

Two distinct overstretched DNA structures revealed by single-molecule thermodynamics measurements

Double-stranded DNA is a dynamic molecule whose structure can change depending on conditions. While there is consensus in the literature about many structures DNA can have, the state of highly-stretched DNA is still not clear. Several groups have shown that DNA in the torsion-unconstrained B-form undergoes an “overstretching” transition at a stretching force of around 65 pN, which leads to approximately 1.7-fold elongation of the DNA contour length. Recent experiments have revealed that two distinct structural transitions are involved in the overstretching process: (i) a hysteretic “peeling” off one strand from its complementary strand, and (ii) a nonhysteretic transition that leads to an undetermined DNA structure. We report the first simultaneous determination of the entropy (ΔS) and enthalpy changes (ΔH) pertaining to these respective transitions. For the hysteretic peeling transition, we determined ΔS ∼ 20 cal/(K.mol) and ΔH ∼ 7 kcal/mol. In the case of the nonhysteretic transition, ΔS ∼ -3 cal/(K.mol) and ΔH ∼ 1 kcal/mol. Furthermore, the response of the transition force to salt concentration implies that the two DNA strands are spatially separated after the hysteretic peeling transition. In contrast, the corresponding response after the nonhysteretic transition indicated that the strands remained in close proximity. The selection between the two transitions depends on DNA base-pair stability, and it can be illustrated by a multidimensional phase diagram. Our results provide important insights into the thermodynamics of DNA overstretching and conformational structures of overstretched DNA that may play an important role in vivo.     

Conformational transitions in DNA polymerase I revealed by single-molecule FRET

The remarkable fidelity of most DNA polymerases depends on a series of early steps in the reaction pathway which allow the selection of the correct nucleotide substrate, while excluding all incorrect ones, before the enzyme is committed to the chemical step of nucleotide incorporation. The conformational transitions that are involved in these early steps are detectable with a variety of fluorescence assays and include the fingers-closing transition that has been characterized in structural studies. Using DNA polymerase I (Klenow fragment) labeled with both donor and acceptor fluorophores, we have employed single-molecule fluorescence resonance energy transfer to study the polymerase conformational transitions that precede nucleotide addition. Our experiments clearly distinguish the open and closed conformations that predominate in Pol-DNA and Pol-DNA-dNTP complexes, respectively. By contrast, the unliganded polymerase shows a broad distribution of FRET values, indicating a high degree of conformational flexibility in the protein in the absence of its substrates; such flexibility was not anticipated on the basis of the available crystallographic structures. Real-time observation of conformational dynamics showed that most of the unliganded polymerase molecules sample the open and closed conformations in the millisecond timescale. Ternary complexes formed in the presence of mismatched dNTPs or complementary ribonucleotides show unique FRET species, which we suggest are relevant to kinetic checkpoints that discriminate against these incorrect substrates.     

Interaction of dihydrofolate reductase with methotrexate: ensemble and single-molecule kinetics

The thermodynamics and kinetics of the interaction of dihydrofolate reductase (DHFR) with methotrexate have been studied by using fluorescence, stopped-flow, and single-molecule methods. DHFR was modified to permit the covalent addition of a fluorescent molecule, Alexa 488, and a biotin at the N terminus of the molecule. The fluorescent molecule was placed on a protein loop that closes over methotrexate when binding occurs, thus causing a quenching of the fluorescence. The biotin was used to attach the enzyme in an active form to a glass surface for single-molecule studies. The equilibrium dissociation constant for the binding of methotrexate to the enzyme is 9.5 nM. The stopped-flow studies revealed that methotrexate binds to two different conformations of the enzyme, and the association and dissociation rate constants were determined. The single-molecule investigation revealed a conformational change in the enzyme-methotrexate complex that was not observed in the stopped-flow studies. The ensemble averaged rate constants for this conformation change in both directions is about 2-4 s(-1) and is attributed to the opening and closing of the enzyme loop over the bound methotrexate. Thus the mechanism of methotrexate binding to DHFR involves multiple steps and protein conformational changes.     

Fast kinetics of chromatin assembly revealed by single-molecule videomicroscopy and scanning force microscopy

Fluorescence videomicroscopy and scanning force microscopy were used to follow, in real time, chromatin assembly on individual DNA molecules immersed in cell-free systems competent for physiological chromatin assembly. Within a few seconds, molecules are already compacted into a form exhibiting strong similarities to native chromatin fibers. In these extracts, the compaction rate is more than 100 times faster than expected from standard biochemical assays. Our data provide definite information on the forces involved (a few piconewtons) and on the reaction path. DNA compaction as a function of time revealed unique features of the assembly reaction in these extracts. They imply a sequential process with at least three steps, involving DNA wrapping as the final event. An absolute and quantitative measure of the kinetic parameters of the early steps in chromatin assembly under physiological conditions could thus be obtained.     

Plasticity of the asialoglycoprotein receptor deciphered by ensemble FRET imaging and single-molecule counting PALM imaging

The stoichiometry and composition of membrane protein receptors are critical to their function. However, the inability to assess receptor subunit stoichiometry in situ has hampered efforts to relate receptor structures to functional states. Here, we address this problem for the asialoglycoprotein receptor using ensemble FRET imaging, analytical modeling, and single-molecule counting with photoactivated localization microscopy (PALM). We show that the two subunits of asialoglycoprotein receptor [rat hepatic lectin 1 (RHL1) and RHL2] can assemble into both homo- and hetero-oligomeric complexes, displaying three forms with distinct ligand specificities that coexist on the plasma membrane: higher-order homo-oligomers of RHL1, higher-order hetero-oligomers of RHL1 and RHL2 with two-to-one stoichiometry, and the homo-dimer RHL2 with little tendency to further homo-oligomerize. Levels of these complexes can be modulated in the plasma membrane by exogenous ligands. Thus, even a simple two-subunit receptor can exhibit remarkable plasticity in structure, and consequently function, underscoring the importance of deciphering oligomerization in single cells at the single-molecule level.The plasma membrane contains numerous membrane protein receptors that assemble into homo- and hetero-oligomeric complexes. The precise composition of these receptor complexes is likely to substantially influence activity, highlighting the central importance of visualizing receptor complex stoichiometry. One prototypic plasma membrane receptor is the asialoglycoprotein receptor, which contains two subunits (i.e., subunits 1 and 2) and is involved in receptor-mediated endocytosis in hepatocytes (1). The asialoglycoprotein receptor binds and internalizes diverse classes of desialylated glycoproteins (including asialofetuin) present in the extracellular environment. This activity is crucial for clearance of thrombogenic material (i.e., clotting factors and platelets) under specific pathologic (2) and iatrogenic conditions (3). A key question related to the asialoglycoprotein receptor, in particular, and other multi-subunited receptors on the plasma membrane, in general, is whether the receptors always exist in the same oligomeric configuration in the plasma membrane or whether there is variability in oligomeric assembly and thus function. In the case of the asialoglycoprotein receptor, this question is particularly important, because it is involved in internalizing hundreds of different types of serum glycoproteins. How this process is accomplished by such a two-subunit receptor complex is unclear.Each of the two subunits of the asialoglycoprotein receptor is a type II membrane protein containing one extracellular carbohydrate recognition domain, a stalk domain, a single-pass transmembrane domain, and an intracellular domain. Only the crystal structure for the carbohydrate recognition domain of receptor subunit 1 exists (4), but the high homology between subunits 1 and 2 suggests that their respective overall structures are similar. The carbohydrate recognition domain is known to mediate binding of terminal Gal and GalNAc residues with high affinity (5). These residues become exposed on many serum glycoproteins when their terminal sialic acid residues are trimmed off by specific enzymes. By recognizing the desialylated glycoproteins (many of which are now inactive) and internalizing them within the cell, the asialoglycoprotein receptor efficiently removes them from the serum. Aside from recognizing desialylated glycoproteins, the asialoglycoprotein receptor has also been reported to bind glycoproteins carrying α2,6-linked sialic acid residues (6) as well as some glycoproteins independently of any specific sugar residues (7).One way that the asialoglycoprotein receptor could be capable of binding diverse ligands is if it exhibited different oligomeric forms having distinct ligand specificities. So far, efforts at establishing this possibility have proven indecisive. Biochemical approaches have reported vastly different stoichiometries for the asialoglycoprotein receptor, with ratios of subunit 1 to subunit 2 ranging from 2:2 to 8:1 (8–14). Whether these inconsistent results arise from contradictory stoichiometry analysis or the receptor simultaneously assembling into multiple functionally distinct oligomers has remained unclear. However, distinguishing between these possibilities could potentially be addressed by direct visualization of receptor subunit stoichiometry in situ and relating this finding to different functional states.Here, we take a visualization approach to clarify the plasticity of the asialoglycoprotein receptor. We use advanced spectroscopic tools, including ensemble FRET imaging and single-molecule counting photoactivated localization microscopy (PALM), to test whether cells display different oligomeric forms of the asialoglycoprotein receptor, what the subunit stoichiometries of these forms are, and whether the different oligomeric forms have distinct ligand specificities. We find that the asialoglycoprotein receptor exists in different oligomeric forms, exhibiting structural/functional plasticity. The different forms can be modulated by exogenous ligands, leading to the preferential internalization of one receptor complex over another complex. As exemplified with the asialoglycoprotein receptor, therefore, plasma membrane receptors may be far more plastic and modular systems than previously thought.     

Hopping of a processivity factor on DNA revealed by single-molecule assays of diffusion

Many DNA-interacting proteins diffuse on DNA to perform their biochemical functions. Processivity factors diffuse on DNA to permit unimpeded elongation by their associated DNA polymerases, but little is known regarding their rates and mechanisms of diffusion. The processivity factor of herpes simplex virus DNA polymerase, UL42, unlike “sliding clamp” processivity factors that normally form rings around DNA, binds DNA directly and tightly as a monomer, but can still diffuse on DNA. To investigate the mechanism of UL42 diffusion on DNA, we examined the effects of salt concentration on diffusion coefficient. Ensemble studies, employing electrophoretic mobility shift assays on relatively short DNAs, showed that off-rates of UL42 from DNA depended on DNA length at higher but not lower salt concentrations, consistent with the diffusion coefficient being salt-dependent. Direct assays of the motion of single fluorescently labeled UL42 molecules along DNA revealed increased diffusion at higher salt concentrations. Remarkably, the diffusion coefficients observed in these assays were ≈10⁴-fold higher than those calculated from ensemble experiments. Discrepancies between the single-molecule and ensemble results were resolved by the observation, in single-molecule experiments, that UL42 releases relatively slowly from the ends of DNA in a salt-dependent manner. The results indicate that UL42 “hops” rather than “slides,” i.e., it microscopically dissociates from and reassociates with DNA as it diffuses rather than remaining so intimately associated with DNA that cation condensation on the phosphate backbone does not affect its motion. These findings may be relevant to mechanisms of other processivity factors and DNA-binding proteins.     

Dynamic force sensing of filamin revealed in single-molecule experiments

Mechanical forces are important signals for cell response and development, but detailed molecular mechanisms of force sensing are largely unexplored. The cytoskeletal protein filamin is a key connecting element between the cytoskeleton and transmembrane complexes such as integrins or the von Willebrand receptor glycoprotein Ib. Here, we show using single-molecule mechanical measurements that the recently reported Ig domain pair 20–21 of human filamin A acts as an autoinhibited force-activatable mechanosensor. We developed a mechanical single-molecule competition assay that allows online observation of binding events of target peptides in solution to the strained domain pair. We find that filamin force sensing is a highly dynamic process occurring in rapid equilibrium that increases the affinity to the target peptides by up to a factor of 17 between 2 and 5 pN. The equilibrium mechanism we find here can offer a general scheme for cellular force sensing.     

Identification of different emitting species in the red fluorescent protein DsRed by means of ensemble and single-molecule spectroscopy

The photophysics and photochemistry taking place in the DsRed protein, a recently cloned red fluorescent protein from a coral of the Discosoma genus, are investigated here by means of ensemble and single-molecule time-resolved detection and spectroscopic measurements. Ensemble time-resolved data reveal that 25% of the immature green chromophores are present in tetramers containing only this immature form. They are responsible for the weak fluorescence emitted at 500 nm. The remaining 75% of the immature green chromophores are involved in a fluorescence resonance energy transfer process to the red species. The combination of time-resolved detection with spectroscopy at the single-molecule level reveals, on 543-nm excitation of individual DsRed tetramers, the existence of a photoconversion of the red chromophore emitting at 583 nm and decaying with a 3.2-ns time constant into a super red one emitting at 595 nm and for which the decay time constant ranges between 2.7 and 1.5 ns. The phenomenon is further corroborated at the ensemble level by the observation of the creation of a super red form and a blue absorbing species on irradiation with 532-nm pulsed light at high excitation power. Furthermore, single-molecule experiments suggest that a similar photoconversion process might occur in the immature green species on 488-nm excitation.     

Pathway of actin filament branch formation by Arp2/3 complex revealed by single-molecule imaging

Actin filament nucleation by actin-related protein (Arp) 2/3 complex is a critical process in cell motility and endocytosis, yet key aspects of its mechanism are unknown due to a lack of real-time observations of Arp2/3 complex through the nucleation process. Triggered by the verprolin homology, central, and acidic (VCA) region of proteins in the Wiskott-Aldrich syndrome protein (WASp) family, Arp2/3 complex produces new (daughter) filaments as branches from the sides of preexisting (mother) filaments. We visualized individual fluorescently labeled Arp2/3 complexes dynamically interacting with and producing branches on growing actin filaments in vitro. Branch formation was strikingly inefficient, even in the presence of VCA: only ∼1% of filament-bound Arp2/3 complexes yielded a daughter filament. VCA acted at multiple steps, increasing both the association rate of Arp2/3 complexes with mother filament and the fraction of filament-bound complexes that nucleated a daughter. The results lead to a quantitative kinetic mechanism for branched actin assembly, revealing the steps that can be stimulated by additional cellular factors.     

The nature of fluorescence emission in the red fluorescent protein DsRed, revealed by single-molecule detection

Recent studies on the newly cloned red fluorescence protein DsRed from the Discosoma genus have shown its tremendous advantages: bright red fluorescence and high resistance against photobleaching. However, it has also become clear that the protein forms closely packed tetramers, and there is indication for incomplete protein maturation with unknown proportion of immature green species. We have applied single-molecule methodology to elucidate the nature of the fluorescence emission in the DsRed. Real-time fluorescence trajectories have been acquired with polarization sensitive detection. Our results indicate that energy transfer between identical monomers occurs efficiently with red emission arising equally likely from any of the chromophoric units. Photodissociation of one of the chromophores weakly quenches the emission of adjacent ones. Dual color excitation (at 488 and 568 nm) single-molecule microscopy has been performed to reveal the number and distribution of red vs. green species within each tetramer. We find that 86% of the DsRed contain at least one green species with a red-to-green ratio of 1.2-1.5. On the basis of our findings, oligomer suppression would not only be advantageous for protein fusion but will also increase the fluorescence emission of individual monomers.     

Central effects of photoperiod on reproduction in the ram revealed by the use of a testosterone clamp

Over a 3-year period eight adult Soay rams were exposed to an artificial lighting regimen of alternating 16-week periods of long days (16 h light: 8 h darkness; 16L : 8D) and short days (8L : 16D) to induce a seasonal cycle in reproduction and wool growth every 32 weeks. Early in the study the rams were castrated (four during long days and four during short days) and 48 weeks later the castrated animals were each given an s.c. implant of testosterone to increase the blood plasma concentration of testosterone to 14-20 nmol/l. The changes in the concentrations of LH, FSH and testosterone were measured in blood samples collected once or twice weekly while records were made of the changes in the size of the testes (before castration), the intensity of the sexual skin flush, the expression of aggressive and sexual behaviour and the rate of wool growth. The results showed that in the castrated rams there were only minor changes in the blood levels of LH, FSH and the expression of aggressive behaviour related to the 32-week light cycle, while the sexual skin flush was permanently absent. However, after the commencement of the constant testosterone therapy, there were major changes in all the reproductive parameters related to the lighting regimen with a similar temporal relationship as observed in the rams before castration. Cyclic variation in wool growth occurred throughout the study related to the changes in photoperiod but this was not markedly affected by castration and testosterone replacement.(ABSTRACT TRUNCATED AT 250 WORDS)     

Conserved pathways within bacteria and yeast as revealed by global protein network alignment

We implement a strategy for aligning two protein-protein interaction networks that combines interaction topology and protein sequence similarity to identify conserved interaction pathways and complexes. Using this approach we show that the protein-protein interaction networks of two distantly related species, Saccharomyces cerevisiae and Helicobacter pylori, harbor a large complement of evolutionarily conserved pathways, and that a large number of pathways appears to have duplicated and specialized within yeast. Analysis of these findings reveals many well characterized interaction pathways as well as many unanticipated pathways, the significance of which is reinforced by their presence in the networks of both species.     

Cognitive,neurophysiologic and metabolic sequelae of previous hypoglycemic coma revealed by hyperinsulinemic-hypoglycemic clamp in type 1 diabetic patients

Metabolic Brain Disease - To examine the relationship between electroencephalographic (EEG) activity and hypoglycemia unawareness, we investigated early parameters of vigilance and awareness of...     

Stepwise assembly of initiation proteins at budding yeast replication origins in vitro

The initiation of DNA replication in the budding yeast Saccharomyces cerevisiae occurs in two sequential and mutually exclusive steps. Prereplicative complexes (pre-RCs) containing origin recognition complex (ORC), Cdc6p, and the MCM2-7 proteins assemble only under conditions of low cyclin-dependent kinase (Cdk) activity during G(1), whereas origin activation is driven by the increase in Cdk activity at the end of G(1). As a first step toward the reconstitution of this two-step process in vitro, we describe a system in which extracts prepared from G(1)-arrested cells promote sequential assembly of ORC, Cdc6p, and MCM2-7 proteins onto exogenously added origin-containing DNA. This reaction requires an intact ARS consensus sequence and requires ATP for two distinct steps. Extracts from cells arrested in mitosis also can support the binding of ORC but are unable to load either Cdc6p or MCM2-7 proteins. This system should be useful for studying the mechanism and regulation of pre-RC assembly.     

Effect of flexibility and cis residues in single-molecule FRET studies of polyproline

Polyproline has recently been used as a spacer between donor and acceptor chromophores to help establish the accuracy of distances determined from single-molecule Förster resonance energy transfer (FRET) measurements. This work showed that the FRET efficiency in water is higher than expected for a rigid spacer and was attributed to the flexibility of the polypeptide. Here, we investigate this issue further, using a combination of single-molecule fluorescence intensity and lifetime measurements, NMR, theory, and molecular dynamics simulations of polyproline-20 that include the dyes and their linkers to the polypeptide. NMR shows that in water ≈30% of the molecules contain internal cis prolines, whereas none are detectable in trifluoroethanol. Simulations suggest that the all-trans form of polyproline is relatively stiff, with persistence lengths of 9–13 nm using different established force fields, and that the kinks arising from internal cis prolines are primarily responsible for the higher mean FRET efficiency in water. We show that the observed efficiency histograms and distributions of donor fluorescence lifetimes are explained by the presence of multiple species with efficiencies consistent with the simulations and populations determined by NMR. In calculating FRET efficiencies from the simulation, we find that the fluctuations of the chromophores, attached to long flexible linkers, also play an important role. A similar simulation approach suggests that the flexibility of the chromophore linkers is largely responsible for the previously unexplained high value of R₀ required to fit the data in the classic study of Stryer and Haugland.