Influence of end-to-end diffusion on intramolecular energy transfer as observed by frequency-domain fluorometry

We investigated the influence of end-to-end diffusion on intramolecular energy transfer between a naphthalene donor and dansyl acceptor linked by polymethylene chain. A range of viscosities from 0.6 to 200 cP were obtained using propylene glycol at different temperatures (0-80 degrees C) and methanol at 20 degrees C. The intensity decays of naphthalene were measured in the frequency domain. Several theoretical models, including distance distributions, were used to fit the data. The results indicate that end-to-end diffusion of flexible donor-acceptor pairs can be detected and quantified using frequency-domain fluorometry, even in the presence of a distribution of donor-to-acceptor distances.     

Resolution of Two Sub-Populations of Conformers and Their Individual Dynamics by Time Resolved Ensemble Level FRET Measurements

Most active biopolymers are dynamic structures; thus, ensembles of such molecules should be characterized by distributions of intra- or intermolecular distances and their fast fluctuations. A method of choice to determine intramolecular distances is based on Förster resonance energy transfer (FRET) measurements. Major advances in such measurements were achieved by single molecule FRET measurements. Here, we show that by global analysis of the decay of the emission of both the donor and the acceptor it is also possible to resolve two sub-populations in a mixture of two ensembles of biopolymers by time resolved FRET (trFRET) measurements at the ensemble level. We show that two individual intramolecular distance distributions can be determined and characterized in terms of their individual means, full width at half maximum (FWHM), and two corresponding diffusion coefficients which reflect the rates of fast ns fluctuations within each sub-population. An important advantage of the ensemble level trFRET measurements is the ability to use low molecular weight small-sized probes and to determine nanosecond fluctuations of the distance between the probes. The limits of the possible resolution were first tested by simulation and then by preparation of mixtures of two model peptides. The first labeled polypeptide was a relatively rigid Pro₇ and the second polypeptide was a flexible molecule consisting of (Gly-Ser)₇ repeats. The end to end distance distributions and the diffusion coefficients of each peptide were determined. Global analysis of trFRET measurements of a series of mixtures of polypeptides recovered two end-to-end distance distributions and associated intramolecular diffusion coefficients, which were very close to those determined from each of the pure samples. This study is a proof of concept study demonstrating the power of ensemble level trFRET based methods in resolution of subpopulations in ensembles of flexible macromolecules.     

Consideration of dipole orientation angles yields accurate rate equations for energy transfer in the rapid diffusion limit.

Dipole-dipole energy transfer between suitable donor and acceptor chromophores is an important luminescence quenching mechanism and has been shown to be useful for distance determination at the molecular level. In the rapid diffusion limit, where the excited-state lifetime of the donor is long enough to allow the donor and acceptor to diffuse many times their average separation before deexcitation, it is usually assumed that the relative dipolar orientation is completely averaged due to rotational Brownian motion. Under this simplifying assumption, analytical expressions have been derived earlier for the energy transfer rate between donor and acceptor characterized by different geometries. Most such expressions, however, are only approximate because complete angular averaging is permitted only in a geometry that possesses spherical symmetry surrounding each chromophore. In this paper analytical expressions that correctly account for incomplete angle averaging due to steric hindrance are presented for several geometries. Each of the equations reveals a dependence of the energy transfer rate on chromophore orientation. It is shown that correctly accounting for this effect can lead to improvements in estimates of the distance of closest approach from measured quenching rates based on energy transfer experiments.     

Brownian dynamics simulations of intramolecular energy transfer

A novel technique for modelling intramolecular energy transfer is presented. Brownian dynamics calculations are used to compute the trajectories of donor and acceptor species, and the instantaneous orientation factor is calculated during each temporal iteration. In this work, several model systems are considered. Trajectories were computed for energy transfer between a flexible donor and a rigidly fixed acceptor. We have considered configurations where the donor is, (1) tethered to a fixed point in space, but free to diffuse rotationally, and (2) constrained to wobble in a cone. The luminescence decay of the donor is ‘measured’, and a non-single-exponential decay is observed for configurations of efficient energy transfer. Luminescence anisotropy measurements of constrained and unconstrained donors reflect the contribution of both energy transfer and rotational diffusion to the shape of the anisotropy decay curve.     

Intramolecular dynamics of chain molecules monitored by fluctuations in efficiency of excitation energy transfer. A theoretical study.

The fluorescence quantum yield of a polymer molecule to which an energy donor chromophore and an energy acceptor chromophore are attached depends on the distance between the donor and acceptor chromophores. If this distance fluctuates with time, the fluorescence intensity is expected to fluctuate as well, and the time course of the intensity fluctuations will be correlated with the time course of the changes in the interchromophore distance. The intensity fluctuations are experimentally measurable if the number of illuminated molecules is small. A theoretical treatment of such fluorescence intensity fluctuations is presented in terms of a parameter that describes the polymer chain dynamics. Computer simulations were performed to illustrate the dependence of the autocorrelation function of the intensity fluctuations on the polymer chain conformation, the interchromophore energy transfer properties, and the macromolecular dynamics. These simulations demonstrate that the intensity fluctuations due to nonradiative energy transfer between chromophores attached to polymer chains can be large enough to be experimentally useful in the study of intramolecular dynamics of macromolecules.     

Evidence that the two amino termini of plasma fibronectin are in close proximity: a fluorescence energy transfer study

A fluorescence energy transfer technique has been used to study the intramolecular distance between the two amino termini of human plasma fibronectin. The glutamine-3 residue near the amino terminus of each chain was labeled enzymatically with either monodansylcadaverine or monofluoresceinylcadaverine by use of coagulation factor XIIIa. The nonradiative fluorescence energy transfer between the dansyl (donor) and fluorescein (acceptor) pair in the same protein molecule was determined from steady-state fluorescence measurements. On the basis of the transfer efficiency of 78%, the intramolecular distance between two glutamine-3 residues of fibronectin was estimated to be approximately 23 A, suggesting that the two amino termini of plasma fibronectin are in close proximity. High salt, which affects the hydrodynamic properties of the protein, has no effect on the measured distance. The results support the contention that both compact (in low salt) and expanded (in high salt) conformers of fibronectin are relatively spherical in shape.     

Structure is lost incrementally during the unfolding of barstar

Coincidental equilibrium unfolding transitions observed by multiple structural probes are taken to justify the modeling of protein unfolding as a two-state, N <==> U, cooperative process. However, for many of the large number of proteins that undergo apparently two-state equilibrium unfolding reactions, folding intermediates are detected in kinetic experiments. The small protein barstar is one such protein. Here the two-state model for equilibrium unfolding has been critically evaluated in barstar by estimating the intramolecular distance distribution by time-resolved fluorescence resonance energy transfer (TR-FRET) methods, in which fluorescence decay kinetics are analyzed by the maximum entropy method (MEM). Using a mutant form of barstar containing only Trp 53 as the fluorescence donor and a thionitrobenzoic acid moiety attached to Cys 82 as the fluorescence acceptor, the distance between the donor and acceptor has been shown to increase incrementally with increasing denaturant concentration. Although other probes, such as circular dichroism and fluorescence intensity, suggest that the labeled protein undergoes two-state equilibrium unfolding, the TR-FRET probe clearly indicates multistate equilibrium unfolding. Native protein expands progressively through a continuum of native-like forms that achieve the dimensions of a molten globule, whose heterogeneity increases with increasing denaturant concentration and which appears to be separated from the unfolded ensemble by a free energy barrier.     

Light and Life in Baltimore—and Beyond

Baltimore has been the home of numerous biophysical studies using light to probe cells. One such study, quantitative measurement of lateral diffusion of rhodopsin, set the standard for experiments in which recovery after photobleaching is used to measure lateral diffusion. Development of this method from specialized microscopes to commercial scanning confocal microscopes has led to widespread use of the technique to measure lateral diffusion of membrane proteins and lipids, and as well diffusion and binding interactions in cell organelles and cytoplasm. Perturbation of equilibrium distributions by photobleaching has also been developed into a robust method to image molecular proximity in terms of fluorescence resonance energy transfer between donor and acceptor fluorophores.     

Attempts to observe through-chain energy transfer and electron transfer on α-helical polypeptide chain

Singlet singlet energy transfer between the two terminal chromophores attached to an α-helical polypeptide chain has been studied. The transfer efficiency was satisfactorily explained by Förster's theory when the interchromophore distance was calculated from the α-helical structure. Therefore, it was concluded that no particular effect from the possible energy band structure of the α-helical conformation was detected in the end-to-end energy transfer. Similarly, end-to-end electron transfer was attempted between the electron donor acceptor pair attached to the ends of α-helcial polypeptide chain. However, no intramolecular interaction was found between the donor acceptor pair, indicating that the exciton structure of the α-helical polypeptides is not effective enough to realize through-chain electron transfer.     

Determination of lipid asymmetry in human red cells by resonance energy transfer

This report describes the application of a resonance energy transfer assay to determine the transbilayer distribution of 7-nitro-2,1,3-benzoxadiazol-4-yl (NBD)-labeled lipid analogues. The validity of this technique was established by determining the relationship between the distance of separation of lissamine rhodamine B labeled phosphatidylethanolamine (N-Rho-PE) acceptor lipid and NBD-labeled donor lipid and energy transfer efficiency. By determination of the distance between probes at 50% transfer efficiency (R0), the distance between fluorophores distributed symmetrically (outer leaflet label) and asymmetrically in artificially generated vesicles was determined. Calculation of the average distance between probes revealed a 14-A difference between NBD-lipid and N-Rho-PE localized in the same leaflet and in opposing leaflets, respectively. Application of this technique to the study of the transbilayer distribution of NBD-lipid in human red blood cells (RBC) showed that exogenously supplied NBD-phosphatidylserine (NBD-PS) was selectively transported to the inner leaflet, whereas NBD-phosphatidylcholine remained in the outer leaflet. In contrast, pretreatment of the RBC with diamide (a SH cross-linking reagent) blocked the transport of NBD-PS. The absence or presence of NBD-PS in the outer leaflet was independently verified by employing "back-exchange", trinitrobenzenesulfonic acid derivatization, and decarboxylation with PS decarboxylase experiments. These control experiments yielded results which confirmed the lipid distributions determined by the resonance energy transfer assay.     

Luminescence energy transfer with lanthanide chelates: interpretation of sensitized acceptor decay amplitudes

Lanthanide chelates used as donors offer several advantages over classical fluorescence probes in resonance energy transfer distance measurements. One of these advantages is that energy transfer can be conveniently measured using sensitized acceptor decay measurements. In these measurements a long microsecond lifetime of the lanthanide donor and a short nanosecond lifetime of the acceptor allow elimination of a signal from the unquenched donor. Therefore, the decay of sensitized acceptor emission reflects decay properties of the donor engaged in energy transfer. The purpose of this work is to point out the importance of the fact that the amplitude of the sensitized acceptor signal is dependent on the resonance energy transfer rate constant. Thus, in the case where there are two or more populations of donors with different energy transfer rate constants, the relative amplitudes of corresponding decay components observed in sensitized acceptor emission do not represent the relative populations of the donors. We use simulations to show that these effects can be very significant. A minor population of donors with a high rate of energy transfer can produce sensitized acceptor decay which is dominated by a decay component corresponding to this minor donor population. Using a simple experimental system of rapid diffusion limit energy transfer between a europium chelate and Cy5 acceptor we show that the predicted dependency of sensitized acceptor decay amplitude on the energy transfer rate is indeed observed. We suggest that the relative importance of decay components observed in sensitized acceptor emission should be evaluated after an appropriate correction of their values such that they properly reflect possible different populations of donors. We describe a method to perform such correction.     

Fluorescence energy transfer studies of transmembrane location of retinal in purple membrane

A diffusion-enhanced energy transfer technique was employed for the determination of transmembrane location of the retinal chromophore in the purple membrane. Theoretical considerations showed that the rate of energy transfer from an energy donor embedded within a membrane to acceptors dissolved in solvent could be described by an analytical function of the distance a of closest approach between the donor and acceptor, if the "rapid-diffusion limit" was attained. The criterion for this limit was given by the relation: (RO)6 much less than 20D tau Da4, where RO is the characteristic distance of energy transfer, D is the diffusion coefficient of the acceptor and tau D is the fluorescence lifetime of the donor in the absence of acceptor. By photo-reduction of the purple membrane with sodium borohydride, the retinal chromophore was converted to a highly fluorescent derivative, which showed a broad emission band in the visible region. From analysis of the fluorescence decay curves of the photo-reduced purple membrane in the presence of various concentrations of cobalt-ethylenediamine tetraacetate (Co-EDTA: energy acceptor), the depth of the chromophore from the membrane surface was estimated to be 8 (+/-3) A. This result was supported by investigations of energy transfer processes in a system where the native purple membranes and the photo-reduced membranes were stacked in parallel: the energy acceptor in this system was the native retinal chromophore.     

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.     

Analysis of resonance energy transfer in model membranes: role of orientational effects

The model of resonance energy transfer (RET) in membrane systems containing donors randomly distributed over two parallel planes separated by fixed distance and acceptors confined to a single plane is presented. Factors determining energy transfer rate are considered with special attention being given to the contribution from orientational heterogeneity of the donor emission and acceptor absorption transition dipoles. Analysis of simulated data suggests that RET in membranes, as compared to intramolecular energy transfer, is substantially less sensitive to the degree of reorientational freedom of chromophores due to averaging over multiple donor-acceptor pairs. The uncertainties in the distance estimation resulting from the unknown mutual orientation of the donor and acceptor are analyzed.     

Statistical interpretation of fluorescence energy transfer measurements in macromolecular systems.

A statistical method is presented for the interpretation of intramolecular distance measurements by the fluorescence energy transfer technique in systems for which the detailed geometries of the donor-acceptor pairs are unknown. This method enables calculation of the probability that a specified distance range corresponds to the actual distance to be measured. It makes use of the numerically calculated probability density function for the distance of interest. The two general systems considered are the single donor-acceptor pair and the multi-donor-single-acceptor transfer. In both systems, the statistical method incorporates the uncertainty in the orientation of the donor and acceptor dipoles. In addition, it can take into account the rotational mobility of the donor dipoles determined by time-dependent emission anisotropy measurements. When more than one donor is involved in the transfer process, the uncertainties associated with the number and location of individual donors and the size and shape of the donor distribution are also incorporated in calculating the distance ranges. Application of the method was demonstrated for a wide range of transfer efficiency and Ro values for the single donor-acceptor system. Specific examples are also presented for interpretation of both single donor-acceptor and multi-donor-single-acceptor energy transfer measurements performed in order to reveal the spatial relationship of the sigma subunit and the rifampicin binding site in the Escherichia coli RNA polymerase (see Wu, C.-W., Yarbrough, L. R., Wu, F. Y.-H., and Hillel, Z. (1976), Biochemistry, preceding paper in this issue). Analysis of these energy transfer data by methods which use average values of the unknown geometrical parameters of the system yielded results similar to those obtained by the statistical method. However, the statistical method represents a more realistic approach to the interpretation of energy transfer measurements since it provides information concerning the entire range of possible distances and their relative likelihood.     

Förster-type energy transfer. Simultaneous 'forward' and 'reverse' transfer between unlike fluorophores

The general case of F?rster-type energy transfer is that in which energy is exchanged in both directions between two unlike fluorophores. In such cases, energy is transferred from the conventionally defined donor to the conventionally defined acceptor (forward transfer) and at the same time from the acceptor to the donor (reverse transfer). Expressions are derived to describe the fluorescence intensities and lifetimes of fluorophores undergoing simultaneous forward and reverse transfer; these are compared with corresponding quantities for the case more usually considered, in which only forward transfer is significant. It is shown that the presence of reverse transfer removes the distinction between donor and acceptor, and allows such anomalous effects as 'acceptor quenching'. A confirmatory example is described. It is shown that the equations generally used in distance determination by steady-state fluorescence spectroscopy can also be applied in the presence of reverse transfer, if a correction term is included; however, for lifetime spectroscopy the correction is more complex.     

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.     

Conformational studies of a peptide corresponding to a region of the C-terminus of ribonuclease A: implications as a potential chain-folding initiation site

Conformational properties of the OT-16 peptide, the C-terminal 20 amino acids of RNase A, were examined by nonradiative energy transfer. A modified OT-16 peptide was prepared by solid-phase synthesis with the inclusion of diaminobutyric acid (DABA) at the C-terminus. The OT-16-DABA peptide was labeled with a fluorescent 1,5-dimethylaminonaphthalene sulfonyl (dansyl, DNS) acceptor at the N-terminal amine and a fluorescent naphthoxyacetic acid (NAA) donor at the gamma-amine of the DABA located at the C-terminus of the peptide by using an orthogonal protection scheme. Energy transfer was monitored in DNS-OT-16-DABA-NAA by using both fluorescence intensity (sensitized emission) and lifetime (donor quenching) experiments. The lifetime data indicate that the peptide system is a dynamic, flexible one. A detailed analysis, based on a dynamic model that includes a skewed Gaussian function to model the equilibrium distribution of interprobe distances and a mutual diffusion coefficient between the two probes to model conformational dynamics in the peptide [Beechem & Haas (1989) Biophys. J. 55, 1225.], identified the existence of a partially ordered structure (relatively narrow distribution of interprobe distances) at temperatures greater than or equal to 20 degrees C in the absence of denaturant. The width and the position of the average of the distributions decrease with increasing temperature, in this range; this suggests that the structure is stabilized by hydrophobic interactions. In addition, the peptide undergoes cold denaturation at around 1.5 degrees C as indicated by broadening of the distance distribution. The addition of 6 M guanidine hydrochloride (Gdn-HCl) also broadens the distance distribution significantly, presumably by eliminating the hydrophobic interactions and unfolding the peptide. The results of the analysis of the distance distribution demonstrate that (1) nonradiative energy transfer can be used to study the conformational dynamics of peptides on the nanosecond time scale, (2) a partially ordered structure of OT-16-DABA exists in solution under typical refolding conditions, and (3) structural constraints (presumably hydrophobic interactions) necessary for the formation of a chain-folding initiation site in RNase A are also present in the OT-16-DABA peptide in the absence of denaturant and are disrupted by Gdn-HCl.     

Contribution of Fluorophore Dynamics and Solvation to Resonant Energy Transfer in Protein-DNA Complexes: A Molecular-Dynamics Study

In Förster resonance energy transfer (FRET) experiments, extracting accurate structural information about macromolecules depends on knowing the positions and orientations of donor and acceptor fluorophores. Several approaches have been employed to reduce uncertainties in quantitative FRET distance measurements. Fluorophore-position distributions can be estimated by surface accessibility (SA) calculations, which compute the region of space explored by the fluorophore within a static macromolecular structure. However, SA models generally do not take fluorophore shape, dye transition-moment orientation, or dye-specific chemical interactions into account. We present a detailed molecular-dynamics (MD) treatment of fluorophore dynamics for an ATTO donor/acceptor dye pair and specifically consider as case studies dye-labeled protein-DNA intermediates in Cre site-specific recombination. We carried out MD simulations in both an aqueous solution and glycerol/water mixtures to assess the effects of experimental solvent systems on dye dynamics. Our results unequivocally show that MD simulations capture solvent effects and dye-dye interactions that can dramatically affect energy transfer efficiency. We also show that results from SA models and MD simulations strongly diverge in cases where donor and acceptor fluorophores are in close proximity. Although atomistic simulations are computationally more expensive than SA models, explicit MD studies are likely to give more realistic results in both homogeneous and mixed solvents. Our study underscores the model-dependent nature of FRET analyses, but also provides a starting point to develop more realistic in silico approaches for obtaining experimental ensemble and single-molecule FRET data.     

Contribution of Fluorophore Dynamics and Solvation to Resonant Energy Transfer in Protein-DNA Complexes: A Molecular-Dynamics Study

In Förster resonance energy transfer (FRET) experiments, extracting accurate structural information about macromolecules depends on knowing the positions and orientations of donor and acceptor fluorophores. Several approaches have been employed to reduce uncertainties in quantitative FRET distance measurements. Fluorophore-position distributions can be estimated by surface accessibility (SA) calculations, which compute the region of space explored by the fluorophore within a static macromolecular structure. However, SA models generally do not take fluorophore shape, dye transition-moment orientation, or dye-specific chemical interactions into account. We present a detailed molecular-dynamics (MD) treatment of fluorophore dynamics for an ATTO donor/acceptor dye pair and specifically consider as case studies dye-labeled protein-DNA intermediates in Cre site-specific recombination. We carried out MD simulations in both an aqueous solution and glycerol/water mixtures to assess the effects of experimental solvent systems on dye dynamics. Our results unequivocally show that MD simulations capture solvent effects and dye-dye interactions that can dramatically affect energy transfer efficiency. We also show that results from SA models and MD simulations strongly diverge in cases where donor and acceptor fluorophores are in close proximity. Although atomistic simulations are computationally more expensive than SA models, explicit MD studies are likely to give more realistic results in both homogeneous and mixed solvents. Our study underscores the model-dependent nature of FRET analyses, but also provides a starting point to develop more realistic in silico approaches for obtaining experimental ensemble and single-molecule FRET data.