Distance distributions in proteins recovered by using frequency-domain fluorometry. Applications to troponin I and its complex with troponin C

We used resonance energy transfer to examine the distribution of distances between two sites on troponin I (TnI). The donor (D) was the single tryptophan residue at site 158 (Trp 158), and the acceptor (A) was cysteine 133 (Cys 133) which was labeled with N-(iodoacetyl)-N'-(1-sulfo-5-naphthyl)ethylenediamine (IE). A distribution of D-A distances results in a distribution of donor decay times, which were resolved by using frequency-domain fluorometry. In the native state we recovered a relatively narrow distribution of D-A distances. The widths of the distance distributions were found to increase progressively and dramatically with increasing concentrations of guanidine hydrochloride. Binding of calcium-free troponin C (TnC) to troponin I did not alter the distance distribution. Addition of Ca2+ to the TnI.TnC complex resulted in a sharper distance distribution and protected against the guanidine hydrochloride induced increase in the width of the distance distribution. Additionally, the same distance distributions were recovered for native and denatured TnI when the Forster distance for energy transfer was decreased by acrylamide quenching. These results demonstrate that distance distributions can be recovered with good accuracy, to the extent of revealing modest changes due to binding of other components. This technique should have widespread applications in studies of protein folding.     

Simultaneous determination of intramolecular distance distributions and conformational dynamics by global analysis of energy transfer measurements.

Fluorescence energy transfer is widely used for determination of intramolecular distances in macromolecules. The time dependence of the rate of energy transfer is a function of the donor/acceptor distance distribution and fluctuations between the various conformations which may occur during the lifetime of the excited state. Previous attempts to recover both distance distributions and segmental diffusion from time-resolved experiments have been unsuccessful due to the extreme correlation between fitting parameters. A method has been developed, based on global analysis of both donor and acceptor fluorescence decay curves, which overcomes this extreme cross-correlation and allows the parameters of the equilibrium distance distributions and intramolecular diffusion constants to be recovered with high statistical significance and accuracy. Simulation studies of typical intramolecular energy transfer experiments reveal that both static and dynamic conformational distribution information can thus be obtained at a single temperature and viscosity.     

Distance distributions in native and random-coil troponin I from frequency-domain measurements of fluorescence energy transfer

We used time-dependent fluorescence energy transfer to determine the distribution of donor-to-acceptor distances in native and denatured troponin I(TnI). The single tryptophan residue (Trp 158) of TnI served as the donor (D), and the acceptor (A) was a labeled cysteine residue (Cys 133). The time-dependent intensity decays of the donor were measured by the frequency-domain method from 10 to 320 MHz. The frequency response of the donor emission, in the absence and presence of acceptor, was used to recover the distribution of D to A distances, using an algorithm that accounts for the intrinsic multiexponential decay of the donor. In the native state the D–A distribution is characterized by an average distance of 23 Å and a half-width of 12 Å. Denaturation results in a modest increase in the average distance to 27 Å, and a dramatic increase in half-width to 47 Å. We believe the ability to recover distance distributions will have numerous applications in the characterization of biological macromolecules.     

Correction for incomplete labeling in the measurement of distance distributions by frequency-domain fluorometry.

Measurements of time-resolved fluorescence are now being used to recover conformational distributions of biological macromolecules. The fluorescence data of the donor are easily corrupted by incomplete labeling of the macromolecules by the acceptor. In the present paper we describe a general procedure to correct for incomplete acceptor labeling in the determination of distance distributions from frequency-domain measurements of the donor fluorescence decay kinetics. The method can also be used to determine the extent of acceptor labeling. Simulated data were used to determine the effect of incomplete labeling on resolution of the distance distribution and the effect on the recovered distributions if one fails to account for incomplete labeling by the acceptor. The expressions and implemented algorithm were verified using known mixtures of donor-control and donor-acceptor pair molecules, which simulated the presence of a donor population lacking the acceptor. Finally, we present data on the distance distributions between two labeled sites in myosin S1 (Cys-697 to Cys-707) where it was not possible to obtain complete labeling of the acceptor site.     

Comparing methods of acquiring mammalian endozoochorous seed dispersal distance distributions

Research on endozoochorous seed dispersal is needed to further understand plant ecology and evolution. There are several methods for calculating the distribution of seed dispersal distances, although many studies use the “combination of gut retention time and movement data” (CGM) method to determine the potential seed dispersal distance distribution (PSD). However, there have been no evaluations of between PSD values acquired by CGM and seed dispersal distance distributions calculated using other methods. The main purpose of this study was to compare methods of determining seed dispersal distance distributions using raccoon dogs (Nyctereutes procyonoides). We calculated estimated seed dispersal distance distribution (ESD) using the bait-marker method and PSD using the CGM method. There were no differences between the ESD and PSD results with regard to basic dispersal distance distributions. The results indicate that if the region from which animal movement data was acquired and the region from which markers for the bait-marker method have been collected are the same, the distance distributions using the two methods may match. Additionally, though there were differences in seed mimic gut retention times (GRTs) between the two baits used (median GRT, fruits: 8 h 50 min, animal materials: 12 h 55 min), there were no differences in PSD between the two baits. This indicates that disperser movement has a stronger effect on dispersal distance distribution than GRT when using the CGM method.     

Resolution of end-to-end diffusion coefficients and distance distributions of flexible molecules using fluorescent donor-acceptor and donor-quencher pairs.

We used time-dependent fluorescence energy transfer, time-dependent collisional quenching, and global analysis of the data resulting from these through-space and contact interactions to recover the end-to-end distance distributions and diffusion coefficients of flexible fluorescent molecules. The fluorescence decays of covalently linked tryptamine-acceptor and tryptamine-quencher pairs were measured by the frequency-domain method. These data were fit using numerical solutions of the differential equation, which predicts the time- and distance-dependent population of the excited state donors in the presence of energy transfer or collisional quenching, followed by transformation to the frequency domain for nonlinear least-squares comparison with the experimental data. We found that the energy transfer data for the donor-acceptor pair alone were adequate to recover the starting distribution and the end-to-end diffusion coefficient; however, the resolution is dramatically improved by the use of both the through-space and contact interactions.     

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.     

Conformational distributions of melittin in water/methanol mixtures from frequency-domain measurements of nonradiative energy transfer

We used fluorescence energy transfer to examine the effects of solvent composition on the distribution of distances between the single tryptophan residue of melittin (residue 19) to the N-terminal alpha-amino group, which was labeled with a dansyl residue. The tryptophan intensity decays, with and without the dansyl acceptor, were measured by the frequency-domain method. The data were analyzed by a least-squares algorithm which accounts for correlation between the parameters. A wide distribution of tryptophan to dansyl distances was found for the random-coil state, with a Gaussian half-width of 25 A. Increasing concentrations of methanol, which were shown to induce and alpha-helical conformation, resulted in a progressive decrease in the width of the distribution, reaching a limiting half-width of 3 A at 80% (v/v) methanol. The distance from the indole moiety of Trp-19 to the dansyl group in 80% (v/v) methanol/water was found to be 25 A, as assessed from the center of the distance distribution. A distance of 24-25 A was recovered from the X-ray crystal structure of the tetramer, which is largely alpha-helical. At low ionic strength (less than 0.01) the CD spectra revealed a small fraction or amount of alpha-helix for melittin in water, which implies a small fraction of residual structure. This residual structure is apparently lost in guanidine hydrochloride as demonstrated by a further broadening in the distribution of distances. These results demonstrate the usefulness of frequency-domain measurements of resonance transfer for resolution of conformational distributions of proteins.     

A molecular ruler for measuring quantitative distance distributions

We report a novel molecular ruler for measurement of distances and distance distributions with accurate external calibration. Using solution X-ray scattering we determine the scattering interference between two gold nanocrystal probes attached site-specifically to a macromolecule of interest. Fourier transformation of the interference pattern provides a model-independent probability distribution for the distances between the probe centers-of-mass. To test the approach, we measure end-to-end distances for a variety of DNA structures. We demonstrate that measurements with independently prepared samples and using different X-ray sources are highly reproducible, we demonstrate the quantitative accuracy of the first and second moments of the distance distributions, and we demonstrate that the technique recovers complex distribution shapes. Distances measured with the solution scattering-interference ruler match the corresponding crystallographic values, but differ from distances measured previously with alternate ruler techniques. The X-ray scattering interference ruler should be a powerful tool for relating crystal structures to solution structures and for studying molecular fluctuations.     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

Nanometer distance measurements in RNA using site-directed spin labeling

The method of site-directed spin labeling (SDSL) utilizes a stable nitroxide radical to obtain structural and dynamic information on biomolecules. Measuring dipolar interactions between pairs of nitroxides yields internitroxide distances, from which quantitative structural information can be derived. This study evaluates SDSL distance measurements in RNA using a nitroxide probe, designated as R5, which is attached in an efficient and cost-effective manner to backbone phosphorothioate sites that are chemically substituted in arbitrary sequences. It is shown that R5 does not perturb the global structure of the A-form RNA helix. Six sets of internitroxide distances, ranging from 20 to 50 A, were measured on an RNA duplex with a known X-ray crystal structure. The measured distances strongly correlate (R(2) = 0.97) with those predicted using an efficient algorithm for determining the expected internitroxide distances from the parent RNA structure. The results enable future studies of global RNA structures for which high-resolution structural data are absent.     

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

Förster Resonance Energy Transfer (FRET) experiments probe molecular distances via distance dependent energy transfer from an excited donor dye to an acceptor dye. Single molecule experiments not only probe average distances, but also distance distributions or even fluctuations, and thus provide a powerful tool to study biomolecular structure and dynamics. However, the measured energy transfer efficiency depends not only on the distance between the dyes, but also on their mutual orientation, which is typically inaccessible to experiments. Thus, assumptions on the orientation distributions and averages are usually made, limiting the accuracy of the distance distributions extracted from FRET experiments. Here, we demonstrate that by combining single molecule FRET experiments with the mutual dye orientation statistics obtained from Molecular Dynamics (MD) simulations, improved estimates of distances and distributions are obtained. From the simulated time-dependent mutual orientations, FRET efficiencies are calculated and the full statistics of individual photon absorption, energy transfer, and photon emission events is obtained from subsequent Monte Carlo (MC) simulations of the FRET kinetics. All recorded emission events are collected to bursts from which efficiency distributions are calculated in close resemblance to the actual FRET experiment, taking shot noise fully into account. Using polyproline chains with attached Alexa 488 and Alexa 594 dyes as a test system, we demonstrate the feasibility of this approach by direct comparison to experimental data. We identified cis-isomers and different static local environments as sources of the experimentally observed heterogeneity. Reconstructions of distance distributions from experimental data at different levels of theory demonstrate how the respective underlying assumptions and approximations affect the obtained accuracy. Our results show that dye fluctuations obtained from MD simulations, combined with MC single photon kinetics, provide a versatile tool to improve the accuracy of distance distributions that can be extracted from measured single molecule FRET efficiencies.     

On the relationship between distance information derived from cross-linking and from resonance energy transfer, with specific reference to sites located on myosin heads.

The techniques of fluorescence resonance energy transfer (FRET) and cross-linking can provide complementary information concerning the relative separation of a pair of sites. Cross-linking experiments provide an assessment of the distance of closest approach between a pair of sites. FRET measurements, by contrast, yield information about the average distance between the pair of sites. We have taken advantage of hybrid myosins to understand the relationship between distances obtained for a pair of equivalent sites, one on each myosin head, using both FRET (steady-state and time-decay) and cross-linking techniques. The rigid cross-linker, 4-4'-dimaleimidyl-stilbene-2-2'-disulfonic acid (DMSDS), can efficiently cross-link the two myosin regulatory light-chains, each at residue Cys50 of the Mercenaria regulatory light chain (Chantler, P.D., and S. M. Bower. 1988. J. Biol. Chem. 263:938-944), indicating that these sites can come within 18 +/- 2 A of each other. In a complementary set of experiments, steady-state and time-decay measurements using fluorescence donor/acceptor pairs located at these same sites indicate transfer efficiencies of somewhat less than 20%, suggesting an average separation of greater than 50 A between sites (Chantler, P. D., and T. Tao. 1986. J. Mol. Biol. 192:87-99). Here, we present theoretical calculations which show that efficient cross-linking can be achieved readily in dynamic systems such as the heads of myosin, even though the necessary subpopulation of proximate molecules at any instant may be below the detection limits of time-decay-FRET.(ABSTRACT TRUNCATED AT 250 WORDS)     

Fluorescence resonance energy transfer (FRET) and competing processes in donor-acceptor substituted DNA strands: a comparative study of ensemble and single-molecule data

We studied the fluorescence resonance energy transfer (FRET) efficiency of different donor-acceptor labeled model DNA systems in aqueous solution from ensemble measurements and at the single molecule level. The donor dyes: tetramethylrhodamine (TMR); rhodamine 6G (R6G); and a carbocyanine dye (Cy3) were covalently attached to the 5'-end of a 40-mer model oligonucleotide. The acceptor dyes, a carbocyanine dye (Cy5), and a rhodamine derivative (JA133) were attached at modified thymidine bases in the complementary DNA strand with donor-acceptor distances of 5, 15, 25 and 35 DNA-bases, respectively. Anisotropy measurements demonstrate that none of the dyes can be observed as a free rotor; especially in the 5-bp constructs the dyes exhibit relatively high anisotropy values. Nevertheless, the dyes change their conformation with respect to the oligonucleotide on a slower time scale in the millisecond range. This results in a dynamic inhomogeneous distribution of donor/acceptor (D/A) distances and orientations. FRET efficiencies have been calculated from donor and acceptor fluorescence intensity as well as from time-resolved fluorescence measurements of the donor fluorescence decay. Dependent on the D/A pair and distance, additional strong fluorescence quenching of the donor is observed, which simulates lower FRET efficiencies at short distances and higher efficiencies at longer distances. On the other hand, spFRET measurements revealed subpopulations that exhibit the expected FRET efficiency, even at short D/A distances. In addition, the measured acceptor fluorescence intensities and lifetimes also partly show fluorescence quenching effects independent of the excitation wavelength, i.e. either directly excited or via FRET. These effects strongly depend on the D/A distance and the dyes used, respectively. The obtained data demonstrate that besides dimerization at short D/A distances, an electron transfer process between the acceptor Cy5 and rhodamine donors has to be taken into account. To explain deviations from FRET theory even at larger D/A distances, we suggest that the pi-stack of the DNA double helix mediates electron transfer from the donor to the acceptor, even over distances as long as 35 base pairs. Our data show that FRET experiments at the single molecule level are rather suited to resolve fluorescent subpopulations in heterogeneous mixture, information about strongly quenched subpopulations gets lost.     

Conformation of prion protein repeat peptides probed by FRET measurements and molecular dynamics simulations

We report the combined use of steady-state fluorescence resonance energy transfer (FRET) experiments and molecular dynamics (MD) simulations to investigate conformational distributions of the prion protein (PrP) repeat system. FRET was used for the first time to probe the distance, as a function of temperature and pH, between a donor Trp residue and an acceptor dansyl group attached to the N-terminus in seven model peptides containing one to three repeats of the second decarepeat of PrP from marsupial possum (PHPGGSNWGQ)nG, and one and two human PrP consensus octarepeats (PHGGGWGQ)nG. In multirepeat peptides, single-Trp mutants were made by replacing other Trp(s) with Phe. As previous work has shown PrP repeats do not adopt a single preferred stable conformation, the FRET values are averages reflecting heterogeneity in the donor-acceptor distances. The T-dependence of the conformational distributions, and derived average dansyl-Trp distances, were obtained directly from MD simulation of the marsupial dansyl-PHPGGSNWGQG peptide. The results show excellent agreement between the FRET and MD T-dependent distances, and demonstrate the remarkable sensitivity and reproducibility of the FRET method in this first-time use for a set of disordered peptides. Based on the results, we propose a model involving cation-pi or pi-pi His-Trp interactions to explain the T- (5-85 degrees C) and pH- (6.0, 7.2) dependencies on distance, with HW i, i + 4 or WH i, i + 4 separations in sequence being more stable than HW i, i + 6 or WH i, i + 6 separations. The model has peptides adopting loosely folded conformations, with dansyl-Trp distances very much less than estimates for fully extended conformations, for example, approximately 16 vs. 33, approximately 21 vs. 69, and approximately 22 vs. 106 A for 1-3 decarepeats, and approximately 14 vs. 25 and approximately 19 vs. 54 A for 1-2 octarepeats, respectively. The study demonstrates the usefulness of combining FRET with MD, a combination reported only once previously. Initial "mapping" of the conformational distribution of flexible peptides by simulation can assist in designing and interpreting experiments using steady-state intensity methods, and indicating how time-resolved or anisotropy methods might be used.     

Analysis of fluorescence decay kinetics measured in the frequency domain using distributions of decay times

We describe the theoretical and practical aspects of analyzing complex fluorescence decay kinetics using continuous distributions of decay times. Our analysis uses frequency-domain data, provides for global analysis of multiple data sets and includes the possibility of excited-state processes. Simulated data were used to estimate the types of distributions which can be reasonably recovered from the measurements. Additionally, we describe a variety of distributions recovered from experimental data. For mixtures of one, two or three exponentially decaying fluorophores we recovered narrow lifetime distributions, which are essentially identical to a multiexponential decay. Similarly, a two-state excited-state reaction also yielded a narrow distribution with negative preexponential factors. The presence of time-dependent spectral relaxation of labeled lipids results in a wide distribution of decay times, which becomes narrower for faster relaxation rates at higher temperatures. Hence, the decay-time distributions appear to be sensitive to the dynamics of the environment surrounding the fluorophore. Additionally, distributions of decay times were observed to result from transient effects in collisional quenching, from energy transfer in the presence of a range of donor-to-acceptor distances, and for several single-tryptophan proteins.     

Distance distributions from the tyrosyl to disulfide residues in the oxytocin and [Arg8]-vasopressin measured using frequency-domain fluorescence resonance energy transfer

We have examined the fluorescence intensity decays of oxytocin and [Arg⁸]-vasopressin resulting from the single tyrosyl residue in each peptide, and the intensity decay of the Asu ^1,6-analogues in which the disulfide bridge is substituted by a CH₂-CH₂ bridge. Viscosity-dependent steady state and intensity decay measurements indicated that fluorescence resonance energy transfer (FRET) from tyrosyl phenol to the disulfide bridge is responsible for the decrease in fluorescence relative to the Asu-analogues. The frequency-domain phase and modulation data for the tyrosyl donor were interpreted in terms of fluorescence resonance energy transfer (FRET) to the weakly absorbing disulfide bridge and a distribution of donor-to-acceptor distances. Energy transfer efficiencies were determined from both time-resolved and steady-state measurements. Fitting the frequency-domain phase and modulation data to a Gaussian distance distribution indicated that the average inter-chromophoric distance (R_av) is similar in both compounds, R_av=7.94 Å for oxytocin and R_av = 8.00 Å for vasopressin. However, the width of the distance distribution is narrower for vasopression (hw =2.80 Å) than for oxytocin (hw =3.58 Å), which is consistent with restriction of the tyrosine phenol motion due to its stacking with the Phe³ side chain of vasopressin. Finally, the recovered distance distribution functions are compared with histograms describing the distance between the chromophores during the course of long, in vacuo, molecular dynamics runs using the computer program CHARMm and the QUANTA 3.0 parameters.Abbreviations AVP [Arg⁸]-vasopressin - FRET fluorescence resonance energy transfer - FD frequency-domain - D donor - A acceptor - DTT dithiothreitol Correspondence to: J. R. Lakowicz     

Frequency-domain fluorescence spectroscopy resolves the location of maleimide-directed spectroscopic probes within the tertiary structure of the Ca-ATPase of sarcoplasmic reticulum.

We have used fluorescence spectroscopy to characterize three covalently bound spectroscopic maleimide derivatives with respect to their location within the tertiary structure of the Ca-ATPase of sarcoplasmic reticulum (SR). These derivatives include (1) 2-(4'-maleimidoanilino)naphthalene-6-sulfonic acid, (2) 4-(dimethylamino)azobenzene-4'-maleimide, and (3) fluorescein 5'-maleimide. Biochemical assays demonstrate that modification with any of these three derivatives results in the same functional effects, observed following derivatization of cysteines 344 and 364 by N-ethylmaleimide [Saito-Nakatsuka et al. (1987) J. Biochem. (Tokyo) 101, 365-376]. These residues bracket the ATPase's phosphorylation site (Asp 351) and thus may provide spectroscopic probes of the protein's conformation in this essential region. In agreement with sequencing results, SDS-polyacrylamide gels show that maleimide-modified SR exhibits fluorescence exclusively on the A1 tryptic fragment of the Ca-ATPase. Extensive tryptic digestion followed by centrifugation demonstrates essentially all of the fluorescence was associated with the soluble rather than insoluble (membrane-associated) peptides, confirming the predicted extramembranous location of these residues. Utilizing frequency-domain fluorescence spectroscopy, we were able to recover the transient effects associated with a distribution of donor-acceptor distances. We find from these fluorescence resonance energy transfer measurements that covalently bound maleimide probes are 36 A apart, independent of whether a discrete distance is assumed or a distance distribution model is utilized, in which the conformational variability of the protein is taken into account. While a unimodal distance distribution is adequate to describe the intensity decay associated with maleimide-directed donor-acceptor pairs, a bimodal distribution of distances is necessary to describe the frequency response associated with the energy transfer between maleimide-directed chromophores and other covalently bound probes on the Ca-ATPase, consistent with the large spatial separation observed between maleimides. We recover mean distances of 42 and 77 A between maleimide sites and bound FITC (Lys 515) and mean distances of 28 and 37 A between the maleimide- and the iodoacetamide-directed probes (Cys 670 and 674, whose close proximity approximates a single locus). The measured distances are presented in a model and have permitted us to describe a unique arrangement of these covalently bound probes within both the secondary and tertiary structure of the Ca-ATPase. The resolution inherent in the frequency-domain fluorescence technique to multiple donor-acceptor distances should be generally applicable to a wide range of biological systems in which specific labeling of single unique donor-acceptor sites is not feasible.     

Kinetics of Fast Changing Intramolecular Distance Distributions Obtained by Combined Analysis of FRET Efficiency Kinetics and Time-Resolved FRET Equilibrium Measurements

Detailed studies of the mechanisms of macromolecular conformational transitions such as protein folding are enhanced by analysis of changes of distributions for intramolecular distances during the transitions. Time-resolved Förster resonance energy transfer (FRET) measurements yield such data, but the more readily available kinetics of mean FRET efficiency changes cannot be analyzed in terms of changes in distances because of the sixth-power dependence on the mean distance. To enhance the information obtained from mean FRET efficiency kinetics, we combined the analyses of FRET efficiency kinetics and equilibrium trFRET experiments. The joint analysis enabled determination of transient distance distributions along the folding reaction both in cases where a two-state transition is valid and in some cases consisting of a three-state scenario. The procedure and its limits were tested by simulations. Experimental data obtained from stopped-flow measurements of the refolding of Escherichia coli adenylate kinase were analyzed. The distance distributions between three double-labeled mutants, in the collapsed transient state, were determined and compared to those obtained experimentally using the double-kinetics technique. The proposed method effectively provides information on distance distributions of kinetically accessed intermediates of fast conformational transitions induced by common relaxation methods.     

Kinetics of Fast Changing Intramolecular Distance Distributions Obtained by Combined Analysis of FRET Efficiency Kinetics and Time-Resolved FRET Equilibrium Measurements

Detailed studies of the mechanisms of macromolecular conformational transitions such as protein folding are enhanced by analysis of changes of distributions for intramolecular distances during the transitions. Time-resolved Förster resonance energy transfer (FRET) measurements yield such data, but the more readily available kinetics of mean FRET efficiency changes cannot be analyzed in terms of changes in distances because of the sixth-power dependence on the mean distance. To enhance the information obtained from mean FRET efficiency kinetics, we combined the analyses of FRET efficiency kinetics and equilibrium trFRET experiments. The joint analysis enabled determination of transient distance distributions along the folding reaction both in cases where a two-state transition is valid and in some cases consisting of a three-state scenario. The procedure and its limits were tested by simulations. Experimental data obtained from stopped-flow measurements of the refolding of Escherichia coli adenylate kinase were analyzed. The distance distributions between three double-labeled mutants, in the collapsed transient state, were determined and compared to those obtained experimentally using the double-kinetics technique. The proposed method effectively provides information on distance distributions of kinetically accessed intermediates of fast conformational transitions induced by common relaxation methods.